Memo for Assignment #3

I have three basic areas of interest: How do teacher’s beliefs of student-centered learning (SCL) and the function approach to teaching algebra (FATA) change? How do teachers see, from their viewpoint, the effects of SCL and FATA on student attitudes toward learning mathematics? and How does a change in teacher beliefs to SCL and FATA effect student achievement? As stated in previous memos/assignments, I have an interest in the function approach to teaching algebra courses due to my work with the new mathematics course, Algebra, Functions, and Data Analysis (AFDA). The vision of the course is for it to be student-centered, based on real-world situations and with students understanding conceptually the topics being addressed. National Council of Teachers of Mathematics (NCTM) published a document revealing the Process Standards: communication, collaboration, representation, problem solving, and reasoning and logic. The representation standard has been elaborated by several to include graphs, tables, symbols, concrete, and communication. Again, a focus and correlation with the NCTM Standards.

A grant from the Math and Science Project (MSP) through the University of Virginia is offering a professional development to teachers for the summer and school year 2010-2011 based on the function approach to teaching the algebra courses. As an extension of the course and to include more teachers our school district is also offering a similar professional development. The grant participants will meet for four days face to face during the summer and then monthly online sessions throughout the school however the school district sessions will only be two days during the summer and quarterly meetings with Algebra I and Algebra II teachers separately, all face to face. Follow up meetings will include additional modeling but also time for the teachers to plan out the following quarter.

Prior to any of the professional development sessions beginning teachers will be asked to complete a belief survey based on student-centered learning which will have the function approach concepts inbedded in the questions. The belief survey will be repeated at the end of the professional development, around December, to determine if there has been any change in the beliefs of the teachers involved. During the school division professional development a unit of study will be presented for first quarter concepts with several lessons modeled. Lessons from an additional unit for each of the following quarters will also be discussed and modeled. These units of study will be created so that teachers will have some guidance and examples on how to create additional units.

I would like to select 4 teachers with varying ranges of beliefs, from very traditional to constructivist, to interview. The interviews would be conducted after a specified unit of study is completed and assessed. Data from the pre- and post-test for the chosen unit will be gathered without identifying information other than numbering of the test so I can see and compare student number 1 pre- and post-test results. Additional data will be their Math 8 end of course grade and the Math 8 SOL score. Again student identification numbers will be used to correlate end of course grade with the SOL grade. Our data mining department may be able to correlate those on a print out without identification numbers – checking on that since I cannot observe students or have access to identifiable data I would like to see if the unit of study correlates with their past performances in mathematics. Some of the interview questions might be:

o In your own words define student-centered learning and how that looks in a classroom?

o What goes in to planning a SCLesson that is based on the FATA?

o Select a student that is having difficulty in your class and discuss how they participated in and reacted to the unit of study? Compare their performance with prior lessons.

o Select a study that did very well in your class and discuss how they participated in and reacted to the unit of study? Compare their performance with prior lessons.

o Discuss how you presented the lesson to the students.

o Discuss the support you are receiving in lesson design, classroom management, and instructional delivery.

At the beginning of the professional development I expect teachers to be fearful of the unknown which is why a unit of study will be given to the teachers with various lessons modeled. I have found that teachers in high school courses are very procedural and many do not understand concepts to the level that they can make connections between concepts and to real-world situations. Time is another issue. Reusing or tweaking lesson plans are common place with secondary teachers so this new approach will entail an additional work load of creating and developing new units of study and the lessons that go along with it. Teachers will then be expected to create an additional unit of study implementing the strategies and concepts requested. Our curriculum maps have been rewritten by teachers to reflect a student-centered learning approach as well as a function approach to teaching Algebra I and Algebra II. I thought I would focus on the Algebra I teachers for the interviews and follow ups. I would also like to observe the teachers when they are teaching the specified unit. Observing the same lesson by all the teachers would be impossible due to time constraints but I could observe as close to the same time frame as possible.

The end result, I hope, is an appreciation and understanding by the teachers for SCL and FATA. Positive attitudes toward facilitating mathematics classes using the new ideas and an increase in self-confidence in creating units and lessons is also a hopeful outcome. I would also like for the teachers to acknowledge positive student attitudes toward mathematics along with increased achievement. The true test will be in future courses if students are able to retain material taught using the new approaches. I think that is when teachers will have the buy-in and ownership to continue.

Some threats to the validity will be when the teachers facilitate the units of study which is why I really need to observe some of the lessons as they are presented. Each teacher, even though they are following the same unit of study and lesson, will infuse their own personality and beliefs in to the class. My observations, along with their belief questionnaires, student assessments, and interviews will provide a way to triangulate the data. Another threat will be that I will be the one observing. It is a professional development so there will not be grades involved for the teachers however I do work for the central office as the mathematics coordinator. I would need to select teachers that I have a good rapport with and would be willing to be truthful with me during the interviews (response bias). All are aware that I do not evaluate them however there may still be the fear that I am from the central office. I observe teachers all the time but would need the approval from our central office to use my observations, where the students will be in the classroom being observed, as part of the pilot study. Another concern is that I will only be evaluating growth for one unit of study. If concepts are taught using the new approach then I am not sure the teachers will see a change in the students but will need to compare the students to past years. It takes time to change teacher’s beliefs, so again, the time frame of the pilot study will probably not reveal significant changes but instead there may be some acknowledgement of increased student involvement and attitude changes.

The concept map attached, to me, is more like a flow chart instead. I have revised it several times but the outcome is still very similar. The specific unit of study I believe I will do will be based on writing equations for real-world situations. This is a topic that begins in Math 8 and is repeated in Algebra I, Geometry, Algebra II, Math Analysis and Calculus. I hear Calculus teachers every year state that they have to teach the basic of writing equations of lines. Teaching for understanding will hopefully help the teachers to learn from their students as much as the students will be learning. I believe that if we can get through one year with some successes the teachers will be more receptive to additional education and encouragement in the future. That is where the cyclic effect is shown on the concept map. Changes in beliefs will result in teachers taking more professional development, considering where the students are at the beginning of the year or unit and then again where they are at the end, academically and in their self-confidence with understanding and doing mathematics.