Running Head:  STUDENT-CENTERED TEACHING AND LEARNING

 

 

 

 

 

 

 

 

Student-Centered Teaching and Learning: A Mock Study

Pamela R. Hudson Bailey

George Mason University

November 29, 2009

EDRS 812: Qualitative Methods in Educational Research

 

 

 

 

 

 

 

 

 

 

Student-Centered Teaching and Learning: A Mock Study

Student-centered teaching and learning is one way to inductively present lessons to students. Teachers’ work is done prior to the lesson presentation and then the students take over during the lesson. Students explore, explain, and elaborate on the mathematical concepts while representing the problem using multiple methods. The main idea is for the students to communicate, math talk, so that they expound on the concepts.

The Topic

I would like to investigate the inductive mathematics teaching methods used by high school teachers in algebra courses. The investigation would include the teachers describing a lesson they have taught and/or facilitated to discern their definition of how to approach a topic inductively. Teachers will be encouraged to elaborate on how they planned the lesson, their personal concerns, and the concerns they perceive that they will encounter from their students even prior to the lesson being taught. In addition to concerns, I would like to explore the benefits they or their students may encounter. Using the process standards from NCTM, I would like to delve into teacher remarks about whether the lesson involved problem solving, the connections they made in their lesson to other mathematical content as well as student’s lives, the representations they employed or expected the students to create, the teacher expectations of reasoning and proof of the student’s procedures and thoughts, and how the student’s communicated their understanding and knowledge. Lastly, I would like to hear about how and if the teachers feel that their students retained the knowledge and understanding of the concepts taught.

I would like to learn from this study if teachers really know what is meant by teaching inductively – employing a student-centered approach. This would involve knowing if teachers know and understand the NCTM process standards and how they affect the teaching and learning of mathematical concepts. I have heard teachers make some remarks about time always being an issue so how does that affect the planning of student-centered lessons, their concerns. My thoughts of their concerns may not be what are true. The benefits of teaching and learning inductively is something I don’t think teachers think enough about so having them delve into that line of thought may be worthwhile. A teacher may state that it is good to be student-centered but what is good and why? Not just canned answers but hopefully obtaining some insight into a student that was affected by the inductive approach to learning positively and/or negatively. Retention of material is always an issue so probing into whether the teacher was able to ascertain whether or not the students not only retained the material but could apply the concepts after the lesson was taught will be interesting.

I would like to interview teachers that I know have taught some inductive lessons. Preferably interviewing at least one teacher that instructs the Algebra, Function and Data Analysis (AFDA) class since the vision of the course is teaching using a function approach inductively. Interviewing all the AFDA teachers would not be possible since two of the four are taking a course I am teaching on how to effectively teach the course. The third teacher will be going on maternity leave within days.  However the remaining interviewees may be selected from those that have shown an interest in active teaching but may not be solely sold on the concept. The teacher will be one who is or tries to be creative as well as willing to try new ideas.

The teachers I have selected or wish to interview would be the one AFDA teacher, a teacher that has expressed concerns about her teaching methods in her Algebra II classroom and a department head/teacher that instructs a lower level of Algebra I but is concerned with teachers and students and the scores of his school. The three are from different high schools and different ethnicities: Hispanic, African-American and White. I don’t think this is an issue but it just worked out that way.

Why This Topic

            A focus on algebra courses is due to the many changes in the mathematics standards of learning that are expected to be taught next year along with the discussion going on in the state regarding the function approach to teaching algebra. A Math Science Partnership Grant proposal is currently being developed at UVA where the focus is on teaching algebra using the function approach which involves facilitating mathematics courses using NCTM’s process standards, the Rule of 5 and the 5 E’s. The Rule of 5 involves approaching a concept or big idea using tables, graphs, symbols, math talk, and concrete examples or manipulatives; the 5 E’s are a focus on types of interactions with students and include engagement, exploration, explanation, elaboration, and evaluation. Another reason for my selection is due to the expectations to meet Annual Yearly Progress (AYP) standards. Spotsylvania County Schools is having trouble with one high school not making AYP along with many of the middle schools. Teachers blame the students and their home lives and not their approaches to teaching the courses. Mentality that students need to adapt and they don’t. Research has shown that students involved in their learning will retain material and be more willing to become involved with and take ownership of their own learning. Recognizing and becoming aware of one’s concerns and benefits with regard to his or her teaching method is a step toward change. Along with the teachers viewpoint into their own actions is their viewpoint into how their students regard active learning. This would not be a surface statement but delving into analyzing what is truly happening in the classroom.

            The high schools chosen does not include the one that did not make AYP as the teachers are already saying and being negative about any statements made about teaching methods and feel that they are to blame. However these teachers do converse with other teachers in the county and will hear about their successes. One of the chosen teacher’s schools last year did not make AYP. That department again was feeling that they were being blamed by everyone. The department head, who is also taking master’s level courses, remained positive and is also working to change the culture of the department. It took a larger portion of the year to rebuild rapport with the remaining department members and begin the path toward positive actions. The chosen teacher is learning to be a leader for the department as well as in mathematics as she works toward presenting lessons using student active strategies. 

The third teacher chosen is the AFDA teacher in her high school. She is creative and strives to present lessons that are investigative and encourages students to discover the concepts. Occasionally I have seen her resort to traditional methods but on the whole she facilitates the learning of the concepts. The teacher has seen a change in her students due to her teaching methods. Concerned about students from different cultures, the teachers strives to develop lessons that will encourage involvement from all and wants to show students that everyone can learn as well as being a good role model for them.

I hope to gain insight into what teachers perceive as an inductive lesson and how it correlates to the NCTM process standards. Along with this I would like to understand the teacher’s concerns for this method and how they perceive student’s concerns. Choosing an Algebra I and an Algebra II teacher, courses taught prior to and after AFDA, was done on purpose. If students in the AFDA course are productive, want to learn, and are able to communicate mathematically while being taught using a completely different approach than  they are accustomed then what would a mathematics class look like if the approach was employed in additional courses. The insight I gain will aid in my thoughts toward my dissertation topic. Currently I am toying with the idea of a mixed method approach to analyzing student data/scores from AFDA to data/scores in Algebra II. Our county will not allow us to involve students so all research would need to be approached through the teacher and using data gathered from SOL scores. I feel that a qualitative approach would be a great addition to analyzing the data but the teachers involved might need to be sequential teachers. SOL scores will not be available for AFDA for a couple of years since the class is not currently be assessed, begins next year with a baseline assessment.    

Potential Difficulties

Personally I have an interest in student-centered teaching since I have been in the teacher’s shoes exploring inductive approaches and at times without the encouragement or support from my peers or administration. My master’s is in diversity and I began my teaching career in a school system where my own children were the minority and the feeling/expectations of the students were low. I expected the students to learn and strove to find methods to engage them. The course selections for the school in mathematics increased till we were able to offer AP Calculus and the students were successful. It was not easy overcoming the barriers put up by peers but at that time I did have a very supportive administration that honored student learning and mastery learning.

I do have some concerns about the interviews. My job as the mathematics coordinator is to develop and facilitate professional development (PD). PD’s are part of the teacher’s contract however many choose to take sick leave instead of attending the contractual 20 hours. I am not only working to change mathematics teaching methods but also dealing with a unique culture. Of those that have been attending the PD’s I am now beginning to see small changes after three years. Selecting teachers that already know my beliefs but are still willing to be frank with me has taken considerable thought. Many I had to eliminate as they are currently taking an AFDA course I am teaching through UVA. I also did not want to select a traditional teacher that thus far has been unbending. Practical issues have played a part in the teacher selection as many are overwhelmed taking master’s level courses and having small children at home - the time issue.

With the chosen teachers I perceive that time will be an issue but feel that they will work with me. I will need to reinforce the concept that being truthful about their concerns and beliefs and their knowledge and understanding of inductive approaches will help them, as well as me, to determine how to help them to be better teachers. I will probably need to be encouraging but also to watch that my questions are posed in a positive, non-threatening tone and are non-judgmental.

Prior Experiences, Beliefs, and Assumptions

My past has definitely influenced how I perceive mathematics being taught in the classroom and is twofold. First and the initial influence would be my children. My husband and I have two grown sons but while they were in school each posed different challenges. Our oldest had a learning disability so getting his thoughts down on paper was a nightmare. However he was a very hands-on student. You could show him something, making it relevant to him, and he could apply the concept. Our youngest was gifted in mathematics so were always watching how he learned and wanted to be challenged. Even though he could do the computations, a hands-on relevant experience always made understanding conceptually the topic more applicable in the long run. With each of their unique needs it still came down to active learning and relevancy of the topic in order for our children to be successful. In addition to our children, my first teaching experience gave me the opportunity to spread my wings.

The county I taught in was rural with white students the minority. There were four math teachers with one of them only part-time. Qualified math teachers were hard to find and hard to keep in the county. Many years I was the only licensed math teacher in the department. I walked in at the beginning of my first year and proceeded to teach mathematics with a traditional approach, the way I had been taught. The next thing I knew some of the girls were crying and the boys were frustrated. During my discussions with the students they recognized that my expectations were high but they were very behind in what they should know. I had read the county expectations for each course and what the students were learning in each subject but realized that even the pre-calculus course was just the last part of Algebra II and the calculus course offered was by video/phone. 

After talking with the principal I decided to put the textbooks away and teach mathematics for understanding. The students loved it. Straight rows did not exist in my room and students were expected to talk and ask questions. We might even leave the class that day with big questions still looming that we would dig into deeper the next day. I convinced the county to assign graphing calculators (that had just became popular) to the students which permitted them the opportunity to try and delve into concepts at home, coming back with even more questions. It was exciting for me as well but the big concept I had to get over was not knowing the answer to all of the student’s questions. My third year of teaching I had enough students to offer a calculus course. I tried to know everything to answer their questions but realized I had resorted to that traditional mode due to my own fear of not knowing the material. The first time I answered the students with an “I don’t know but let’s find out” response was a huge turning point. I realized, as well as the students realized, that I wasn’t the god of mathematics. The students were empowered to learn the mathematics.

Then came the standards of learning (SOL). The county maps were adjusted and I continued to teach in my normal investigative student-centered mode. Next were the SOL assessments. I didn’t have anyone to tell me that what I was doing was wrong so I continued. My students that were considered to be low level mathematics students were passing the assessment and several were passing with advanced scores. The vast majority of the calculus students were scoring three or higher on the advanced placement exam. Students were coming back from UVA, VA Tech, and Radford telling me that they had formed study groups to help others pass calculus.

My situation was different. I did not have someone to tell me that I had lost my mind and that students could not transfer concepts learned during an active lesson so they could answer a multiple choice question. Today, teachers have a fear of not being successful and appear to be afraid of going out on a limb to try something new or different. The county I currently work in is larger and the teachers are all licensed. Peer pressure may even be an influence on them as they seem to all commiserate together on why their students are not learning. Discussions involve what students cannot do but now how to overcome their concerns unless it is breaking the concept down into still smaller steps. This does not allow the students to become engaged and see the big picture. From my viewpoint the students are bored and therefore shut down. From the teacher’s viewpoint the student appears lazy, disorganized, and unproductive.

My goal is to determine what I can do to help guide and encourage teachers to facilitate mathematics lessons actively. Guidance would be in the form of professional development sessions or activities that the teachers might engage in or professional learning communities formed to provide support. So in order to obtain my goal two research questions were determined with the assistance of my EDRS 812 class. The questions that I hope to answer are “What are these teacher’s perceptions of student centered lessons?” and “How have these teachers experiences affected their desire of teaching student-centered lessons?” This would include eliciting comments about planning, presenting and reflecting on a student-centered lesson. I hope to encourage the teachers to discuss the challenges and successes they experience based on their personal outlook, their professional knowledge, and how the students perceive and act during a student-centered lesson. The goal is to determine methods, professional development sessions or activities that might aid teachers on their road to facilitating instruction inductively or encourage teachers to begin down the path.

Questions and Possible Responses

To determine the answers to the above questions an interview guide has been created how to draw out that information and include:

1.  Describe a student-centered lesson that you have taught?

2.  When did you first realize that a lesson taught actively is something that you

     wanted to try?  What was the attraction?

3.  What was the process that you went through to get to where you are now in

     your efforts to facilitate instruction?

4.  When planning a student-centered lesson describe some of the concerns you

     might have personally, professionally, and for the students.

5.  What are some of the positive outcomes that you have experienced as the student-

     centered lesson was presented? Outcomes might be personal, professional or for your

     students.

6.  What are some concerns/frustrations you have experienced as the student-centered lesson was

     presented? These might be personal, professional or for your students.

7.  What are some wishes/desires with regard to your students that you might have for your

     students as a new year begins?

8.  What are some of your overall goals when facilitating a student-centered lesson that you

     will want students to leave with at the end of the year?

9.  How do you view technology’s role in a student-centered classroom?

10. What is your level of comfort when using technology and implementing technology into

                  lessons?

            I believe the teachers will acknowledge the importance of the student-centered lessons by saying that the students are involved in the lesson. The student engagement will be a positive but also a concern as the teachers struggle with classroom management in group situations. Also I believe that a frustration will be that after the activity is completed that the students will still not be able to answer an abstract problem. This will in turn affect students and the long term assessment results. Research by Topcu and Ubuz (2008) reveals that lessons taught inductively versus lessons taught using direct instruction resulted in different results on a midterm and final. Those taught using direct instruction did well on the midterm and poorly on the final exam. The opposite was true for those taught inductively thereby implying that inductively learned concepts are retained in long term memory more than those learned through direct instruction. I feel that the teachers view short term assessments and panic, resorting back to direct instruction. Knowing how teachers feel about student-centered learning and assessments may be something valuable when encouraging others to begin the journey. J. Boaler (2002) states that students learn more when math has meaning than when taught procedurally. I also feel that the teachers acknowledge what Boaler states but creating problems that have meaning and then determining how to transform that meaning into the abstract will be overwhelming for them. Most teachers have been taught mathematics procedurally so do not have any idea what a student-centered lesson is. From my personal experience I see teachers having their students working in groups on a worksheet and stating that the students were actively engaged. Not having the opportunity or experience to develop or create mathematical concepts may lead teachers to fear the unknown but they might not state or even realize that they do not have the knowledge required as they have a degree in mathematics.

Potential Advantages

Borko and Putnam (1995) discuss the importance of teachers learning to construct knowledge and having the support to take the risk. I hope to find what I can do to change the culture of the system so that the teachers will have the support needed. The support I will be able to offer will probably be in the form of professional development or workshops. My desire is also to use my findings to help influence administrators to be more supportive of student-centered endeavors. Being in my current position I hope to have the opportunity, if needed, to work with the administrators on best practices in mathematics but need to know where the teachers truly are and what is needed for success. My bias toward the topic will need to be always on the forefront of my thoughts so I don’t influence the teacher’s remarks or my interpretations of what is needed. I was fortunate to have had a supportive administration as I began down the road to facilitating instruction and must maintain in my endeavors that many evaluators are now concerned with scores or not making AYP. They want to see passing scores on short and long term assessments. The education and awareness may need to go further than the teachers.

 Research Setting and Participants

My research setting is the secondary mathematics classroom of each of these teachers that are interested in student-centered learning.  Not a lot of research is done on this level compared to the elementary and middle school levels.  The new mathematics course, Algebra, Functions and Data Analysis (AFDA) is a new course in our state but it also carries with it a different vision of teaching and learning mathematics. One that is different from the traditional classroom and was developed with the vision of the NCTM process standards of communication, reasoning and proof, problem solving, connections, and representations. On the high school level NCTM came out with the main key aspects for the secondary level as sense making and reasoning and proof. All of these aspects went in to the creation of the AFDA course.

My concern is that many high school teachers are traditional, students sit in straight rows, classes are very structured and usually begin with a warm up, then proceed to lecture, dependent practice, independent practice, and closure. Providing instruction using a discovery or investigative approach is not the norm so how do teachers get the support and training needed to begin a journey down the path toward student centered teaching and learning? So teachers that are interested in student-centered learning and that teach AFDA, or may teach the course prior to or after AFDA, (an Algebra I and Algebra II teacher) was part of the selection criteria. Some of the other criteria included the availability of the teachers to speak with me, that they were not taking a course I was teaching, and that they were outspoken with an interest for student learning as shown by past actions. Two of the selected teachers have used student centered learning quite frequently and have seen its’ benefits. The third teacher uses student centered learning infrequently but has acknowledged it benefits.

