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Original
Goal
Statement 		Revised
Goal
Statement - 2009
 Revised
Goal
Statement - 2010

Revised Goal Statement - Fall 2011


As schools and its’ teachers journey toward standards-based reform teaching and learning there are some individuals that are reticent about the transformation.  The discrepancies in beliefs about teaching and learning mathematics leads to classrooms in the same school, teaching the same course, being taught at two extremely different levels of cognitive demand and rigor.  Standards-based reform mathematics allows students opportunities to learn by addressing problems through different avenues of thought, through different lenses.  The teachers that are open to the change and the challenge will do so but my interest lies in how we can encourage and support all teachers so that the opportunity to learn is maintained between these classrooms at the same cognitive demanding level.  This does not mean they teach or facilitate their classes using the same words, motions, and/or activities.  By collaborating together or being a participant in a professional learning community, teachers develop lessons, assessments, and activities together as well as discuss issues regarding instruction and assessment.  The group would have a common goal or vision that helps them focus their actions during the collaborative sessions.  Teachers will be able to work to gain a better understanding of how students learn and strive for a higher level of cognitive demand and rigor within their classrooms.  The key is for all students to have the opportunity to learn mathematics whatever their situation may be with administrators and teachers obtaining the support they need to do so. 

Using the dissertation by Trujillo (2010) I have developed instruments to be used in my study for central office mathematics leaders, high school administrators, and teachers.  All three surveys deal with questions about what these individuals understand and know about opportunity to learn, doing mathematics, NCTM Process Standards, and expectations.  Comments and questions about expectations of the expectations of teachers as they collaborate and facilitate instruction but turned around to obtain other views by the teacher and central office leader.  The surveys also include a belief instrument created by the National Science Foundation that I have used in my pilot study on the implementation of standards-based reform philosophy. 



I am looking at a case study approach combined with survey analysis.  The two instruments will be sent to as many principals and assistant principals in the state with a request on the document if they would like to participate further with interviews and observations.  At this time I am torn as to whether to select a high school that perceives themselves as standards-based and one that is not OR to select two standards-based schools.  I envision my flow to send the two teacher instruments to be completed by teachers that agree to participate.  When I go to the school I would like to meet with the principal and do a walk-through of the mathematics classrooms and then go back and discuss what he saw, what was good, what was not so good.  Would also like to meet with the teachers as a group and talk about how they plan, create assessments, and perceive their role in the classroom.  Also would like the Algebra I teaches to bring a copy of their lesson plans (or whatever they record what they are doing), a unit plan if they have one, and assessments given.  Principal's documents might include walk-through forms, observation forms, expectations of collaborative sessions and if any type of documentation is expected, and any forms for guidance from central office.  I would also pick up the teacher instruments while there. 

Analyzing the data would begin by translating my scribbles about what I saw during the walk-through, transcribing the principal and teacher conversations, looking for key points about beliefs and actions regarding teaching and learning.  This would permit me to see if the principal’s thoughts correlated to the teachers and vice versa as well as if their actions correlate with their words.  Lastly would be the survey question analysis to determine teacher and principal beliefs, content knowledge assessment to determine if teachers have a deep understanding of some of the concepts and how much the principal knew about Algebra I, the gatekeeper to higher mathematics and to “life”.  Through the observations, interviews, and surveys my goal would be to see if the teacher’s beliefs were similar, how much they worked together to plan and analyze assessments, what professional development is offered to help them on their journey and what they believe they need in the future.        

Revised Goal Statement - Fall 2010

My thoughts and interests are evolving and becoming more explicit.  In my heart I am still interested in professional development and encouraging teachers to become more student-centered or standards-based with their instruction.  However, my coursework and current experiences have helped me to look at these topics in a different light.  As a mathematics leader I am concerned with the results and progression of professional development, teacher growth toward being more standards-based, and the usage of technology.  But there are additional aspects that influence instruction, the mathematics leader and the school administration.  This has led to exploring research of teacher change through the lens of the mathematics leader.

          Susan Printy’s (2008) study was the first piece of research that I found that delves in to the affects of leadership of principals and department heads on the teachers communities of practice and standards-based pedagogy.  I am not interested in department heads as the position is viewed differently with every principal, from deliverer of information to an evaluator of instruction.  Mathematics leaders however have the task of guiding a school district with content, pedagogy, classroom management, plus numerous other tasks.  However, the mathematics instructional leaders role is also different in various school systems.  In addition, we are dealing with individual's beliefs and attitudes toward what constitutes quality mathematics instruction.  My thoughts are going toward what the mathematics leader does to encourage teacher growth toward a more standards-based instruction and how do they work with administrators so that they will recognize and encourage the same.  Research was difficult to find so Printy’s reference list will provide a beginning.     