I also needed to select participants that would be upfront and straightforward with their comments. As the secondary mathematics coordinator for our county many of my professional development sessions are about student-centered learning so the teachers know how I feel about the subject.  This is the fourth year that I have been in the position and I am beginning to see teachers acknowledge the need to teach in a student-centered learning format. My concern is why they don’t take the challenge and use their collaborative sessions to develop lessons that fit this need and what could we do on the county level to help facilitate this change? The two teachers, Susie and Mark, are one of the first that took the challenge and openly began facilitating instruction and encouraging their peers to do so as well. I felt that their viewpoints would provide some insight into what might be needed to encourage others. My third interviewee is very outspoken, teaches Algebra II, and is trying within her collaborative group to encourage them, and herself, to teach more actively.                             

If I had the opportunity to do it over I would select only teaches of AFDA. One could be in our county but I would also want viewpoints from teachers outside of our school district. This would enable me to be sure that what is being said is not due to my being the interviewer. A concern would be that in other school districts the teacher might not have the opportunity to have had the professional development or an understanding of student-centered teaching and learning. I would need to select individuals who understood the vision of the course and the importance of implementing the NCTM Standards.

Relationships With Participants

I have known all of the teachers since coming to the county and have had the opportunity to have had all of them assist in some professional development sessions over the years. Two of them have shown an interest in encouraging others to become “change agents” and join the journey. The same two have also elicited my help and support on rare occasions in their journey to discuss ideas and methodologies to implementing active student participation. Interviewing these individuals was an extension of some of these surface discussions we have had in the past. I believe we talked in the past but maybe I was not truly listening to what they were saying about their needs and concerns. Interviewing these individuals is an attempt to delve deeper into what their needs are and what they feel might be useful to others. I feel that their agreement to the interview was also a way for them to reach out to obtain support outside of their peer groups. It is a method that might let their side of the journey be heard and to obtain the support that would reach out to administrators and central office personnel.

I believe it will also help the teacher to feel empowered instead of being on the receiving end of administrators asking why their students did not perform during benchmarks. Susie and Mark have hung in there and even though the benchmark scores might have been low during the school year, they have shown that the final SOL assessment scores have been exceedingly good.  Not only might they feel empowered but they will also acknowledge that I want to help support them in any way that I can. The teachers have been open and honest with me in the past. Letting me know if there was something that they disagreed with or something that they don’t feel will work or be productive. Each of them has been wonderful to collaborate with over the years in attempts to create better learning situations for the students. All of the teachers have a desire to be lifelong learners and want to share their desires with their students. Taking courses within our school district or courses to obtain advance degrees, the teachers have shown their desire to continue to become better teachers.

Data Collection

The first interview was with Mark who is the department head for the biggest high school in our district, teaches Algebra I, and is well thought of by administrators.  He was waiting for me when I got to the school that morning with a cup of coffee in his hand. We went in to the library so we could talk without being interrupted. I explained to him about the confidentiality, changing his name, destroying the tape after the class was completed, and to be very straight forward with his responses and as clear as he could be. Mark was very attentive, making sure that the tape recorder picked up what he was saying since we were speaking quietly in the library. He would lean over to the recorder as he responded to the questions. It seemed like we were just talking in a casual situation about our thoughts on something that was near and dear to each of us but this time I was listening to what he was saying.

His main theme seemed to be collaboration and that being able to dialogue with others was important to being able to think through an active lesson. Talking about determining the “big idea” and teaching so students understand the what, why, and how was emphasized by Mark. “It’s kind of like a puzzle. Most people do not start a puzzle without looking at the big picture on the front of the box first, and wanting to be able to see that.” This concept is shared with his peers and encouraged as they are now required to develop unit plans in an effort to gently shove teachers in the student-centered teaching and learning direction.

The second interview was with Suzie, the AFDA teacher. She teaches two sections of the course which is more than any of the other teachers in our county. Suzie met me in the teacher workroom on the second floor near her. She travels to different rooms as well as having a teacher in the room that she calls home base. The workroom was empty when we entered so we settled in to talk. Suzie has always shown an interest in all students learning and that all students have the opportunity to do so. Staying after school, searching on the internet and asking questions about how to present a topic so that her students will see why they are learning the material, and sponsoring a foreign language student club are just a few of the extra activities she does. Being Hispanic, a career switcher, just obtained her master’s degree, and now working on her doctorate in education makes Suzie a good role model for students. After several minutes it became a little noisy and busy in the workroom where we had the interview so we had to keep our minds on what we were saying. This, along with Suzie’s thoughtful personality, caused her to pause several times during her responses. She was very excited to be able to talk about her love of teaching and especially student-centered teaching. Suzie was easy to talk to, laughing about the activities in her AFDA classes that included her goof ups and her successes. Knowing what and how the first interview turned out, I tried to see if there was any correlation to some of the statements made by Mark. This was trying on my interviewing skills, trying to keep my thoughts on what Suzie was saying but to also think about what and how it might link to what I have already heard stated. The noise in the workroom while talking to Suzie was not the best situation. While teachers were in the room I attempted to tailor my questions to items that were not linked to administration or her fellow teachers. I didn’t want Suzie to feel uncomfortable speaking in front of others about how or who she felt needed to say or do something in support of her endeavors.

Suzie was concerned with the rapport she has with the students and stated that she “…built a relationship and work with them [students] in that relationship so it’s almost like you are there on the discovery together. … I’m leading the tour.” The relationship helps her to know the students so she can  determine how to help the students overcome the rigid way that they had been taught mathematics in the past. She wants her students to really know the mathematics. “I think it is the way that we have to go. I think it is the essential knowledge for them to be successful, they really need to be able to use this.” Truly believing that mathematical knowledge was the door to the type of thinking students will need to be productive citizens.

Mary’s interview, reflecting back on it, seemed quite different. I have seen her teach or at least gather data for a supposedly investigative lesson. However now from what she stated during the interview it appears that her definition of student-centered learning is not the same as mine. Mary talked about group work a lot and using stations to review for assessments. She even stated that she didn’t want to waste time as she needed to be the giver of all foundation concepts. Teaching procedures and drilling students on them was revealed when she stated “…teaching them how to do it right.”  “…this is how you do it and you are going to do it on the test.” Teaching very rigidly as Suzie referred to it.

My two research questions are “What are these teachers’ perceptions of student-centered lessons?” and “How have these teachers experiences affected their desire of teaching student-centered lessons?”  Responses from the teachers have given me a lot to answer each of these so far. Suzie loved to tell me stories about activities that had been done with her classes as a way to tell about how she perceived teaching in this manner and her desire to continue to do so. Mark was more subtle in his enthusiasm. My overall goal is how I might be able to support their endeavors through professional development workshops or activities to encourage others to begin or continue on their student-centered journey.

During the past interviews I have stated the questions differently. For example, I ask more of the questions about the personal aspect then followed with additional questions about the professional aspect and then the students. On the second interview I asked all of the questions by stating the general format and asked Suzie to respond to the question with regard to herself personally, professionally and with regard to her students. With Mary I ended up doing a combination of both. At times it felt like I had to really pull the information out of her. Overall asking them separately seemed the best as I felt that questions with many aspects led to the interviewees getting side tracked and therefore not responding fully to each one.

Process

My analysis of the data has been ongoing since the day that each interview was conducted. Reading and re-reading the interviews prior to doing any kind of coding and continuing to read them over periodically throughout the process helped to keep all in perspective. I decided to first attempt to code the interviews and to develop a matrix. The coding was my way to label the interviews with topics being discussed. Labeling the columns and rows with these codes and the interviewees was as far as I got with the matrix as I was frustrated and didn’t see anything but the obvious in each of the interviews. I stopped working on the matrix and wrote my first memo for the interview with Mark summarizing the interview and combining them with some of my personal comments. During my second peer consultation it was brought to my attention that I had put down organizational categories for the codes and that I needed to look for substantive codes instead. This led to doing substantive coding (Appendix A) on each piece of data and writing a memo for each of the interviews (Appendix B, C, D). In addition to the substantive codes, which are highlighted in the document, I also began making comments on the transcribed interview in a side column. The focus for each of the memos (Appendix E, F, and G) was to summarize each and put down my personal thoughts. At the end of the memos I listed some of the quotes from each interviewee that I found to stand out in my mind. This really helped me to reflect more on the interviews than the “categorizing” that had been done previously and to notice similarities between the collected data as well as the very opposing view that was held by one interviewee.

Patterns were being revealed as I dove deeper in to each of the interviews. Mark was constantly talking about collaboration and Suzie talked about applications that brought the mathematics to life. Many of Mark’s comments were dealing with how he dealt with encouraging change within his department as the department head. Suzie had a very realistic view and shared experiences of student-centered learning that she had with her Algebra, Functions, and Data Analysis (AFDA) class. Bringing mathematics to life and relevant to the students appears to be her theme. Mark was more into developing the lessons from the teacher/leader perspective and Suzie was more into sharing about how the students perceived the lessons and working with students. Mary’s interview was completely different than the first two. I felt that she was on and off base with what student-centered learning meant and seemed to be more into herself as the giver of all important information and learning. This came to be more obvious as I was doing the coding and when I wrote her memo. “I have to teach them how to do that” and “I dictate how I want it done” was stated by Mary with a tone of the all knowing person. Dictating how to do something and student-centered learning are not the same. Mary did not go into the planning like Mark nor the concern for student learning and engagement like Suzie. This study revealed that many might believe they know and understand the concept but truly have no idea. Mary discussed the importance of content knowledge and that those who knew their content were more likely to release or relax control of the learning process. On the flip side she reveals that she doesn’t use student-centered teaching with the lower levels as she can’t trust them to do what she says and even states that she has a control issue.

After determining the substantive codes for each of the interviews, I entered them into an Excel spreadsheet, labeling each so I can tell which of the interviewees each code came from. A cut and paste activity on the computer using a table was next. Cutting up the codes and sorting them into piles to find themes. Some themes stood out and were easy to recognize like blame and fear, administration and support, planning, professional development, issues and concerns, content, and student benefits. A matrix (Appendix H) was created using the substantive codes organized into the themes and broken down by interviewee. The top row is organized by interviewee and the columns by the organizational topic. Filling in the matrix with the substantive codes was the final step in putting it together. Similar codes were placed next to each other to aid in visualizing correlations between the data.           

            The two research questions were also in the back of my mind as I was creating the organizational categories. Areas that will address the teachers’ perceptions of student-centered teaching and learning include teacher and student knowledge, definition of student-centered learning and what might be seen in the classroom, benefits to the students, and issues and concerns about teaching with a student-centered approach. My second research question, “How have the teachers’ experiences affected their desire of teaching student-centered lessons?” was more difficult to determine from the statements made within each of the interviews. I had hoped to get each of the interviewees to expound on their journeys to becoming a student-centered teacher. Their remarks to any type of question about what led them to where they are now resorted in very short statements. They were bored, saw how bored the students were, or they were naturally inquisitive. I went back to the research question and determined that the experiences did not have to be what led them to student-centered learning but could also include what they have gone through or events that they experienced upon trying to do a student-centered lesson.  

Results

            Each of the participants had slightly different views on the definition of student-centered teaching and learning. Mark and Suzie view the method as a way to have students become engaged in the mathematics by discovery or investigation and drawing on prior knowledge. Everyone that is breathing would benefit from student-centered learning according to Mark. Suzie acknowledges the importance of knowing her students. This goes beyond their mathematical knowledge stating that she “…built a relationship and work with them [students] in that relationship so it’s almost like you are there on the discovery together. … I’m leading the tour (p.13).”  All of the participants interviewed discussed student engagement but with a different meaning. Mark spoke about actively being engaged in a discovery or investigative activity that involved a challenge and Suzie talked about students truly understanding the relevancy and deeper meaning of the mathematics and how it relates to the scenario. Mary also saw the method as students being involved but normally in stations answering questions that should not take a lot of time. It is Mary’s way of reviewing material quickly while allowing the students to talk about the mathematics in order to answer the questions. Suzie and Mark felt that retention of the material was much better when students are actively engaged in making the connections and learning the material whereas Mary feels that a good foundation in mathematics should come through her. 

            Students benefited from student-centered learning in many ways. Truly learning mathematics resulted in it becoming a life skill. All interviewees acknowledged the improved attitude of students toward coming to class and doing the required work. Students realized that they could be successful with mathematics and feel good about what they did in class according to Mary.   

            A teachers’ perception of student-centered learning may also be due to their content knowledge and their pedagogical content knowledge. In order to feel comfortable with students leading the discussion and the investigations, teachers need to feel comfortable with their level of content knowledge. All interviewees felt that content knowledge was important but only Mark and Suzie mentioned or alluded to pedagogical content knowledge. The ability to go beyond the procedural knowledge and make connections is a necessary skill for a teacher was she moves with the class (Suzie).

            Issues and concerns were centered on five areas: control, time, resources, assessment, and cost. Everyone mentioned resources but, again, in different ways. Mark did not have any trouble with obtaining resources but did have trouble with finding the time to dialogue or collaborate with his peers to create the activities. Suzie also had trouble finding the time to create the activities and units of study but she mentioned that it was difficult for her to create them as well as the cost involved. She was thankful for the new book for the AFDA class as it is full of labs and ideas to gather data thereby making the mathematics relevant for the students. Resources to Mary were a need for several different textbooks so she can get or copy questions from each.

            Time was interwoven in to the concerns for assessment, control, as well as resources. Assessments, if created in the same format as the instruction, takes longer to create and sometimes longer for the students to take. There was also the concern that the state was going to begin making the students take an end of course test for the AFDA course which would have repercussions on how teachers provide instruction and assessment. Students in the county take quarterly benchmark assessments. Teachers fear or feel threatened by these assessments.

            Fear and blame are due to the time needed to complete the objectives for the quarter so students will be ready for the benchmark tests. Administrators, when evaluating teachers, will use their benchmark results as one aspect in the assessment. Research has shown that students do not do well with short term assessments when instruction is provided through active learning but their long term retention is much better. Mark mentioned that teachers do “get called down” but that good teaching is good teaching whatever the method employed. This leads to the support that teachers need.   

            Teachers fear and feel threatened by their administration. Educating the administrators on best practices for mathematics teaching and learning as well as how they can support their teachers was suggested by Mark. All of the interviewees did not feel threatened by administrators but stated that their peers did. When getting called down they would blame what they did that was new to them or their students. Mary states that teachers might blame students for their lack of knowledge or the method used to present the material. Blame was on everyone else but themselves. Educating the administrators on best practices needs to be complimented with some mathematics. It is hard to assess something of which you have no knowledge.  

            Planning was also something that these teachers mentioned as something that would affect one who wants to implement student-centered teaching and learning. Unit planning was a way that Mark was trying to get his teachers to implement more active learning. By thinking about the big ideas teachers would make connections and hopefully think about how to make the content relevant to students. Mark and Suzie mentioned that students should be challenged, need to make sense of the material and be based on students and their interests. Practical applications were the focus Suzie employed and is the driving force in making the material relevant. She also mentions the importance of creating a relationship with the students, one of being on the journey together with herself “leading the tour” (13). Unit planning, practical applications, challenging scenarios….all take time to plan. The planning is less strenuous if done in collaborative groups but there is a concern about lack of knowledge in other content areas.

            Collaboration was an important way to plan together as seen by the interviewees. Being able to dialogue with a colleague about your big ideas and the mode of which you plan to implement them is worth the time as mentioned by Mark. Bouncing ideas off of others prior to implementation helps to flesh out the activity and to possibly smooth the process (Suzie). Mary only wants to collaborate with someone of like mind. Working with peers led to discussions on peer observations. Mary and Suzie mentioned that they would not mind someone watching them but Suzie also wanted to work with someone as well.

            Professional development was a big topic for Mark. He felt that teachers needed to learn to develop student-centered lessons in a structured environment. They could be given examples and be led through the examples so they might experience what the students will during the lesson. Examples based on other content areas and applications in real life may be given and experienced during the professional development. In order to pace the instruction to fit student-centered learning Suzie would like to realign the county curriculum maps. This could also be a learning experience as the teachers make connections and look at “big ideas”.

            This all leads to the characteristics of teachers who employ student-centered teaching and learning. When Mark and Mary decided to implement some active lessons, they did so because they were bored and the students were bored. Being tired of doing all the talking was mentioned Mary and Suzie. Being the “sage on the stage” was not leading the students into retaining the material. Suzie additionally talked about her inquisitiveness and that it was an evolving process. Personality, patience, being flexible, being creative, having self-confidence, and enjoying what she does are additional characteristics that Suzie talks about during the interview.

            My view on how my research questions would be answered by the interviewees changed as each was conducted. Just like Suzie is evolving as she does more and more student-centered learning so did my analysis of the data for the research questions. My research questions stayed the same but how I viewed the second one especially did change from a focus on the path that led teachers to active teaching to experiences and concerns they had during the learning and implementation process. All in all the answers I received were what I expected on the surface but after analysis of the data I realized that even though I thought these teachers knew and practiced some amount of student-centered teaching and learning that each looked at it differently and with different needs and concerns. Educating teachers and administrators on the student-centered teaching and learning approach will be beneficial for all involved. In the future data may be collected on a professional development series of sessions that deal with student-centered learning and follow up sessions so that teachers may be supported in their endeavors.

              Teacher perceptions in general were very favorable for student-centered learning. Acknowledging that planning active lessons takes time, these teachers felt collaborating with others is helpful to come up with ideas and then streamline them for an effective lesson. Blame and the feeling of being threatened for not producing positive results on quarterly assessments may be a factor that holds others back according to the interviewees. Educating the administrators in each of the schools would be a step in the right direction so that would know what a well facilitated mathematics lesson looked like with respect to the teacher and the student. Even though the teachers in the county have had workshops on creating student-centered lessons and multiple representations a lot more is needed. More specific instruction and examples are needed so the teachers will know what is meant by student-centered teaching and learning. Teachers also need similar instruction to what the administrators might receive along with follow ups to provide additional guidance. Even though I thought all of the teachers I interviewed were well versed in what student-centered teaching and learning was, I was wrong. Change does take time, support, and education.    

Limitations or Threats to Validity

The limitations to the study centered on who I could select/request to be a participant and the relationship I had with each. Due to my role in the county as the mathematics coordinator and as the instructor for a graduate level course that many of the teachers in our area were taking narrowed my choices. Furthermore, I was looking for teacher that had experienced teaching using a student-centered approach in secondary mathematics, more specifically in Algebra I, Algebra II, and AFDA. In addition there was a concern for how the teachers would respond to my interview questions by telling me what they truly believed or felt or by telling me what they thought I wanted to hear. So choosing teachers of which I had a good rapport that would speak their mind, and appeared to want to change or had started on the journey to change was the selection criteria.

Even though the criteria were used for participant selection there is still the threat that they would not speak honestly. If more time was given to the project I could have created a mixed method approach incorporating into the project observations of each of the teachers during instruction and gathering data by looking over lesson plans to determine how many student-centered lessons the teachers facilitated within a specified time period and benchmark and the end-of-course standards of learning results. Most teachers keep the past years lesson plans so these could be used for the count along with the scores for last year. These would be better to use since they were completed without influence from being part of the project. Pre- and post- tests for students to assess mathematical growth along with a pre- and post- test to help assess teacher understanding of student-centered teaching and learning would also be beneficial. Additionally, teachers participating from other districts may also provide a different viewpoint.

What I Learned

            All of the interviewees were selected because I felt they had facilitated some instruction using student-centered teaching. What I learned was that each held different definitions and approaches to the methodology of student-centered teaching and learning. In the past I felt that these teachers held the same views and still did upon first reading of the transcripts. It was after I started my analysis that I realized I was wrong and probably had not truly listened to the participants during past conversations. The quality of this type of analysis never held any importance to me in the past because I felt that these types of studies were very subjective. Now that I have had the opportunity to do some interviews, reflect on what I have done, and to realize that the validity of my study was foremost on my mind from the beginning, has changed my thinking. The validity of my project was through the selection process, having the participants explain a student-centered lesson (rich data), and a type of triangulation. By talking to three participants to gather data and then putting the substantive codings in a matrix I was able to see similarities and difference between their statements.     

One of my main interests is in the student-centered approach used by teachers of AFDA and how these approaches are affecting students learning and application of mathematical concepts. My research has changed some of my thinking about the topic. During this study I interviewed teachers of students in courses prior to and after AFDA. All subject areas teachers need assistance in some manner with implementing the approach and would see advantages of participating in guided collaborative meetings and reflections in order to be successful in change. This will probably leads to my wanting to focus on just the AFDA teachers and their assessment results. Quantitative assessments based on the first semester of the course along with qualitative interviews and observations will increase the knowledge and validity of the teacher and student growth.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

References

Boaler, J. (2002). Learning from teaching: Exploring the relationship between reform curriculum and

equity. I, 33, 239-258.

Borko, H., & Putnam, R. (1995). Expanding a teachers’ knowledge base: A cognitive psychological

perspective on professional development. In T. Guskey & M. Huberman (Eds.), Professional

development in education: New paradigms and practices (p. 35-65). New York: Teachers College Press.

Topcu, A. & Ubuz, B. (2008). Effects of the asynchronous web-based course: Preservice

teachers’ achievement, metacognition, and attitudes towards the course. Educational

Technology & Society, 11(3), 181-197.

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix A

Substantive Codings

MARK

SUZIE

MARY

administration

adaptive intelligence

Definition

applications

administrative support

a lot of work

assessments

Assessments

administration

big ideas

Attitudes

better students

Blame

better learning environment

bounce ideas

boredom

big ideas

central office

centered on students

bounce ideas

Checklist

challenged

can't depend on prior knowledge

Collaborate

classroom management

Collaboration

comfortable with content

collaboration

Content

common planning

collaborative learning

control

Control

conceptual understanding

controlled chaos

do something different

connections

Cost

does not envision teaching SCL a lot

content knowledge

Creativity

don’t trust lower levels

continual learning

Discipline

Experts

control

Disconnect

get material quickly

deeper meaning

Discovery

gets them moving

develop concepts

Engagement

good foundation - tchr lead

dialogue

Enjoyable

handle it

discovery

Evolve

higher ability students

don’t understand

Expensive

if they let me do it

encouragement

Fear

Investigative

engagement

Flexibility

make it their own

expectations

Freedom

Maturity

facilitate

Frustration

not boring

failure

hands-on

peer observation

freedom

helping others

Personality

get called down

Inquisitive

plan individually

good teaching

Insight

planning

graphs tell a story

kids now know

pre-service education

guidance

know the math

puts responsibility on stds

individuality

lack of other subject area knowledge

Resources

know your students

leading the tour

Retention

learn to develop

life skills

self-confidence

life skill

live the mathematics

sick of talking

look at your kids

maps redone

sit down and do (plan)

math talk

meaning to the math

Stations

not compatible

move with students

stations - benchmarks

pedagogical content knowledge

never go back

std collaboration

planning

not knowing practicality

std more involved

practice

not lack of intelligence

std not going to struggle with material

problem solving skills

Observation

std successful

professional development

open up lesson

stds a disservice

promote learning

Ownership

stds felt good

resources

Pacing

stds lead

responsibility

Patience

stds talk to each other

retention

pedagogical content knowledge

stds w/ motivation

self-confidence

peer observations

tch control for max learning

selling the SCL concept

Personality

tchr facilitator

skills

practical application

tchr forced to try

std self-confidence

Presentations

teach themselves

success

problem solving

Threatened

tangible

really are learning

time  

tchr evaluation

Reasoning

time goes faster

teacher support

Relationship

type of questions

technology takes time

Relevance

up to stds to be successful

time

Resources

use books for problems

training

Responsibility

with like minded people

unit plans

Retention

works with higher levels

 

Rigid

you taught us

 

Scenarios

 

 

science lab

 

 

self-confidence – teacher

 

 

sense making

 

 

std disposition

 

 

std interests

 

 

std motivation

 

 

Time

 

 

trust and support

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix B

 

Interviewing Mark -- Friday, October 16, 2009.

Interview is regarding student centered learning concerns frustrations expectations and desires.

Mark was informed that he would be taped and the tape would be destroyed after the class that I am taking is finished. His name would be changed later to ensure confidentiality.

Pam: My research question is about your perceptions of student centered learning and experiences you've had, your concerns and your frustrations. So the very first question is can you describe a student centered lesson for me. Something that you have already done

Mark: let me think what I have done recently, uhmm I did one last year where we were beginning a unit on writing equations and students had a background in kind of going in the other direction given an equation they could generate a graph they were familiar with, tables. They were familiar with functions and the unit itself centered on they would be able to take information given in various forms whether it is two points, the graph, a point and the slope - it was a story problem or whatever you want to call it. The story we gave them was actually a travel agency with a variety of travel brochures and they needed to on each one - of the brochures for each presented information in a different manner like a graph, or table of prices, whatever the case may be and they needed to basically take the information they were given and find the formula for the equation. And they basically had to do that in a variety of different ways - they could have done - because of their different experiences and use those different equations they came up with to make sense, make some decisions in terms of which travel agents they would go with and which package they wanted to pick and things like that The part that was student centered, I guess, they were working in groups collaboratively to figure this out when we have not talked about what they are actually doing. This was before, previous to any direct instruction, and writing equations so they were really relying on their problem-solving skills, their collaboration and their prior knowledge to come up with the answer

 

 

 

 

 

 

 

 

 

 

Portrays a common usage of student-centered teaching but pulled a lesson from a year ago to share.

 

 

 

 

 

 

 

 

 

 

Pam: when did you realize that a lesson taught actively was something that you wanted to try?

Mark: I couldn't even tell you, I think to be honest it just gets boring to standing up there and teaching. I could just see the boredom on the kids faces a lot of the times to and you realize that you got to do something different. In terms of when that happened I don't know.

Pam: in all the years I have known you, you have always taught like that. I have seen you do various things with it, with a student centered approach.

Mark: It is something I have always tried to do. And I think it is something but first starting out as a new teacher you're trying to find your way. Trying new things. I have slowly been incorporating more and more each year, and once you become accustomed to doing it, it is easier to incorporate it more and more.

Pam: was there anyone that influenced you in the very beginning.

Mark: honestly no, the school I was at previously didn't do a whole lot of collaboration and I was a new teacher and I wasn't really, I don't think I saw the big picture. I don't know that I took advantage of the collaborative opportunities that were there. So as a result, I just scratched out my own way.  When I came to my current school is when I think that my professional development really started taking off and I was exposed to new ideas and new ways of teaching. So I guess in that regard I would say that my growth as a teacher accelerated at that point.

Pam: is there anything about teaching, you say that when you taught a student centered lesson you noticed the kid’s eyes. What are some of the positive aspects or things that you're seeing with teaching this type of lesson?

Mark: Engagement obviously is a big one. I also I believe very strongly that it is kind of a no-brainer as kids learn more and better. When they know what they are learning and why they are learning. And I think that if the lesson is student centered they develop those concepts for themselves. They, the meaning is inherent in the lesson for them. They find, if it is a successful lesson, obviously. Whereas any time it is a direct instruction a very small percentage

 

 

 

 

 

 

 

 

 

 

 

 

Collaboration seems to be a common theme

 

 

 

 

 

 

 

 

 

 

 

of the kids will actually see the meaning in it and they may if they are your best kids probably make some connections with other stuff that you have done so that will be the meaning, that would be the purpose, but most of the kids I don't think get it that way.

Pam: so how does that affect your planning, if you are planning a student centered lesson? What does it take?

Mark: a lot. I think first you got to look at your kids and you got to look at where they all are in the material because they have to be able to do it. I think it needs to be challenging but it also needs to be assessable to them. So you have to figure out what kind of a lesson they can get into that will keep them interested but they can’t figure out in two minutes at the same time not frustrate them. I think it depends on the material. You know, I think, let me rephrase that. I think, depending on the material, it's going to affect how you handle your lesson, whether you want it to be strictly discovery, isn't something that they can, they can discover on their own. What are the supports that you are going to need in the lesson to keep them moving through it? I think you also have to have a pretty good grasp of what the big idea is that you're trying to get across.

am: was that ever a concern for you? We have talked about big concerns, big ideas before, what does that entail getting those big ideas together

Mark: I think it's really I, and my department hates me for talking about this, but you got to ponder it. I think and you really have to. I don't know if there is really any one answer to the big idea in terms of how you bring it across. But for example, solving equations, you know if you are just teaching the procedures in the process of solving an equation you are not really hitting on the underlying idea, you know, the concept of balance. The concept of how you maintain balance by doing the same thing to both sides of the equation.

Pam: okay, so teachers have to - it takes time. Time to think about it, what else do you think might help them?

Mark: I think collaboration is a big part in that regard. Particularly for your new teachers because I think there is a learning curve and that I think is a big hurdle. Most teachers can come up with an

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

More to just knowing and being able to DO mathematics – there is the knowledge of connections and conceptual understanding

 

activity and obviously I, as I said, the more you do student centered activities, the easier it is to figure out what works and what doesn't. But anybody can start coming up with them. But if you don't have the big conceptual understanding that you are after your student centered idea isn't necessarily going to be hitting at the right thing.

Pam: so that goes back to what you are referring to as content?

Mark: yes, I think so.

Pam: being able to pull all the big ideas together

Mark: Yea

Pam: to get where you are now. It has taken a long long road to get here. You have been growing every year. Are there any processes that you have used that have helped you to get to where you are now?

Mark: collaboration is a big one. I'm a big fan of just talking about things. Some people, you know, like to be more efficient, to sit down and come up with a plan and then execute it and then I'm sure that there is some reflection and some revision. But I tend to try to just talk about things and think about things ahead of time. And I change things a lot. So I think the key part there is to have someone that you can dialogue with. You know whether it is on the county level, an administrative level, the department level, but it is just fostering an environment that it's okay to talk about things and to try things that might not work.

Pam: how do you feel student centered teaching and learning has affected you professionally? You are department head. So how has it affected how you'd deal with or your outlook on your department or career, what you're looking forward into your career?

Mark: obviously, I buy into it so in terms of how I lead my department – I encourage that. I think, and it is the case in most schools, that when you walk in to your average classroom, your average classroom will still do more direct instruction than student centered so in that regard I try to promote student centered structure or student centered planning. So for example in planning. I have tried to promote unit plans as opposed to daily lesson plans,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

because I feel that that will help us focus on the bigger ideas. And I think, I think that that is one of the biggest hurdles to teaching student center is if we are teaching skills then I don't know if student centered fits the bill.

Pam: what do you think would be as far as looking at concerns and frustrations were a couple different ways, what are concerns and frustrations when you teach a student centered lesson, whether it's planning, executing, when you reflect back on it. What are your concerns?

Mark: I don't know that I have any real concerns. I am pretty comfortable with teaching a student centered lesson and having it not work. I think that is one of the big ones is, that it doesn't always work and you know, sometimes it is downhill. You scratch your head and you start over.

So, you know, I think time is always a concern. I think, you know there are many times when I'm in the middle of a lesson I think I should have done that. Maybe it occurred to me earlier but I decided I did not have time to do it. Maybe I wish I had …….

Resources, I don't think are a terribly big deal. I think most lessons, you can pull off with limited resources. Whatever it is there are ways to do that. So I don't really worry myself too much with that.

Pam: do you think that is a concern of being able to conduct a student centered lesson and as you said have it flop or not being able to have all the right answers at that moment. Do you think it is a concern for a lot of people?

Mark: Yep I think so.

Pam: and what do you think we could do to help them?

Mark: well, I again, part of it goes back to the environment and realizing that that is how we learn. That is how our kids learn, they learn by making mistakes, and that's how we learn as teachers. I have made plenty of them (mistakes). It is okay to make mistakes as long as you know you're using those mistakes in a productive manner. So, I think that is a problem. I also think there, and it is a problem and maybe it is just a human thing, but often when something goes wrong we tend to blame what we do as opposed to

Skills vs conceptual understanding

 

 

 

 

Self-confidenceà practice

 

 

 

 

 

 

 

 

 

 

 

 

Blame—

What we are doing that is new

Being held responsible

Administration – may not be supportive

Everyone but oneself

 

how we did it. And then we don't want to do it anymore. And, you know, I am guilty of that. I have tried doing writing assignments year after year and they just don't go well, and I don't stick with it. And, again, I'm sure that if I worked at it and I changed how I did it that it would be successful. I just have not done it yet. It is on the list [Laugh]. It is part of my school improvement plan. That is what our department is doing. So I'll give it another shot this year.

Pam: More Verbal?

Mark: Right. But I do think that that is, that is typical of a lot of people, a student lesson goes wrong. The problem is with the student lesson, but no it's not. We need work on how we did it.

Pam: you mentioned that there are problems with the student lesson. What about the outlook of the students - any frustrations for them?

Mark: Uhhhh. I'm sure there can be. Uhhhmmm. Obviously, students get frustrated and depending on your level they can be quite vocal about it. A poorly tailored lesson, whether it is student centered or direct can go off-track and then lead to student frustrations. So I don't think there's anything unique about student centered lessons that are any more or less frustrating to students apart from the fact that maybe the teachers are not used to doing them and perhaps those lessons are not quite, as you know, fleshed out and polished.

Pam: You teach a lot of the lower levels in algebra so when you teach a student centered lesson - What about the retention? There are a lot of concerns over the years I have heard that when you teach something of this nature that it is just fun for the kids and they do not retain or see the concern, what is your feelings on that statement?

Mark: I think that is way off. I mean this idea that fun sometimes interferes with learning. I mean isn't learning supposed to be fun? Don’t we tend to enjoy and remember the things that are fun as opposed to the things that are boring. I don't, I don't see how fun interferes with learning. It certainly can, you know, if your kids are running around playing duck duck goose when they should be doing an activity. Then sure, the activity … As long as the fun is directed in some manner. And I'm not really sure that fun , if it is

 

 

 

 

 

 

 

Blame

 

 

Good teaching is good teaching regardless of method

 

 

 

 

 

 

 

 

 

Teachers need to learn to how to develop SCL and consider student needs/abilities/ interests.

even a word that my students would ever really describe activity as fun. Some may be, but I think the key is engagement and whether the kids are actually interested and motivated by what they are doing as opposed to being interested and motivated because the teacher told them this is what they are doing and they will be getting a grade on it. And all of those external motivators are great, but they're not really promoting learning and retention, they’re promoting task completion. They are promoting whatever you want to call it but it is not learning.

Pam: with student centered learning how do you think it is affecting assessments with benchmarks with SOL assessments - how do they affect that? What are your feelings?

Mark: I don't think they, really I think they are two separate things. I know, the popular thing to say is SOL and benchmarks are ruining instruction. I don't think it. It is just, and assessment I mean, you give different assessments as a teacher or you should be. You need to give formative assessments, you need to give summative assessments, you need to give them different forms. The benchmark and SOL are just one form. And if you allow those things to dictate how you teach then obviously it is a problem. But that is your choice and I think we give benchmarks every nine weeks and I think they're useful for what they are and I, you know, I look at them and I am, you know, aware of what my kids are doing well and where they are doing weak, poorly, and usually with the feedback I get from them corresponds with the feedback I have already gotten. So you know, at worst it is just reinforcing, you know, what I have already seen in the kids anyway and it is data to use.

Pam: for long-term, do you feel that student centered lessons are more profitable for the kids for recall?

Mark: again, because they are engaged and they are responsible for their own learning and they are driving the lesson. I mean, who doesn't remember something they have chose to do and wanted to do as opposed to, to something they had to do, you know, it's almost common sense to me and it kind of makes sense.

Pam: if you had any wishes or desires for your students as they come in the very beginning of the year, what would they be?

Teacher knowledge –pedagogical content knowledge

Retention--

Learning is due to

--relevancy/student interest

--engagement

--student ownership in the lesson

--classroom management

 

 

 

Assessment-  feedback

Appears to drive instruction for most teachers

 

 

 

 

 

 

Ownership by students

Student freedom – choose to be engaged vs forced to due to be graded

Mark: Hummmm  interesting. Uhmmm…. I don't know. You know, I guess I kind of, I'm so used to taking what I get that I don't really think about that too much. I suppose any exposure to those types of lessons. Exposure to problem solving and reasoning skills…. I know they are doing the exemplars program in the middle school. I'll be excited to see if there is a difference in how the kids approach a task with the kids that have gone through that program to see how that, I would be interested because that would certainly help by having kids who are used to engaging in more challenging tasks and used to approaching a problem where there isn't an obvious solution would certainly help implement student centered learning and foster that environmental little more. So that would be interesting to see other than that. I don't know.

Pam: as your students leave, let's put it on the other end. What are some of your goals as your students walk out of the classroom at the end of the year?

Mark: …. I would like them to have a better conceptual understanding of math and hopefully with that a little bit more appreciation of math and why they do it. …If a kid walks in to my class asking why they have to do this and walk out saying the same thing, then I think I have failed. Uhmmm I, I mean, I would love to have all of them to walk out and be ready for calculus too but that, realistically, that's not what I teach. But I would like to try to prepare them. It's almost a life skill in a way as much as it is a math skill. But just to prepare them to face challenges and problems and to not throw up their hands if they are frustrated or they don't see an easy solution. That is the case with a lot of my kids. They are used to failure, and they are okay with failure, and their way of failing is not trying because that feels a little better than trying and failing.

Pam: are there certain characteristics of a child that would excel in student centered learning versus not excelling?

Mark: they need to be breathing, other than that, I don't think there is. Obviously we have different kinds of learners, but I think you can tailor student centered learning to still suit the needs of all your students. That is a matter of differentiation, to have, you have interpersonal and intrapersonal learning, and obviously student centered learning is often associated with collaborative learning.

 

Student benefits -

Early exposure to problem solving skills/activities

Begin SCL earlier

Multiple solutions and being able to defend their results and approaches

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

But it doesn't have to be. I'm not the biggest group learner. I tend to be a very individual learner. I like to just play with it, and then get with the group and share what I have thought. But I think you can meet those needs and I don't know if there is such a thing as who benefits more. They all would.

Pam: with our curriculum maps …were talking about big ideas now… how do you get your big ideas? When you look at the first quarter or the second quarter how do you come up with those things that I hear the teachers say, what is unit? But how would you guide someone into determining what would be the big idea?

Mark: well, I sit down and I take the map. And I look at the different strands. I'm a visual person so I usually write them up on the white board. And I kind of… It is like my rough draft. I put them up there and I put them in groups. And when I put them into groups it's kind of looking at similarities and differences. I'm sorting and I'm trying to put stuff together that makes sense together and then I asked myself why it makes sense together. Why do I want to teach these together? What am I really teaching that holds these things together, these skills? And sometimes I go through them and man … I should have taught this with this and then sometimes I change it on the fly and sometimes I am too late and have already taught it. But that is the kind of process I go through and it changes from year to year. Sometimes I do decide I'd rather teach this here and this here. And sometimes, you know, the big ideas can change. And sometimes, you know, I have taught equations separately from inequalities where your, with the equations, I focused on the balance and with the inequalities the difference from equations. And sometimes I focused on the contrast. I have also taught them similarly, as parts of the same picture relying more on the graph. Basically treating the graph as a story…. you got the point where they cross and the before and the after and then there is your inequalities. So there again, it is a work in progress.

Pam: so then how do you determine if a student centered lesson is a success?

Mark: to be honest with you it is more formative than summative. I don't really look at my kid's grades to determine whether the lesson was necessarily a success. I ….. obviously, the grades show me

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

what the kids understand and know but there is a lot of other factors that go into that and it is not one lesson that is responsible for a grade. So I really look at my observations during the lesson, look at the student’s engagement, the questions. As I listen to what they are saying, where they are running into problems and where they are succeeding. So I would say that it is more formatively.

Pam: so it is okay with you if students are not okay, are not happy with the material as they walk out of class each day? If you're talking about encouraging problem-solving so it is okay for them to ponder something over time.

Mark: [agreed, shaking head] oh yeah I know the traditional lesson plan is that you have a warm-up, you know, an engaging activity, direct instruction, guided practice, independent practice, closure. I'm not a big fan of closure. At some point you do need closure. But no, I think it’s better that they go home and think about something. If they are done for the day then they are done for the day and that is the last they will think about it until they walk back in the next day.

Pam: actually, you are saying that there are different kinds of closure. You may have closed out the lesson, but you have not closed out the thinking process. [agreed] Is there anything that you feel that would help you or your staff to grow in this manner?

Mark: ideas? [Pause to move to another area of the library.]

Pam: is there anything that you can think of, any guidance that you may wish or want from your administration or central office that would help?

Mark: In terms of administrative support, I think just fostering 1) encouraging new ideas , encouraging that kind of thing. We are actually under a new administration right now so we’re still trying to feel out how that is going to go . Our previous principal was very much a promoter of new ideas and, and let's keep looking. A constant search for new ideas, new thoughts, and new strategies and some we try and some of them we didn't and some of them worked and some of them didn't. But there was that still constant, you know, sense of professional development and professional inquiry, whatever you want to call it. And I think that needs to continue, and I think that it manifest itself in a number of ways .

 

 

 

 

 

 

 

 

 

Continual learning

Closure may be different for a SCL

 

 

 

 

 

 

 

 

 

 

 

 

 

One way is just the obvious vocal support and sharing of ideas, and one is just the way that the school handles professional expectations and observations, to walk thrus, the kind of feedback that is given and what the feedback focuses on.

Pam: do you think that the administration needs more guidance in that area as they go through their walk-throughs?  Especially in a student centered classroom?

Mark: [agreed] . That would help obviously, if they are looking for structured transition and warm-ups, the process, then that is not going to promote student centered activity. If they are looking for objectives and rationale being clearly stated ahead of time and this is what we're doing and that this is how we are going to get there … that is not really student centered learning. At the same time, if they're looking for engagement , looking for focus, listening for math talk, if they are listening to… Are they really getting it. Really getting to the deeper ideas, what is the concept that we really want these kids to get and how that concept really coming across in the lesson. That is the kind of stuff that does promote the kind of learning and the kind of teaching that we are talking about. I think it is also tough because there's not a lot of administrators who have any math background and so it is difficult for them to look for those things in particular, the content related stuff. It is hard to go looking for the deeper meaning when you do not know what the deeper meaning is. When you are not familiar with it you can get a sense of it, but it is hard to promote something that you do not understand. That is the difficulty.

Pam: so with that train of thought with teachers, we need to promote some kind of deeper learning of content.

Mark: I think that would be beneficial in terms of professional development for teachers. I think it goes both ways. I think one of the things that you will hear teachers say is that, yes, they really want to do this but they don't know how or they would like to see an example. It is not so much that they necessarily want the lesson handed to them. Although some do. And that is not necessarily a bad thing. But a lot of times seeing it first helps and then they can put the pieces together. It's kind of like a puzzle, most people do not start a puzzle without looking at the big picture on the front of the box first, and wanting to be able to see that. So I think that it

 

 

 

 

 

 

 

 

 

Admin looks for traditional flow à doesn’t correlate with SCL

Causes fear, frustration in teachers

 

 

 

 

 

 

 

 

 

Need to see the “big picture”

 

helps them and in terms of the big picture, that is what they are talking about that needs to be tangible for them to see the big picture. A lot of times it is “here is an activity, here is a lesson, this is how I did it, these are my questions, and this is why this is the kind of stuff that I try to share. A lot of my folks try to share and collaborating is not just .Here is the activity … but here's why I did this and, and this is what I wanted to come out of it. Here's why I did this part, and here's what I was trying to get the kids to get out of this part. Here's the building of conceptual understanding, but I think that is the part that teachers need to see in professional development. And it needs to be … it needs to get to that level, because, again, that is the part of the challenge … is not just here's the activity I did but if the teachers don't understand each part of the activity they don't understand the conceptual progress that you are hoping that the kids make during that part of the activity, in this part activity, in this part... then it is not going to work. They are going to get to the end and not know why they just did it. And you know, it is a challenge and is part of the... I'm speaking on a personal note, level ... I have a difficult time teaching someone else's lesson, because if I have not created it. Then I have not gone through the conceptual process of why I am doing this and why I am doing this. So in order for me to teach someone else's activity, I really have to, to sit down and go through it myself and figure out and then a lot of times I will change it as I go, because their conceptual development for their kids is not quite what I would do with it . And the other part of it is that we all think differently and there is more than one way to get there conceptually.

Pam: as far as your peers, your department, what might be some of their frustrations as they change with teaching, changing from direct instruction to something that is more student centered?

Mark: time I think is a concern. Time is tight for a teacher. They all recognize that it does take a little more time to put something together …on the flip side of that we do a pretty good job of collaborating. So that has eased some of our burden, the bigger picture of time is not so much the time during the day. But there is still this sense, and I combat it is much as I can, but there is still that sense that we have benchmarks and SOL assessments looming and we have to get through all this material. I believe I'm making progress, selling people on this idea that you can get there and get

Examples for teachers to experience as a student will

What collaboration is not…

 

Need to understand conceptually – not just receive handouts

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Concern about getting through material àdrill and kill is the result

 

there better doing it student centered but not sure if everyone is sold on it yet. And it is just going to take some time. It's also going to take some success on their part doing it student centered in order for them to buy into it. We’re going to get there and they will probably retain more and I might even get there faster. So, I think that is the bigger picture, and in that, I think we talked about earlier... there is still that perception, that student centered learning is not compatible with standardized tests, and there is a sense, obviously, that teachers are evaluated using the standardized test. And I have tried to encourage them that that is not the case and I think administration has done the same. Our benchmark scores are for formative feedback but at the same time, the reality is that they are formative about the kids but they also, to a degree, tell a lot of information about the teachers and teachers do get called down on their scores if there is a problem. And the first thing that gets blamed is, what am I doing differently ... I didn't have this problem last year. And I did not do that last year. It is an incremental process in the philosophy and mindset.

Pam: technology. How does technology play a part in a student centered classroom?

Mark: not as much as I should… and I... this goes back to how I learned and they say we teach how we learn. I was not a technology person, I didn't use calculator in high school. We did have them and I didn't use them in college. So I never used the calculator as an exploratory tool and have always used it to just get an answer. So while I have never wanted my students to use a calculator to get an answer I have never really put the emphasis on the calculator. The other technologies... not that they are used to get an answer, I just not have been exposed to them. Most of my activities are not heavy on the technology . That said, I think there is a lot of room for improvement in that area. I think the calculator does have a lot of power, as an exploratory tool. Smart Board and TI SmartView programs, basically the calculator, but all of those things I basically think really help and in a way it is the same task, student centered learning, but it does take time... and it takes playing with it and figuring out exactly how you want to incorporate these kind of things into your lesson and how to keep them so that they are assisting the learning and not interfering or lowering the level of the challenge. So I think that it is an integral

Effort & practice à successà self-confidence

 

 

 

Teachers held accountable for benchmark results -- fear

 

 

 

 

 

 

 

 

 

 

 

Doesn’t see any importance in using technology

 

Needs training on how to implement technology that will enhance instruction

part that I have not mastered yet.

Pam: technology is changing so much that it is sometimes very difficult for teachers to keep up with technology and to use. I know that in this school that you have a lot of opportunities to use technology such as smart board, you use that a lot. I just wondered if that was something that a lot of teachers you or anybody else in the department have focused on. Some feel that a student centered lesson has to be in this day and age focused around technology... and that is not what I am hearing you say.

Mark: I don't think it has to be. It has to be centered on the students. And technology can certainly assisting that and can enhance that. But I don't think it is a necessary component... and there again. It also depends on what you were doing... what the contents and how the calculator fits with that.

PM: is there any comments, any last wishes or desires assistance or help that you might have just as you focus on student centered learning?

Mark: besides time, again, I think it's just facilitating the dialogue, the sharing of ideas, and time plays a part in that to. It is hard to set and have a two hour long conversation on why we care about slope when you don't have two hours when you have papers to grade. But it is that dialogue that really gets people there. Not everybody thinks the same and not everybody has the same ideas.

Pam: we do need the dialogue and is there any concern that when you do collaborate of not having the same views . We all have different views on how to teach the same things. Has that been a concern?

Mark: no, and then again it goes back to the administration and what their expectations are. I know there is some places where the expectation is that everybody teachers the same. If you walk into a room with the idea that we’re coming up with a plan and this is what we are all going to do... I don't know if that is the best way to go about it. I think then you are forcing people into a mold that they are not comfortable in and if they're not comfortable doing it then I think you're not going to get the best out of them. We try to share ideas, we value the similarities and differences. I think you walk into the... may I backup for a second... Some of our groups

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Different ways to collaborate –different expectations of the teachers and administration

that do common planning very much do take a kind of let's figure out what to do and let's go with it, actually teaching to the consensus. They look at things very similar. Other groups get together, put their heads together, share thoughts and ideas and strategies then go their separate ways in the way that they implement it. I think that if you walk into the classrooms of any of the people in our common planning groups. I think you will see similarities and I think you will see differences. I think that you will find some strain of pushing towards a common idea, a common concept, a common goal. Maybe not the same way... I think that is there. [thereby honoring everybody's individuality].

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix C

Suzie Interview -- October 19,2009.

 

Location: teacher workroom. Doesn’t have her on classroom.

Time: end of the day and during her planning.

I explained to Suzie that the interview would be recorded and transcribed, her name changed for confidentiality. Records will be destroyed at the end of the class at this is a class project. The goal of the project was explained as looking at student centered lessons, concerns, frustrations.

Pam: so first of all, could you describe for me a student centered lesson that you have taught. Just pick one and describe.

Suzie: just recently I did the Archimedes principle where the students were discovering the steady... direct variation change of rising water when putting canisters with a certain amount of pennies in each film canister. So they were placed in a group for the activity, and based on them doing the exploration and questioning those individual groups. And them being able to see the pattern and create the function from that laboratory and understanding the relation of the function to the situation.

Pam: what was their prior knowledge before beginning the lesson?

Suzie: all students should of had algebra one and the basic idea of set up for a linear equation... y = mx+b.

Pam: when did you realize that the lesson taught using student centered activities is something that you wanted to try?

Suzie: oh many years ago. I mean... five years ago maybe. It might've been six years ago. My personality …I don't like doing all the talking. I don't like delivering information. I just... the kids learn so much better when it is hands on, a student centered lesson. They are more engaged, a better learning environment, their dispositions are nicer, discipline goes down so much, they pay better attention. So I think it was about five years ago.

Pam: was there anyone who influenced you when you first started?

 

 

 

 

 

 

 

 

 

 

 

 

Sees mathematics as a student should see it.

 

 

 

 

 

 

 

Student benefits

 

 

 

 

Suzie:.... When I first started student centered teaching...uhmmmm…. I can't think of anybody in the beginning, and then beginning in my strive for student centered teaching, no, as I evolved and tried student centered teaching, especially with algebra two, I would say... you.

Pam: but at the start. You can’t remember a certain individual that kind of turned you on to it?

Suzie: I'm trying to remember?

Pam: I find that interesting, not too many people can recall somebody. That's interesting.

Suzie: I can't.

Pam: is there any... what was the process that you have went through to get to where you are now?

Suzie:... the struggle of finding practical applications to make it student centered. That was, that was what motivated me to start becoming student centered. I wanted to say that it became more of a... mathematics started to be more evolved as a science lab than me just delivering equations and information - making things more student centered in the sense of practical applications. So, that was. I want to say that that was the beginning of the journey was even being naturally inquisitive, how can I use, what was this used for, a reason for why I am teaching this. Just me as the teacher needing to know the reason, why am I teaching this, why is this so essential and going out and finding and discovering and then creating practical application to teach them, in themselves, become student centered.

Pam: did you start out as trying to do just one student centered lesson a quarter... a unit... how did you, how did you evolve , because now with AFDA I believe you are doing a lot?

Suzie: I am doing tons. I don't want to say it was one a quarter or one a week... I can't recall a specific amount. It was, it was a venture to try to open up every new concept or lesson with a practical application. So it was an ongoing evolution. It wasn't one. It wasn't two. It was... I started changing my whole view of delivery. I wanted to deliver the lesson with a practical application

 

 

 

 

 

 

 

 

 

 

Practical applications appears to be the theme

 

 

Students taking ownership of the lesson

 

 

 

 

 

 

A whole new outlook on how to deliver the lesson

and so with trying to evolve with algebra two... I would say at least once a month I was doing it. When I finally, when the light bulb went on as a teacher and I figured it out That, that was what really needed to be taught first... or how the lesson really needs to be delivered.

Pam: now as far as those lessons have you evolved with the specific lessons like the one that you started out with? Do you keep reusing them or do you do something with them or do you create new?

Suzie: some of them I reuse, like linear programming... I. reused a couple of those lessons from algebra two. The AFDA though with the labs, the actual hands-on labs, are so brand-new for me that I say that they are pretty much…. pretty much replaced my old lessons, because they are so good. They really are.

Pam: when you plan your lesson. How do you do your planning? Give me some of your thoughts of your personal motives, professionally, how do you plan?

Suzie: first I have to go by my curriculum map... is there a strand, this is the area, these are the things I need to teach given within a certain timeframe. And I start with the lab with the practical application and then almost move from that particular practical application or lab. I used to try to check for prior knowledge, strengths, and witnesses. But then I found that that became a sage upon the stage approach. So I let the lab run, the practical application go and then as the lesson evolved, If I saw weaknesses... the kids were already so motivated that it became, the review became more efficient, quicker, and was able to intertwine with the whole environment. So the lesson always begins with a practical application or lab 99.9% of the time. That is how I want to begin the lesson. I begin with that and then move forward.

Pam: when you are planning you have your students in mind. How do you in such a student centered lesson... how do you plan for differentiation?

Suzie:... on the particular student’s needs I would say that I know when I deliver lesson. I try to deliver the lesson from many different aspects. From the visual, from the abstract, some auditory

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Shares a lot about how the students are perceiving this type of instruction and the benefits to both the teacher and the students

 

 

lecturing, from hands-on. I try very hard to intertwine all the adaptive intelligences and beyond just the intelligences of the students and their strengths and the graphs, the algebra, the delivery, the auditory, visual, kinesthetic. Besides even that, sometimes I am able to mold my lesson around the actual student’s interest. Like, for example, we just had a lesson starting linear equations and direct variations and functions. I started off the lesson with... how was your weekend? Asking the kids what they did, so forth and so on. And one young lady was telling me about her adventures with her horses and she has one horse that is very ornery named peaches. And she has already been denied by, by something like five trainers. Okay, so this horse... nobody wants to train the horse so I said okay lets go with this young lady's predicament this weekend with her horses. Peaches has already been denied by five trainers. She is averaging getting denied by two trainers a week. What is the... what is a simple graph going to look like? What is the starting point? We are not talking x and y axes... I don't even bring that up. That's way beyond [discussing it in terms of the scenario], that's past [x and y axis]... I even say that this is the vertical line and the horizontal line. What are these lines going to mean? We give them meaning. One line was the week, the horizontal, which is what we used to call the x axis and then the denial of trainers was the vertical, which is what I used to call for the kids when I started teaching as the y axis. Then we went and graphed it, the beginning. She was already denied by five. The kids knew that that was going to be plotted on the vertical line, used to be called the y intercept. The kids now know, evolved around their situation or any situation, that it is the starting point or what has already been obtained in any situation. And then we go on how the situation is changing, which we call the slope. And even writing the functions I don't do y=mx+b. It was t(w) -- trainer denials per week... and it became meaningful. This class now that I just taught evolves the situation around a student. I have a bunch of football players in that class. And so the situation was that whether they would be able to beat a local high school. We looked over their points. We did the total number of points that they had already scored during the past seven games. Then we looked at the average. How are they averaging per situation? And they were able to graph it knowing the starting point, what they already had, the

 

 

 

 

 

 

 

 

 

Practical application taken from student experiences

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

average number points... and then we looked for the local high school. It really hit home and actually they got a little depressed, because they could see in the math that they were averaging less than nine points a game. And that the local high school had already obtained quite a bit. The kids got really involved, it became student centered, because football players were basically very keened in to the situation. The local high school didn't take their first string out until after the first half for many of those games. We pulled our first string and played our third string most of the time. And I said, you're right. So it is not a very level playing field analysis... not everything is static, and the same. And then uhmmm  another football player said that did we know that we play different teams in those points. And I said, you're exactly right. And the lesson started to evolve and the students were getting involved,... and then we started another analysis. When the boys came in right after lunch with the points for each of the same teams played and we did a different analysis. So, in that way, were able to start using very practical, observations using their own scenarios from linear functions, and they loved it. Seeing the practicality behind the math... I will never go back to teach the other way. I don't even want to say y-axis or x-axis now, it doesn't have meaning.

Pam: it does change a lot. Working on that scenario and that one class -  Trying to give meaning to the axis. Now you have already kind of answered this but positive outcomes of a lesson... as you’re teaching the lesson, for you personally, this is threefold: personally, professionally, and for your students.

Suzie: personally. It is more enjoyable. Oh, oh. I just love it. Even from an innate mathematical inquisitiveness that I have seeing the practicalities and just the evolution of the math itself from the situation... personally, student centered... it is wonderful. My face muscles are not hurting by the end of the class because I'm doing all the talking. Matter of fact, I can count now when I've talked for about five minutes because I will start to get a twitch in my cheek. And I think this is starting to become the sage on the stage. And this is just not where I want to go. My muscles now, and my cheeks are just as stiff. But, uhmmm, I just don't like teaching that way.

Professionally. I have evolved so much of a better teacher, and that is almost entwined with the students. Actually, it really is

 

 

 

 

 

Students extended lesson with additional experiences and data

 

Taking ownership in the lesson

Based on the students and not centered on the teacher

 

 

 

 

 

 

 

 

 

 

 

 

 

entwined. I'm looking at the students and they are full bore engaged. They actually really are learning. They know the math now as far as practically using it and it becomes exciting and being able to… you need to be able to do from a professional aspect... you have to be able to move with them as you become student centered like that. You have to be able to give them the freedom to create within the mathematics. Just like the football scenario or the horse scenario. And we did another scenario about a cue ball. The guy was playing pool this week and you have to give them the freedom to create within the mathematics and be able to move with them. And make sure that the math, the underlying math from each scenario or situation within their own desires is correct so, but...

Pam: what would be some of the concerns or frustrations. Personally, professionally, and with your students?

Suzie: personally and professionally. It's, it's... they are taught differently. So, sometimes coming from this angle. They are so used to may be, only knowing it a certain way, very rigid. Like y=mx+b. Not knowing the practicality behind it. So when they come in, and that easiness of prior knowledge that you would have or think you would have... you do and you don't as far as being an asset to you. So... you mentioned slope intercept form. They have no... it is frustrating, because they don't understand the practicality of it is and that is kind of what is frustrating. I find that I can’t depend on their prior knowledge... even though it is there. It has been laid in such a way that when I am going in teaching it in this perspective, the students react positively. But they react as if this was the first time that they have seen it. So... you cannot take anything for granted. None whatsoever. So, that is why it changed over the years to not being so worried about being structured about prior knowledge. But just going with it as the lesson evolves, because the prior knowledge was not delivered in the same form. So that sometimes can be, uhmmm, student centered does take a lot of patience, a lot of group work, a lot of innovation, a lot of creativity. So, you have to be 1) patient and let the students have that freedom. That is sometimes like controlled chaos sometimes, especially in the lab work and then being able to bring them back in to may be analyzed a lesson as a whole sometimes as a whole class delivery, because they are so used to sometimes working in the group work.

 

 

 

 

 

 

 

 

 

 

Students have been taught procedurally (rigid) taking away their opportunities to problem solve.

 

Frustration by students

 

 

 

 

 

Students can learn mathematics!!

 

 

Pam: so the students have to learn a whole new way of learning the math, also how to act?

Suzie: yes as a teacher, too, you have to give up control. So if you like controlling, and you like to teach that way - I used to be that way. Very structured. Your warm-up is on the board... ohhh structure is good, don't get me wrong. But I don't begin, per say, with a warm-up usually anymore. Like today's class began again with how was your weekend? And evolving the warm-up just even around their scenarios.

Pam: so the class is even more personable? What about your peers? How would that... you have evolved, and it has taken time and you still are working it. What do you think is sometimes a deterrent for them to try this method of teaching?

Suzie: I think one of the things that make it easier for all teachers is the materials. I will say right off the bat that when I got the AFDA book that it was amazing because I had all of the labs, all the student centered activities. Before the AFDA materials I was struggling so hard to find the practical applications as far as a lab or discovery type of experiment. There is discovery geometry, and there was a book called discovery algebra, but they weren't the concrete examples and the lab work and the student centered activities really were not cohesive... it's just. It was, it didn't appeal to me, it didn't appeal to the kids in the class. So I think a big one is that the books now have to be written differently. So I think that once the books start being written differently then everyone will have it on their fingertips. It's going to make it easier to do the student centered activities. One. Two, the assessments. If you're going to have to give standardize assessments and benchmarks that are not student centered assessments and teachers are being held by those standards, those benchmarks... it's going to make it very difficult. You do hope - for and there should be that transference of knowledge, but I think students react given the environment that they are in. The student is taught and is used to being in a practical application setting and in a lab and is seeing names like t(g) and t(w)= 5w +100, or whatever that scenario is and then you give them a test and then everything is X and Y... it's, it's not that they didn't learn the material, it’s not that they don't know the material, it is that it's presented in a different form and so what happens... the student does not do as well, because they are not used to that

 

 

 

 

 

 

 

 

 

Materials need to be available for teacher usage – time and pedagogical content knowledge

 

 

 

 

 

Assessment à match instruction

 

 

 

 

 

 

certain vocabulary, the certain presentation of the algebra. Then it goes back on the teacher that they did not do their job well, maybe. And so then what happens is that the teacher is going to wind up teaching to what that test is structured to be. So given the materials so --- If you don't even structure the assessment the same way that the materials are presented then, or taught, then that leaves a big disconnect for the students. And I think it leaves a teacher quite frustrated. And then third, the teaching style. The teacher has to be comfortable with teaching student centered. It becomes an owness on the teacher’s personality and that is where you get into the art form of teaching more. And I think teachers observe other teachers who are more student centered again with the assessments written differently. They would be more apt to do it. The assessments were written student centered, then the teachers would probably feel more comfortable teaching student centered or would have to teach student centered then. You can't... I don't think you should be assessing differently than how you expect things to be delivered and taught.

Pam: and we are taught that way all the way through school. So... I can see that with assessments... that assessments is driving how we teach? Is that what I am hearing you say? So I guess my thought is that is there something we can do to help them see and make that link between doing a student centered lesson and, and taking it into the abstract, a very traditional mode as well.

Suzie: logically, one says that if you are taught student centered it shouldn't matter… that they should have that transference of knowledge and if you do they should do well on any assessment. That is a logical approach, but I can tell you from seeing how children I want them in the environment and how they behave in that one environment, the setting, and then another that that may not always be the case. But to fundamentally answer the question, given the materials, let them observe and give them almost the freedom to not feel that if things don't quite work out that their professional status would be in jeopardy.

Pam: would that help from the support end... what kind of support would be helpful from the administration, from the central office... just anything that we can do as far support.

 

Fear – blame by teachers  and with a fear of being ostracized by peers

 

 

Students confused after being taught relevant applications

Peer observations would be advantageous

 

 

Given materials and matching assessment may lead more teachers to trying SCL.

Concern: if teachers are handed materials then will they be taught using the correct methodology or resort to direct instruction and teacher led.

Will the teachers see the importance of time for sense making and reasoning by the students?

Fear – need for support by administration

Suzie: support would that be like uhmmm . I know when I was starting to be really student centered lessons were taking longer than our mapping allowed. So what was coming about was that my students have trouble passing the benchmarks, and it wasn't because they did not know the content, it was because of my pacing, it was so far behind what was actually expected for them to learn on the benchmark. At one time I was up to three weeks behind.

Pam: okay, but when you were behind though and in units that you were planning -- did the students always make up by the end of the year.

Suzie: I always made it by the year.

Pam: now explain to me how... so you are actually when you decide on a unit and you are going back to your plan... if you're going back to the planning stage you are actually planning big ideas... is that what I am hearing you say? You are deciding what just makes good common sense to you for that big idea? So is that why you are behind because you had more, actually more mathematics going on?

Suzie: I had more of a spectrum of mathematics going on with it, intertwined in the lesson... going back to previous concepts. Everything well, most of the times it was building on a previous concept. They were separated little segments of content, so there was always some type of review within the lesson, within the application that the kids were doing. But it did take longer.

Pam: so the curriculum maps need to be revised?

Suzie: the maps, the pacing... yes, because I was caught up at the end. I was always caught up at the end so it was funny and actually the kids retain the material better but, what was nice about the administration that actually helped me was that they were not quick to put my feet to the fire when my benchmarks results came up. They understood what I was doing, they were very supportive about it. Technically with the rate that I had failing my benchmarks that at that point I was surprised that I was keeping my job. So the teacher has to be very confident. And, and the teachers must trust the administrator and the administrators must trust them. Especially when moving in a new direction.

 Fear

Units are more in depth, taking more time but covering material with more meaning .

Need curriculum maps realigned to meet SCL needs

 

 

 

 

 

 

 

 

 

 

 

 

 

Teacher Characteristics

Strong, self-confident, need to feel supported, trust

 

Pam: do you think any guidance or education of the administration would help them to encourage teachers to take this leap.

Suzie: Yes, I think they need to understand that this type of teaching is at the moment more encompassing of the material but it is going to take, it cannot run at the pace that has been set in the past. You know they have come... that big argument of do we want to just skim a lot off of the top and give them a lot of mathematics or do we want to give them a deeper, very concrete grasp of mathematics. We want quantity or do we want quality? And I know we try to grasp both and you can with student centered learning with all the intertwining in the bigger concepts coming in but that may not become as evident until you get towards the end. You have to be very patient upfront with the teacher, with the lesson. It just takes a lot of patience on both, it take patience on their part as administrators with the scoring and the mannerisms of the pace of the teacher. And it also has to take a lot of patience of the teacher also teaching in this new form pretty much the students... I don't want to say that the students are running the show but having a lot of say in the lesson. You'll allow them to have that say and because it is based around that... they have a lot to say once they get really engaged.

Pam: now as far as planning the lesson you are the only one teaching AFDA here?

Suzie: yes.

Pam: collaboration. How would that play a part if you had others? Do you think that might help you in some way?

Suzie: yeah yeah, and it would help me to be able to bounce more ideas off another teacher and I even kind of do that now. Even though I don't teach the same content as other teachers, their class management, the way they may be delivered, their reviews, using things like foldables and just different encompassing techniques in the classroom that do group work and student centered activities... I used those. But I would love to have someone else to tell me how their classroom went, how their lab went, what did they run into it... oh this is a good idea, this is not a good idea, this kind of worked out, this did not work out. I have kind of been through the gamut of the book that we have and the lab and other things that I

 

 

 

 

 

 

 

 

 

Patience – students, teachers and admin

 

Student ownership

 

 

 

 

 

 

 

 

 

 

 

 

grab and so I also found, and some of the weaknesses I can patch up. And even mathematical things... like right now I struggle with the stats part of AFDA. And right now it would be beneficial to me to find more hands on activities and help somebody, and  [have them] help me with the time constraints, because part of teaching this way is very time-consuming. You just don't want to open up the book and say do the prompt and sometimes I may have had to in trying stats, but that's not how I want to teach. I want to teach with the situation first. Like here's the survey and so one of the projects I am working on next year to really fine tune is to start the students with a survey. So I need a survey that I could use within the school and see if the administration would allow the students to survey students at lunch. Really an active, beneficial survey for the school. It would be great if I could collaborate with someone on that.

Pam: and hopefully if the class grows that eventually there will be more and that would be wonderful. For students coming in at the very beginning of the year what would be some of your wishes or desires of the students as they come into your room?

Suzie: uhmmm. One of the things that disturbs me about the group of students that I usually get is that they come to me with such a poor self-esteem in mathematics and it is heartbreaking. And they really don't understand the difference between not being good in math and, in most cases, being lazy or irresponsible. They haven't been able to distinguish between the two. I hate math. I'm not good at math. I barely passed math. Well, let's get to the heart of the matter. Did you do your homework? No not really. Did you study? No I didn't study, how do you study for math? So you pretty much didn't do your homework, you didn't study for math and you got a D or a C. I don't think that is a lack of intelligence, you know, that is more of a lack of motivation, irresponsibility, even laziness. And so, I kind of have to make them aware of it and I just kind of wish they weren't so defensive about doing math when they walk through the door. They have their armor on, and just like, oh, another math class. I hate it.

Pam: let's take it to the flip side, what is your goal for your students when they leave you?

 

 

Sees the need to help and collaborate with others

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Suzie: 0hhh to have a passionate love of mathematics and not, ohh, just here's a book and do the problems but to be able to look at that situation and to be able to apply the math and to be very motivated to do it. They can now... now. When they leave the class and he has to go to another football game next year... oh, I can figure this out. I can, I can, I am worried about winning the football game, I am, I am going to start drawing those equations out and looking at the slope in the lines and the average rate change. That is what I desire for them... to pick up a pencil on their own and do something with it.

Pam: technology. What do you feel is the role of technology in the student centered classroom?

Suzie: in some ways it is or can make student centered learning a lot easier and it can help. Also a lot with the motivation and it becoming a student centered lesson. One of the lessons that I was struggling with, again, is the stats and so just by allowing them to be on the computer to create a PowerPoint presentation, again made it their own, more student centered. They have to go ahead and gather data on the topic of their choosing, as far as maybe salaries, data salaries of lawyers or real estate agents. One of them was the salary of the quarterbacks of the NFL quarterbacks up to last year. There is a collaboration. And of the basketball players and then they got the data and they made the histogram on the PowerPoint slide and they had to talk about skewedness. And they had to take the data and give the information in the presentation and the delivery was basically saying that when you go out into the real world your boss may say that I am going to go ahead and hire a new quarterback for my football team. Some of you may not be professional football players but you can go and help the manager and work for the football team and your boss comes to you and says... he's a good quarterback but I just didn't know what to pay him... why should I pay him in comparison to all the other quarterbacks in the NFL... what will entice him to come? What is fair, but at the same time, I don't want to pay him over. Well, you can do an analysis on all the quarterbacks in the NFL. And then you can see if it is skewed to the right or skewed to the left. The kids can say that very few in that scenario did extremely well in salaries, very few made over 20 million a year with bonuses in that profession. So maybe they can analyze how good that person is.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Actually, I have two students, because they did it in pairs, did psychiatrists and they found that the data of the psychiatrists, that the histogram and the curve was very symmetrical. Was very close and they couldn’t judge if it was left skewed or right skewed. Well, we had to go back to the fundamentals, the mean greater than the median or was the median greater than the mean? So it started really bringing in more practical applications. While others could see the skewedness then they could verify by the mean and median. The mean and the median in this particular pair had to really look at to make their final judgment, I can't remember what it was right now. But because I had the computers at my fingertips, since I teach in the computer lab, they were able to just jump on the computers and use just simple technology of a PowerPoint. Present it in front of class and talk about it and bring out the practicality of the math. So, technology can definitely make things more practical for them, more hands-on, just like in the lab using the water in the beakers. Linear regressions on the calculator, the smart board, the, the interactiveness... yes, yes, yes... it is essential.

Pam: we talk about the 21st-century, learning and teaching in the 21st-century and what you are explaining to me is it's getting the students to apply it because in the real world we are not going to have the numbers. We are going to have to analyze the numbers so, those are the things.

Suzie: and just to piggyback off of quickly , one of the students actually got a learning experience with PowerPoint and how to do histograms... the learning became infectious in the sense that the lesson actually taught me, he was on Excel spreadsheet and he is able to quickly make the histogram. So they went to.... they began to show each other how to work on Excel, how to make the histogram, how to paste and copy into their PowerPoint presentation. So it became more than a math experience, it was real, real world... I need to learn how to do this stuff. So, there was more than math, again it was centered around them Being able to deliver the final product as they would in the real world. Life skills.

Pam: and is that something that we fail to do a lot? Teach life skills? Is there anything you would like to add that would help make your life easier, something that you would like of anything... any other support.... what you would like to see done?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Learn more than mathematics

Communication skills

Life skills

 

 

 

 

 

 

Suzie: long pause… I think that in teaching AFDA... it is kind of hard to say this when we have such budgetary constraints... it’s not an extremely expensive class but it is more expensive than your average math class. Like, I know I have a lab coming up and, again, it is a direct variation in the next lab we are going to do and the students are going to have to measure the gas pressure release off of the denture cleansers or antacids. So you just have to be ready to find money and spend money. Like I am going to have to go out and buy a box of denture cleansers or antacids. Those things, the department has been really good about paying for, but it is just out of the air I need $30. So it is not like a regular math class, where you know you have your books and you have your paper, you are going to have to buy the chemicals or things just like a chemistry class per se. The budget has to be a little bit more flexible with an AFDA class. Just like the springs, I need new springs this year because the springs in the... the slinky springs in the science lab are too long. So sometimes finding the things you need can be a little taxing.

Pam: how long does it take you to plan a lesson? And when you talk about lessons, are you talking about one block or more than one block?

Suzie: ohhh, more than one block. I'm talking about everything that is focused around that one topic or maybe even just that particular lab per se. This one lab is dealing with just the fundamentals of a linear function, and direct variations and the next lab will not only applied those fundamentals again but, spiraling back, we are starting to use the TI’s and the regressions more and using the calculator with the applications. So, like just for an hour, they are going to four blocks just on each lab. Easy. Easy.

Pam: and the planning of those?

Suzie: and the planning of those [long pause] for that lab session... I have taught it before, but I want to say that the first time that I planned that, that it's about three hours worth of planning. Sitting down and really fleshing it out. And that is not even typing up the assessment. We're talking just setting up the order, the sequencing, the threading, how I would like for it to go, the difference from the variation in the teaching and delivery to leaving time for how I

 

 

 

 

 

 

 

 

 

 

 

 

 

Thinking units of study vs individual lessons

 

 

 

 

 

time

content knowledge necessary as well as pedagogical content knowledge

 

want to get the kids engaged and letting them direct part of the lesson from their experiences.

Pam: you also mentioned that you have to anticipate what they would do... that's probably part of that planning time to?

Suzie: it is, that is part of creating, and letting them have that freedom and creativity. And sometimes that will strain the time, because you hate to cut them off and you don't want to tease them in a sense of letting them go and then pulling them back and saying that time is up. Got to go. And sometimes that will take longer, like one of the things that the kids took a little bit longer to do student centered, again and they struggled with this one, is that they had to create a survey question, and within the survey question they had to explain if it is self selective, what bias they would have to what type of sampling they were going to do. So they had the basics of what self-selecting would be, cluster, stratified, simple random. But they had to look at their survey question and type it up given those guidelines. So, it took a little bit longer. For me it was important for them to create their own survey and analyze their own survey than to give them a quick survey that I might have from a book and let them use it and tell them that it was self-selecting or just quickly hit on it. It took a little longer. They had to really think about it and they just could not look at their neighbor’s paper, because their questions were different.

Pam: what about teacher content knowledge of those who teach it with a student centered approach?

Suzie: you have to have a real strong grasp [emphasized the word strong] of the content. More so than just a practice assessment. You know, it has really tested me. Like, your content is actually going to, your knowledge is going to have to actually spread. Your content in different areas... it's like for example when analyzing Hook’s law, that is why I can't use the real long spring. I will eventually use the extra long spring, but you start to learn in your own analysis that in applying a certain lab that the spring will only have a direct variation when given a certain length of the spring. So when I had the kids last year with this huge slinky spring going from the first floor to the second floor... the data was not linear. I did not understand and in front of the kids I was like... and what is wrong with this? And then you have to be able to go with it and

 

 

 

 

 

 

 

Took ownership in the mathematics – engaged

Problem solving

Self confidence

 

 

 

 

 

 

 

 

 

 

 

 

 

 

say, ahhh, that it is only direct given a certain domain. So then you feed in the domain and feed in the range and you look at the predictability beyond this domain or range and then you segment it, and you look at it piecewise, but you start learning a lot. I never knew Hook's law was like that. I never knew denture cleansers gave off gas that was supposedly at a standard rate of change, usually. And they also have to learn, the students, to do the lab correctly. They live the mathematics so, just for example, the denture cleanser... one of them takes the topper off of the beaker and the data in the graph takes a dip. And you as a teacher can, and now for a math teacher, have to be quick on my feet with my analysis to say... did you take your finger off or did you take the top off the beaker while it was still plugged in to the CBL or CBL2 while gathering the data? So your knowledge gets really stretched. You not only have to prepare mathematically but you have to be aware of the other factors: physics, chemistry, in case you're doing something chemistry-based or physics-based that surround the lab.

Pam: do you also have to be able to say I don't know?

Suzie: oh yeah. Like with the whole Hook's law. I can see that it was working out, but you question yourself. You're like all my gosh. It's like not right? I have to go figure this out. Yes, I don't know. You got me, what do you think because I don't know. And the kids are fine with that, because I think to that you have built a relationship and work with them in that relationship so it's almost like you are there on the discovery together. No, I'm leading the tour. You know, it's just sometimes we walk into different things that I'm not sure about. But I always tell them I will go find out and if I can’t find out on my own then I will find somebody who will let me know. And sure enough, just like with the Hook's law, I went to the physics teacher and he was like, oh yeah only given a certain length... you need slinkies of a certain length and I like said, oh, great. Thanks. Now I know.

Pam: we learn by our mistakes. Okay, is there anything else you would like to add about student centered teaching?

Suzie: I think it is the way that we have to go. I think it is the essential knowledge for them to be successful, they really need to be able to use this. They have to be able to retain it and they have to use it and also leave them with, with a... not being scared of it.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Tchr concern: lack of knowledge of other content areas.

 

Strong feelings – needed for students to be productive in the 21st century.

Because a lot of it too is in their mind set. How they approach it. If they approach it that I am scared, that I hate math, that I can't do math then and they are not even going to look in that direction. And unfortunately, they are going to realize quickly in life that they are going to need those skills. With the technology now everything is going to be at a touch, a button to push and those type of skills need to be fostered.

Pam: even our trades are using a lot of technology and they need to understand what it means.

Suzie: they do, and they don't have to know all the micro-details but they have to have a deep understanding and adaptivity of what is going on. I call it adaptive intelligence. I really do. AFDA fosters what I deem a necessary intelligence that needs to be evolved in kids, and taught and molded in kids That is the ability to adapt to the situation. You know, I teach them math, not so much of the consistency of math throughout the time... you know, a negative number times a negative number will be a positive number. But more so is to be able to have that and be able to use it correctly. To be able to adapt and grow. Almost like that lifelong learner type of adage.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix D

Mary’s interview October 30, 2009

Location:  Classroom

Pam: explained to Mary that she would be recorded in the tape would be destroyed at the end of the course her name would also be changed for confidentiality.

Pam: could you describe a student centered lesson that you have taught?

Mary: what I did today actually. I did stations to review for the benchmark. I'll give you the... we had six different stations, I paired them up. Pretty much what I did, I took the child with the highest nine weeks grade [and matched him or her] with the child with the lowest nine weeks grade. And I paired them up together and I wrote that down. And I told them that is who they had to work with today. I put all the desk in pairs, and then they went around to each station and they worked together. It was open book and open notes. They can ask me questions and I am going to count it as a quiz grade. It seemed to work pretty well considering the day that I had [Mary had been dealing with the incident of a student writing obscenities on a graphing calculator, which was dealt with at the beginning of the block]. Yeah, but that is one of the things that I do.

Uhmmm, what else do I do? Long pause... let's see, that's probably what I- if I do anything student centered I usually make it into a station thing so they are always doing something different.

Pam: Are there any activities that you do with the students?

Mary: Oh there is the airplane activity that I do in stats. That is all investigative and done on their own. I make paper airplanes so that they are all the same. I lay out a tape measures in the hallway and students file out and throw the paper airplane 20 times and record the distances of each throw. This is done in sets of two or three students. The students each have a task, one would be to throw the airplane, one is the recorder and one the retriever. We come back together as a class. We put the data altogether as well. This helps us get closer to the normal curve. From there, we discuss our

 

 

 

 

Mary doesn’t have a good understanding of SCL. Feels group work-stations is SCL.

Motivation is a grade.

 

 

 

 

 

 

 

 

 

 

This activity is just gathering data. The data is then used in a direct instruction class about normal curve and standard deviation.

SCL is viewed as looking up information in a textbook.

love the activity and enjoy gathering the data and then giving it meaning.

Uhmm. Usually after a test I will give them, like after test, a note sheet so that they can kind of find their way through the beginning stuff of the next unit that we are going to do. Uhmmm.

Pam: what about when you first started thinking about doing student centered lessons, how long ago has that been?

Mary: I would say, about three years ago.

Pam: how long have you been teaching?

Mary: this is my eighth year.

Pam: so three years ago, you begin thinking about teaching with a student centered approach. Why?

Mary: just because I had better students, they can handle it. I first did a lot of stuff with my stats, and now I see myself doing it more in algebra two. I want to do more... I want to do something like this in parts [algebra one part two] . But I do not feel like they are quite trained enough yet.

Pam: so what attracted you to wanting to do it?

Mary: something different. I get sick of talking. Uhmmm. They get more working with each other, get more out of it, they hear it explained different ways.

Pam: what is the process that you have used to develop more and become more student centered. Is there any certain thing in that you are trying to do in order to be more student centered?

Mary: long pause. Uhmmm. I feel like in my upper level math classes, especially that if they talk to each other that they get more out of it than me boring them into tears talking about things - like spending an hour lecturing. But I don't think that's what you're asking me or getting at.

Pam: I'm thinking about... you are thinking about creating a student centered lesson, you have decided that this is something that you wanted to try, what did you do? Is there any certain process or activities that you went through?

 

 

 

 

 

 

 

 

Feels that “betters students” are the only students that can handle SCL.

 

 

 

 

 

 

Student interaction is important – math talk.

 

 

 

 

 

 

 

Mary: I think it has to be something that I know that they can handle. I certainly would not have them, like for example in algebra two, I would not have them factor, factor like a, you know, a five term polynomial on their own. There are some things that I just, I guess the checklist that I go through in my head is 1) can they handle it, 2) how many questions will I give them based on me doing this in the past, 3) it is something that I think that they can do, they will get quickly so then I could go and do it, And  4) make it more them - more of them teaching themselves and each other how to do it.

Pam: how do you come up with the ideas?

Mary: I wish I could say that I just sit down and do... a lot of things just kind of come to me, like I will be sitting and looking at it, looking at stuff I did last year and say well, let me try this and it sometimes works and sometimes it doesn't…. I have to say that the times I have tried to do it that it has worked pretty well.

Pam: have you used any specific resources?

Mary: usually what I do is I'll just use different, like for algebra one. I'll just take a bunch of algebra one books just to get questions so I will not have to make them up, make up a bunch of stuff. I definitely use a ton of different stats

resources, because coming up with those questions is just a pain. Out of the blue, like the thing I did today in algebra two, I completely made that up on my own.

Pam: sometimes it is hard to come up with new ideas or how to put the big ideas together. When you plan a lesson, could you explain what goes into planning, a student centered lesson?

Mary: well, I start with what I want them to get out of it. And then try to set it up to where I know that they will hopefully get that out of it...uhmmmm, like today I wanted them to be experts on those six things that I have at the front of my room. So I came up with, using the benchmark blueprint, I took it thing by thing and said that they need to do this. So then they need to see this type of question. They need to do that. So they need to see this type of question.

 

 

SCL is based on number of questions, students being able to do the work quickly, and teach themselves.

 

 

 

Again focus is on questions – not creativity, investigation, owning the problem

 

 

 

 

 

 

 

Preparing for benchmark assessments – Mary sees SCL as questions for each type of item listed on the benchmark blueprint.

 

 

Pam: do you... a lot of people have talked about collaboration... how is collaboration going?

Mary: good with some and not good with others. I find myself planning with people I think, I think the same with. And I definitely, with stats, do it by myself, with parts I'm doing it by myself. But I am, I do talk with two of the double block teachers a lot, because I am pretty much doing the same thing that they are doing. It's just that I have half the time to do it. But for algebra two. I do collaborate with one other advanced teacher and a couple of the regular.

Pam: what about time involved?

Mary: we usually meet, we meet once a week just to be like, okay, this is what we are doing, where are you, that kind of thing….. But we, as far as actually putting stuff together, I find myself doing that a lot outside of school.

Pam: you take a lot of time to plan. How does that affect the students? if you are doing a student centered lesson. How does that affect the students when you do all the planning up front, the work, how does that affect the students when they come into the classroom?

Mary: I try to have it, I mean, I try to have it so that they are not going to struggle with it because you know, when they are kind of taking the lead and I am being the facilitator... you have to try to make them successful and if you give them something that is so complicated and not put into simple language they are just going to flip out. So, that is why I always try what I do give them something that I know that they will look at it and then wonder what in the world is that woman talking about.

Pam: you mentioned your role as a facilitator. How do the kids accept that instead of you being the giver of all knowledge?

Mary: they like it. It is different. You know, I had a bunch today say, wow, class went really fast today. I mean, because they can normally handle doing work, working together, and today I purposely put them with people they do not normally work with. And so I told them that I needed to hear math talk not what they are going to do over the weekend kind of stuff. It worked well.

 

 

Never gave an amount of time to develop a SCL. Time mentioned is required by administration for same subject teachers to collaborate.

 

 

 

 

 

 

 

SCL in Mary’s view should be simple so all students may be successful and not struggle.

 

 

 

 

Class went fast due to students working in groups and moving about the rooms to different stations. L

Pam: you match the lower level with the higher level students, so how does a student centered lesson work better with, better with the higher, better with the lower.

Mary: uhmmmm. I know it works with the higher because I have done it with the higher and like I said with my part twos, I do want to do it. I just, number one. I don't have the time to figure out anything as it is my first year teaching it. And number two, I don't quite trust them to do the right thing. Because I think they will think of it as social time, a more than working-class time. They might surprise me about, you know they can't work really well together some days. I just don't put them together. I'm not at that point yet.

Pam: what about positive outcomes for you personally and teaching a student centered lesson?

Mary: I mean, I thought, you know all the students walking out of here today, I thought that they... I thought they felt good about the benchmark. A lot of them were saying, oh, that’s it? That's all it is? Well, I feel good about this. So, I mean, that's the kind of stuff that I am looking for. And it was good because they have someone to bounce ideas off of and you know if I'm helping somebody then they can ask questions, and they were even working, like to groups, two pairs... if they had a question they would ask each other which I was fine with. So there, I mean they were feeling pretty good about the material.

Pam: what about you professionally. How do you think teaching a student centered lesson has affected you professionally?

Mary: I think it makes them responsible. You know, I don't have to burden that complete responsibility that they have to learn or not, because it is ultimately up to them to be successful or to fail the class. Something else I did this morning that I haven't done is that I made them come up with a nine weeks resolution. And I said okay, this is soul searching time... what could you do better in this class. And a bunch of them put some things down and this one kid, the other day, said I am going to do all of my homework. Well today he did not have his homework assignment. So I said where is your resolution and I had him go up and get it. And he said I'm going to do most of my homework and I said no, You are going to change

 

 

 

As I reflect, it is difficult to remain objective. Students that are just going to stations to work more problems and not striving to problem solve will resort to socializing.

 

Students were graded on the problems completed-material already taught through direct instruction.

Attitude is positive for group work

 

 

 

Resolution has nothing to do with student centered learning. She later states that she still likes to have control of the class. This is evident in the demand for the student to change his resolution.

your resolution to I'm going to turn in all of my homework or Mrs. xxxxx is going to kill me. And he changed it to that, it is up on there [resolutions are posted on her walls].

Pam: so you can hold him to it now. Sometimes putting it in writing makes a world of difference, doesn't it.

Mary: Uh huh. [agreement]. We'll see how it goes.

Pam: as far student centered lessons do you think it affects you as far as, you do really well with your benchmarks and SOL scores, but do you think it affects you in any way getting through the material or the discourse?

Mary: I think both. You know, it's a real pain in the butt to take class time to review for a benchmark, which has its purpose, but ultimately it is not the SOL test. You know, and I really haven't taken a lot of time to review for them in the past. I discuss, what is on them, but I mean, it's what stuck and what didn't stick and then we go from there. Uhmmm me taking the time to review, I mean, it's a great refresher but, I don't know, I feel like there are bigger fish to fry than just reviewing for the next test, the next benchmark, SOL test.

Pam: so you do not think that teaching a student centered lesson will affect the outcome of an assessment?

Mary: no. I mean, ultimately it, I mean right now it's just like teaching them how to do it right. But at SOL time I do show them the tricks to get a good score. Because you know, that is what they want, but you know, right now. I didn't show them how to do hardly, I mean, this is how you do it and you are going to do it on this test.

Pam: and it's like you said, the benchmark is a very small portion of the SOL. And it is not the bigger picture for everything.

Mary: it is just a snapshot. I mean, that is really all it is.

Pam: do students feel like there is a positive outcomes do you think?

Mary: I mean, I think they feel better about the material. You know, because they hear it explained in different ways. It builds

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

She needs to “…teach them how to do it right.”

 

 

 

For material being reviewed, students are able to explain how they would solve the equation using their own words thereby building confidence.

confidence. I think it definitely builds confidence. I mean, it's like I said they definitely felt really good coming out of here today.

Pam: but it is definitely a good feeling when they walk out making this type of comments. What about concerns and frustrations for you personally?

Mary: uhmmm. It is a lot of work but it is worth it if you do it right. It takes a ton of time to do it, but, I mean, it is worth it. If I do it right then it is worth it. Because, you know, I have had times where if I had done this, I did something like this last year, and I had them check their answers with me, like giving them a second chance - something like the gap activity and you know I just, you know,

to do that, it would've taken so much more time for them to get their answers checked and to do this and do that I was just not going to do and take all the time for a benchmark. Like, if it was the SOL, the ultimate exam, then definitely I would have taken the time to do it, but not for a benchmark test.

Pam: and I don't think that's what the intentions of it was either. What about... is there any concerns about doing student centered lessons or doing more student centered lessons professionally?

Mary: like for professional development kind of thing?

Pam: well, it could be that or what is your outlook on how you picture yourself going in the future?

Mary: I mean, I think I think it would be great to have... I definitely see myself doing more and more of this….uhmmmm… could I see myself teaching every single lesson  I do this way? No way. Because there is just, I don't know so many important things that they have to have a good foundation on that if they don't get it because, you know, because they didn't work at or it didn't take it seriously. Then, they are just kind of opening themselves up to, you know, being bad and it snowballing. Like factoring, all the different functions that we do, I mean they have to know how to do that. And I have to teach them how to do that. So I guess it is kind of a control issue or ahh... my being anal...

 

 

 

 

 

Time to do SCL is not productive usage. Mary can use stations and review for benchmark and only take one day.

 

 

 

 

 

 

 

 

 

Mary does not see the benefits of SCL. A “good foundation” can only be obtained when instruction is given through direct instruction.

Needs to feel that she is in control of the students and what they do in order to be productive.

Pam: research says that you need a little bit of everything. And we do have different students so it’s just like we are different people too. On your changes, how have, you've done some student centered learning... when you first started. What made you want to start? Was there an individual? Was it your department? Was it a goal to school? Or anything like that?

Mary: I don't really remember if it was or not a goal of the school, I could not tell you. But I needed, I mean, I wanted to just, I wanted to do something different. And I thought this would be a good different thing to do, because it puts the responsibility on the students. And I don't, they don't fall asleep on me like when I am lecturing or just doing a practice sheet. Like, it gets them up, it gets them moving. You know, I dictate how I want it done and then they go from there.

Pam: so student centered learning is not just a free-for-all? That is good to bring out. You do a lot of planning to make sure it goes well.

Mary: no. Oh heck no (being sarcastic).

Pam: if you have any wishes or desires as students walk into your classroom, what would they be? This would be at the very beginning of the year.

Mary: I can teach, for my advanced algebra two, I can teach them the algebra two that they will need to get into math analysis and do well, if they let me do it. If they work. If they have the work ethic. I know I can teach them and they can be very good. If they don't do what I asked them to do, well, then they flounder. In my part 2, I feel like well considering the person that was teaching it last year, I feel like I am doing, like I am teaching an algebra one course, and I wish that I could have the assumption that they knew and remembered everything. But I quickly learned that they don't remember a lot of things. But I know that's from a multitude of reasons. But, it is the same thing... if they come to school, if they put any kind of effort into it. Then they will do well. With my AP stats, you know, I, I feel less obliged, even though I do cover everything on the AP exam. I feel less obliged that, you know, I just kind of feel like their chances are to take it again since it is so hard to get a good score on the exam. So if I just teach a good

 

 

When doing “SCL” she is very controlling on how and what the students must do. Instruction is given and then it is the student’s responsibility to do it.

 

 

 

 

 

 

 

Blame – it is the students fault if they don’t do everything she requires.

Student lack of knowledge blamed on teacher they had last year.

 

 

 

 

 

statistics course I know that is going to serve them better than just trying to get them to pass that test.

Pam: in stats, you have done a lot more student centered lessons in stats, do they do well with them? Why?

Mary: I think a lot of it, yeah, has to do with maturity. It has, because it is the seniors and it's the good seniors and the AP calculus teacher here trains them really well. You know, so I am just kind of building on what she does and I do a lot of the same things she does. And, you know, I just tell them on day one that I want to give them time to practice in class, time to -- I just put all of the homework answers up on the board and have them check their answers and have them talk things out. You know, because statistics is a lot of thinking, a lot of analyzing. And I said, if you cannot come up with all of that all by yourself -- you have to have someone to bounce ideas off of. And some of them do real well and some of them don't. And you know, I think with a lot of them that has to do with maturity. As we know some 17-year-olds are more mature than other 17-year-olds.

Pam: so when students leave you at the end of the year, what kind characteristics do you want them to go out with?

Mary: uhmmmm. I want them, you know, I want them to be confident. That they know what they are doing. I actually had a couple of advanced algebra two students from last year came up to me and they were with a couple of students that I have this year. I asked them how math analysis was going? And they said it was so easy. You taught us everything and you knew, you knew that we were going to do this again. And I asked them, I said okay. Last year, when I was saying that, it didn't compute and that you did it again this year. And they went… yeah. And I said, well, and you know, I'm actually going to have a couple of math analysis students, who I had in algebra two last year, I am going to have them talk to my classes about factoring. Because there not, they're not quite getting it till the beginning of this year. And now they're like, I know how to factor because, because I am like, doesn't it come up with everything. Yes. Then, I know I have done my job.

 

 

 

 

 

Stats students are given time in class to discuss problems – feels that this is SCL.

 

 

 

 

 

 

 

 

Having past students share with her class this year that if they do what she says then they will do well next year in math analysis.

 

 

 

 

 

 

Pam: it must be good feeling to, to have them come back and have that confidence that you have left them with last year. Technology. What kind of role in a student centered classroom does technology play? Does it play big role -- what is its’ place?

Mary: I think it depends on what you're doing. I mean, the calculator just does so many things, and it is very tempting to show them a lot of the tricks. But I mean, I hope I don't do a lot of that. Like, I'll show them how, how to check their answers with a lot of things like using graphing and tables and that kind of thing. Because, I think, you know that it boils down to confidence. If they put it in the calculator and they see they have the right answer then they know that they know what they are doing. I don't, you know, I don't teach a class for them to know how to push buttons.

Pam: that would be counterproductive to what you're doing in a student centered classroom and you are comfortable doing technology? Is there anything that, in your department, in your administration or central office that would help you to be more student centered? When you need to be when it is appropriate? Now I'm talking student centered, is there anything that you could use that would be helpful?

Mary: I mean, it would be, I mean, it would obviously be ideal to have, the common planning is nice. But of course we do not have all of the algebra two teachers to plan together, because algebra one and geometry are the focus. So I have always kind of thought that algebra two is the redheaded stepchild. You know, if you teach both then you are usually lumped with either algebra one or geometry, and not lumped with algebra two. But, I mean, teaching algebra two I have realized how important it is, like, it is kind of the make or break course -- that if you do not have a good grasp of algebra two and all of the things that we do in algebra two then you’re just, you are preparing for just one huge headache in the future. And I don't think everyone really realizes that. You know, because the people who do take algebra two are supposed to be smart enough to handle it. But that is not always the case either.

Pam: what about content knowledge of teachers, and I am talking about people you know that teach mathematics, and it does not have to be just algebra two... do you believe knowledge of content affects student centered learning?

 

 

 

Calculator usage builds confidence – used to check answers.

 

 

 

 

 

 

 

 

Course she teaches is not important therefore common planning is not scheduled by administration.

 

 

 

 

 

 

 

Mary: oh yeah. If you don't feel comfortable with it, then you're not going to go out on, you know, go out on a whim and do student centered lessons. Your, you know, you're going to feel very, I don't know, I just feel that you're going to want to control things a lot more and you are going to do just what you feel comfortable with. But if you are okay with them kind of having to go at it and you see that they do it differently. And you are okay with the way that they did it... if you do not feel comfortable with it, then,  you're going to think that you did wrong even when they have a perfectly good way of doing something.

Pam: so you probably think the content has something to do with student centered learning. I know that some of your peers are very traditional. Is there something else that might affect an individual in their attempts to want to try student centered learning?

Mary: I think some of it is because of personality and I think it is kind of how you have been trained to do things too, I mean, if you, you know, you've had a cooperating teacher when you student taught that did think out-of-the-box then you are more willing to do it. But, you know, when you have been teaching something long enough and feel comfortable with the material, I kind of think you are doing the students a disservice if you don't give them another way of looking at things.

Pam: now we have talked in the past about teaching objectives versus big ideas, units. Do you think back that it has any effect on teaching student centered?

Mary: definitely.

Pam: so how can we encourage that?

Mary: I mean, I think, I don't want to say that you have to force people to do it. But sometimes you do need to force people to do it. And you need people, you need people to sit down and give examples. And maybe that's the biggest thing. If you want to do something student centered. It would be great if you found something that you could kind of tweak and make it your own. I don't think, I know, I can't find that all the time. So I feel like I'm kind of thinking on my own, and it is kind of hard when you have people who just stand at the black board and do their thing every

Need to be comfortable with the content in order to do SCL. Knowledge and confidence equates the ability to step back and let students do the work.

 

 

 

 

Personality and pre-service education will determine if a teacher is willing to try SCL.

Some thoughts are in line with SC teaching – think out of the box, give students another way to do something.

 

 

 

For those unwilling to try Mary feels that they need to be forced.

Also feels that examples need to be given with the ability for the teacher to adapt to fit their “personality”.

day. You know, to bounce ideas off of, I think, I do think those people do want to do it, they just don't know how. And then I am the one who is expected to do it for them. And I'm not going to do that.

Pam: my concern is, how can we encourage, sometimes being uncomfortable...

Mary: you can lead a horse to water but you cannot make him drink.

Pam: right, and being uncomfortable sometimes will help someone to step on over and to try something new?

Mary: and I think you're in the perfect position, where if someone is uncomfortable that I know that you are there to help and that you will, you're there to bounce ideas off of. But I also know that some people are intimidated by the position that you have, you know or personality conflict or whatever and they are not going to take advantage of the resources like other people that have.

Pam: is there anything else that you can think of that will be a concern or something that you would wish to have or be able to do?

Mary: I mean, I think that professional development that we have had, it was really nice that even though it was under this topic that we could kind of make it our own and I know that ours was a special case and we have necessarily had that flexibility. So that was really nice. I kind of wish that professional development, and I know that we have to jump through certain hoops, but it would be really nice if we could kind of do our own thing. And I know that we can't because not everybody, you know, does what they say they are going to do. So I understand the rules that we have. But it would be nice to kind of say that at our school in our department this is what we need and let us do, let us become better.

Pam: what about peer observations? Do you do peer observations here and do you think that they would help in any way to see what the others are doing and then later to sit down and actually talk about it?

 

Teachers do not know how to teach a SCL.

 

 

 

 

 

 

Acknowledges that help is available for those who do want to try.

Teachers do not take advantage of resources available.

 

 

 

 

 

 

 

 

 

 

 

 

Mary: yeah, I think it would be a great idea. Uhmmm. You know, but you know, I don't know how open a lot of people will be. Me, personally, I could care less who comes in here, because I am doing my job. But if you feel like or are not comfortable with what you're doing or feel you're not doing what the higher ups are expecting you to do. Then they might take that as you're trying to single them out, whatever, whatever.

Pam: if administration walks in and you were doing a student centered lesson would they have any remarks or would you have any feelings about what they are perceiving?

Mary: I think, no, I think it would be fine. You know, they would walk in and see me, you know, everyone is working together, everyone is learning, everyone is having a good time and that is what he would tell me. I feel like that is what he expects us to be doing. And he really doesn't mess with us a lot because he knows that is what a lot of us do.

Pam: so you're administration is very supportive of students being involved in the lesson and not just sitting in rows with their hands folded?

Mary: oh yeah

Pam:  is that one of the concerns -- administration and what they are perceiving is going on when they walk into a classroom? It may seem like chaos, however, it is structured chaos .

Mary: I would find it very hard for an administrator at our school to not tell the difference. And I know the administration here can tell the difference.

 

 

 

 

 

 

 

Peer observations “would be a great idea”. But feels that teachers who do well will feel comfortable being observed and those who are not comfortable will feel threatened.

Administration – Mary feels they are supportive and understand SCL.  

 

 

 

 

Mary seemed very defensive about the support of the administration. They don’t “mess with us a lot…” so she is not going to be negative.

 

 

 

 

 

 

 

Appendix E

Mark Memo

Mark’s beliefs are very strong that SCL is the way to go and the way that students will retain the material. But, interestingly, when asked to describe a SCL he hesitated and then described a lesson he had taught over a year ago. Began teaching using SCLesson when he became bored.

Mark felt that thinking about the topic, “ponder”, what you need to do.

Collaboration is a theme that runs through the entire interview. Given the time to collaborate, even though we might do that in different ways, it appears to be what is needed to grow in SCL.  Discusses that teachers need the content and also to see and experience SCL in order to understand the what and how. So peer observations and/or promoting SC teachers as lead teachers and a process that would enable them to observe and collaborate with teachers already doing SCL.

Other ideas/themes are: knowing your students – “where they are all in the material”, developing concepts, making connections, big ideas, content knowledge,

Mark described “lesson study” and said that it would be good for all teachers in their professional development.

In addition to the collaboration it came out that teachers need to understand the content, the conceptual understanding behind what they teach – pedagogical content knowledge.

Students would rather not do the work so they won’t fail.  Math is a life skill.

As the department head his approach to changing or encouraging change is in the planning. Refers to unit plans he implemented last year to help encourage the teachers to find the big idea. Trying to force the teachers into more SCL vs direct instruction but also states that most of them teach using a DI approach. He goes through the process of how most teachers instruct but ends with speaking about closure. Administrators like to see the “process” in mathematics and it tends to be traditional approach that they are looking for. Mark’s comments about closure was that he wasn’t a fan but in the end acknowledges that he has closure but not the traditional type of closure - likes students’ to continue thinking about what they were learning.

So this goes back to admin expectations. Education is needed to assist administrators in knowing what they need to be looking for when they walk into a SC classroom. This would also help teachers to feel more comfortable in their attempts to teach in different ways, sharing their ideas with others, and having the administration understand when benchmark scores are not where they need to be. Admin would be more supportive of their efforts and their feedback more useful if they understood SCL.

This lead to the discussion on changing the curriculum maps to meet the needs of teachers who teach SCL.

Teachers need to decide whether it is the skills that needs to be taught vs the concept. This goes back to the teachers beliefs and teachers will provide instruction with what they feel is important. Teachers will need to meet all student needs with AYP and SCL enables teachers to differentiate instruction – again teachers need to know their students.

Also discusses that when things go wrong, including scores on benchmarks and SOL, teachers will blame what they are least comfortable doing – SCL.  He does not feel that these assessments should drive instruction. Goes back to the teacher’s self confidence, what they feel is important to be learned.

Student concerns and frustrations – Mark placed that back on the teacher. If the teacher knows their students then they would know and plan accordingly to stretch their learning but not frustrate them.

Mark would like students to be better problem solvers – therefore that would mean that it needs to be encouraged or maintained throughout a student’s education.  Referred to MS now implementing explorations and is hoping that students will come in the future with the ability and willingness to think.

 

QUOTES

“I think the key is engagement and whether the kids are actually interested and motivated by what they are doing as opposed to being interested and motivated because the teacher told them this what they are dong and they will be getting a grade on it.” (6)

“All of those external motivators are great but they’re not really promoting learning and retention.”

“If they [administrators] are looking for objectives and rationale being clearly stated ahead of time and this is what we’re doing and this is how we are going to get there……that is not really student centered learning. At the same time, if they’re looking for engagement, looking for focus, listening for math talk..if they are listening to ‘are they really getting it’..That is the kind of stuff that does promote the kind of learning and the kind of teaching we are talking about.” (10)

“It is hard to promote something that you do not understand.” (10)  Referring to admin not understanding mathematical concepts or the SCL methodology.

“It’s kind of like a puzzle. Most people do not start a puzzle without looking at the big picture on the front of the box first, and wanting to be able to see that.” (10)

Appendix F

Suzie’s Memo

Suzie focuses more on practical applications and adaptive intelligences.

Teachers need to feel free to be creative in how they develop units of study. Talks a lot about getting the students to have ownership in the mathematics and for the teacher to be able to adapt their instruction and lesson to encourage the students.  Tries to begin every unit of study with a practical application that can be used throughout the unit for relevancy.

Teachers need to learn to give up control.

Materials hard to find and timely to create. Felt that teachers, given the appropriate materials and support, would be more willing to try SCL.

Speaks about the personality of the teacher as being inquisitive, having a desire to know more mathematics and the application of the mathematics. Some additional teacher characteristics include: patience, “owness” of the mathematics,

SCLessons change the classroom.  It becomes a “learning environment”, less discipline problems as students are engaged, student attitudes are more positive, more like a science lab, a lot of group work, creativity and “controlled chaos”, trust, relationship built between students and teacher.

SC Teaching evolves over time and it takes time for the students to adapt. SC teaching is very different from what the students have experienced in their past mathematics classes. Suzie mentions that she can’t count on past knowledge as it was taught ”very rigid”—procedurally with no meaning. By teaching and providing relevancy students see mathematics in a completely different way. She talks about the x- and y- axis now having meaning and the students being able to discuss the domain and range within the given scenario.

Suzie suggested that peer observations may help those who are not student-centered to see how such a lesson is conducted. 

Fear and blame – teachers fear that students will not do well on assessments when they are taught in a different format. Fear that there will be repercussions from administrators as well as peer pressure. Fear of losing their jobs or being put on an improvement plan. Fear that students will not be able to transfer their knowledge to abstract, meaningless problems.  

She felt the above fears even though she also stated that the administration was supportive.

Content – plans using units of study. “You have to have a strong grasp of the content.” Takes more time however students are exposed to connections to past concepts and linking to future concepts. Retention of material is better since the students build and own the concepts. Teachers need to understand how to make the connections between the concepts (pedagogical content knowledge) and make them relevant to the students. Needs to be a restructuring of the curriculum maps so that the content can be covered within a quarter.

Concerned with student attitudes upon entering the class at the beginning of the year. Poor self esteem and lack of motivation. Sees the difference after the students have been involved and part of the class for a while.  Suzie has a desire for students to have an appreciation for mathematics and to see its relevancy in their lives.   Discusses math as being a “life skill”.

Journey to where she is now: Suzie was bored with how she was teaching and saw the boredom on the students faces. When she taught her first lesson in this manner she recognized that the students were seeing mathematics in a new and different perspective but also that they were engaged, more willing to learn concepts that they needed to know.

QUOTES:

“They know the math now as far as practically using it and it becomes exciting….”

“They live the mathematics…”

“…built a relationship and work with them [students] in that relationship so it’s almost like you are there on the discovery together. … I’m leading the tour.”

“I think it is the way that we have to go. I think it is the essential knowledge for them to be successful, they really need to be able to use this.”

“They don’t have to know all the micro-details but they have to have a deep understanding and adaptivity of what is going on.”

 

 

 

 

 

 

 

 

 

Appendix G

Mary’s Memo

Mary is not clear on what a student centered lesson is or how to prepare for it. She speaks about stations and group work as SCL. Instead of using the “SCL” as the motivator she states that they are graded.

She spoke about one investigative lesson but all the students did was to gather data. After the groups threw the airplane they came back into the classroom and combined their data to lead into a teacher led discussion and procedural lesson on normal curve and standard deviation.

Repeatedly speaks about planning a SCL as a way to ask a lot of questions. Mary’s main discussion is about reviewing for the benchmark using stations which includes a number of questions at several different stations. Also mentions that after an assessment she gives a handout for the students to “investigate” concepts in the textbook for the next unit of study. Four steps or thoughts are used to guide her planning: if they can handle it, the number of questions to give, something they can do quickly and they can teach themselves. Does not want the students to struggle with the material. Looks at herself during the station/group work as a facilitator. They teach themselves but it is more important that they can do it independently. Likes to plan with those who think like she does. Feels that Algebra II is the “redheaded stepchild” and not given the ranking/importance like Algebra I and Geometry. Does most of her planning on her own time at home. 

States that SCL “takes a ton of time” (5). She is referring to planning and implementing. Doesn’t feel that the time it takes to do activities is worth it all the time. At the end of the interview she states that she sees herself doing more and not planning all her lessons in this manner or even a majority of them.

Mary feels that SCL is only for the “better students”. Her lower level courses are not given stations and group work as Mary still wants control and feels that the students would abuse the time used for the activity – “I don’t quite trust them.” (4)

Mary’s talks about during SCL that students hear material explained in different ways and that it builds confidence. She wants to do SCL because it is something different, putting the responsibility on the student to complete the work. Mary states that “I dictate how I want it done” and then it is up to the students. Is even planning on having a couple of students from last year come and talk with her current students to tell them that they need to do what she says.

Control is mentioned a few times. Mary speaks about teachers that know their content are more likely to lessen their control and let the students do SCL activities but then goes on to say that she is the one who needs to be the giver of the information in order for the students “to have a good foundation. “(6) If the students do what she says then they will learn the material and if they don’t then they will struggle.

Blames past teachers for student weaknesses and the student themselves because they don’t do everything she demands.

A teacher’s personality and pre-service education is a factor in them trying SCL. Feels that some people need to be forced to do SC lessons.

To help teachers with SCL she suggested giving them examples and letting them adapt it to fit their needs. Feels that many teachers do not know to plan and implement SCL. Discusses professional development and feels that their high school should be able to create and do their own.  Acknowledges that help is available for those who will accept it.

My thoughts: Mary is not using the term SCL correctly. As stated previously she feels that stations and group work is SCL. She also contradicts herself stating that if one has content knowledge then they are more likely to do SCL and lesson their control over the classroom and proceeds to state that she needs to be the giver of knowledge so that the students will learn what is needed to be successful.

Very confident and may be over confident and feels that she is the one that knows about SCL. States that she only wants to plan with those that think like she does.  Later asked who she planned with and found that there is one other teacher – a new teacher who probably is following her lead. Mary appears to be knower of all things and is quite abrupt in her statements – quick to acknowledge to me how good a teacher she is. Peer observations seemed like a good idea for her as she feels that she does her job so therefore she is not threatened but states that others may feel threatened when being observed.

Administration is supportive of their [math department] efforts so leaves them alone. This brings me to thinking about what the administration knows about SCL and what to look for when doing observations. Be able to provide feedback that would entail students being engaged in the material but with a different definition of engagement than Mary is using. Engagement that includes math talk and discussions that might have multiple answers and methods to find an answer. Thinking about the what, why, and how that the mathematics is relevant to their lives.

In general, Mary’s interview was a complete opposite of Mark’s and Suzie’s. Mark and Suzie truly know what SCL is and Mary is off in another land. Mary has taught SCLessons or at least begins with the right intentions but then her own control issues override the activity.

Giving teachers lessons/activities without being or going through them is fruitless. They would not understand why one needs to do certain parts of the lesson and what the goal is for the students without going through it and experiencing it themselves or at least having a discussion regarding the deeper understanding for each aspect of the activity.

QUOTES:

“You have to try to make them [students] successful and if you give them something that is so complicated and not put into simple language they are just going to flip out.” (3)

“…teaching them how to do it right.”  “…this is how you do it and you are going to do it on the test.” (5)

“If you don’t feel comfortable with it [content], then you’re not going to go out on a whim and do student-centered lessons. …I just feel that you’re going to want to control things a lot more…” (8)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix H

Matrix Coding

 

Mark

Suzie

Mary

Teacher Characteristics & why SCL

Bored

Inquisitive

Patience

Personality

Enjoyable

Better learning environment

Creativity

Help other

Evolving process

Self-confidence

Do something different

Bored

Personality

Sick of talking

SCL Definition

Teacher as facilitator

 

 

 

 

Discovery

Math talk

Leading the tour

 

 

 

 

Discovery

Hands-on

Scenarios

Presentations

Science lab

Teacher as facilitator

Students lead

Students collaborate

Students teach themselves

Stations

Experts

Investigation

Issues/Concerns

Resources

 

Control

 

Classroom Management

Time

Assessments

   Not compatible

Resources

 

Control

Controlled chaos

Discipline

 

Time

Assessments

   Disconnect

Cost

Resources

    Book for questions

Control

 

 

 

Time

 

 

A lot of work

Professional Development

Professional                  

                   development

learn to develop SCL

Tangible examples

 Don’t understand SCL

Lack of other subject

                                 areas

 

 

 

 

 

 

 

 

Curriculum maps

                           redone

pacing

Pre-service education

Knowledge

   Teacher

 

 

 

 

 

 

 

 

 

   Student

 

Pedagogical content 

                  Knowledge

 

 

Content knowledge

Meaning to the math

 

Move with the stds.

------------------------------

 

Pedagogical content 

                  Knowledge

   Conceptual

               Understanding

Content knowledge

Deeper meaning

Connections

Self-confidence

-------------------------------

 

Can’t depend on prior

                     knowledge

taught math

         procedurally (rigid)

does not know

                       practicality

do not lack intelligence

adaptive intelligence

 

 

 

 

 

Comfortable with

                          Content

 

Self-confidence

-----------------------------

Planning

Planning

   Unit plans

Problem solving skills

Skills

Centered on students

Know your students

Challenge

 

 

Big ideas

Responsibility

Applications

 

Individuality

 

 

Problem solving

Reasoning

Student interests

Relationship

Sense making

Relevance

Insight

Big ideas

Responsibility

Practical applications

   Open up lesson

Planning

Sit down and do it

 

 

 

 

 

 

 

 

Responsibility on stds.

 

 

Plan individually 

Checklist

Type of questions

Fear/Blame

Blame

Failure

Teacher Evaluation

Good teaching

Get called down

Frustration

Fear

threatened

Administration/Support

Administration

   Guidance

   Expectations

   Encouragement

Teacher support

   practice

Administrative support

   Freedom

   Flexibility

   Trust and support

Administration

Central office

Student Benefits

Develop concepts

Promote continual

                            learning

Engagement

Self-confidence

 

Retention

Freedom

Life skill

Kids now know math

Live the mathematics

Engagement

Student disposition

   Attitudes

Retention

Ownership

 Student motivation

 

Students more involved

Students success

 

Students feel good

 

Retention

Make it their own

Gets them moving 

Collaboration/ Observations

Collaboration

Collaborative learning

   Dialogue

Sell SCL concept

Success

Collaboration

   Bounce ideas

 

 

 

Peer observations

Collaboration

   Common planning

   With like minded  

                     People

 

Peer observation

Opposing Views

 

 

Teacher control for max

                                 learning

   Good foundation – 

                           teacher led

   You taught us

   If they let me do it

Works with higher levels

   Higher ability students

   Don’t trust lower levels

   Better student

Get material quickly

Students with motivation

Maturity

Up to student to be successful

Std disservice if not

        shown alternative   

        methods

does not envision teaching

   using SCL a lot