           Working as an instructor/facilitator for two master's level mathematics courses on the function approach to teaching functions and statistics and a year long professional development on the pedagogy for the approach has helped to solidify my thoughts for research.  Each of the sessions dealt with content and/or pedagogical content knowledge to assist teachers with implementing the functions approach to teaching algebra.  But teacher change does not begin and end during a short professional development.  During the past year our school district has rewritten the Algebra I and Algebra II curriculum maps to match new mathematics standards while providing teachers with professional learning sessions on the functions approach.  What I have found through interviews and discussions with teachers while they are involved in the professional development and afterward during the school year is a concern for the actions and perceptions of administrators.  Many are sold on the approach but concerned with observations and evaluations.  This is a concern I share with them as well.  They still feel the disequilibrium of presenting content differently and some are struggling with making the connections.  Leaders need to all pull together to support them in their endeavors of change. 

          Thomas Guskey’s (2002) model of teacher change in beliefs and attitudes through professional development is the foundation that I have applied as we go through changes in curriculum.  We have set the stage for the change during the last four years with guidance on how to facilitate instruction using the Rule of 5 (graphical, tabular, symbolic, concrete, and math talk).  Instead of piloting the new curriculum in one school the decision was made that all schools would follow the same map.  Teachers are attending professional development sessions, in a lot of situations collaboration is more than passing handouts around, and teacher discussions are centering more on the how and why along with the connections that can be made.  Teachers are presenting mathematics using a standards-based approach at varying levels of confidence.  At the same time the teachers are learning the content from an applied mathematics viewpoint.  The connections that are being made to other concepts and to real life applications is an ah ha moment for many. True to Guskey’s model, as teachers experience their student’s positive attitudes and success their own attitudes and beliefs are beginning to change.  We are in the beginning stages so a lot is yet to come.    

          Administrators have a wide range of concerns that they deal with on a daily basis and one cannot expect them to be experts in all areas of instruction.  Teachers have the support from the mathematics leaders at central office in our school system but this piece may be missing for secondary teachers in some areas.  Another missing piece is the administration of the schools.  At this time my thoughts are going toward surveying mathematics instructional leaders around the state as to their beliefs toward instruction of secondary mathematics, the influence they have or do not have with administrators and teachers, and who or what influences their actions toward administrators and teachers.  If possible, interviews could be conducted in an area that has a great deal of support and with an area in the opposite direction.   

The following are some research questions that are foremost on my mind:

o   What are the beliefs of mathematics leaders on instruction of secondary concepts?

o   What influences the mathematics leaders in their approach to encourage teachers to change their beliefs of instructional practices on the secondary level?

o   What influences the mathematics leaders with how they work with administrators with regards to mathematics instruction?

o   How does the mathematics leader influence administrators and teachers toward a journey of change in beliefs and instruction?

o   How do mathematics leaders educate high school administrators with the expectations of instruction?

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Revised Goal Statement - Fall 2009

          At this time my passion still lies in sharing and encouraging teachers through professional development to become more student-centered and to employ a discovery, inquiry based methodology to teaching and learning mathematics as well as  implementing graphing calculators appropriately with students. Persuading teachers to allow students to construct their own learning, differentiating instruction to meet student needs, promoting conceptual understanding and giving teachers the self-confidence to pursue new avenues is the impetus behind my search for knowledge. Appropriate usage of the graphing calculator would be a secondary goal that I use in my approach to "The Goal". Implementing graphing calculators appropriately into instruction enables students to discover concepts and visualize mathematics. Calculators are a wonderful tool but they are just a tool, one that all teachers need to learn how to use so that it may open doors to more students and their abilities to problem solve. Slope or rate of change has also been intriguing as I find more research on the topic as I work and search for ideas to work with teachers in our county. Students struggle with slope and writing equations of lines mainly due to the teacher's focus on the formulas instead of the concept thereby leading to frustration. Through professional development sessions and my thoughts for my main goal I have been able to share and encourage teachers to take non-traditional approaches to teaching concepts such as slope. Lastly, through my affiliation with the National Education Association Foundation (NEA) and the desire to understand research that I read, I have become interested in obtaining more knowledge in the realm of research. Through many conversations with the NEA, research is needed in education in numerous areas but I feel one must truly understand the numerous aspects of research to know how to conduct a study on a specific objective that will be respected and accepted in the field.
          My readings in Second Handbook of Research on Mathematics Teaching and Learning (2007) by the National Council of Teachers of Mathematics have provided some additional insights into my beliefs regarding teaching and learning mathematics along with calculator usage.
  • Manouchehri (cited by NCTM, 2007, pg 737) stated that there are three factors to create a productive algebraic classroom: the teacher, the task and the technology. A focus on one of the factors alone does not result in productive learning.
  • A meta-analysis done by Ellington (cited by NCTM, 2007, pg 735) discussed the effects of calculators on student attitudes and achievement citing students had a more positive attitude toward learning mathematics and that it was more beneficial when the calculator's role in the classroom was pedagogical.
  • Boaler (2003, pg 742) discussed effective teachers involving students and presenting problems - asking questions prior to answers being obtained, collaboration, students working together to find and make sense of the solution and the mathematics.
          The research by Manouchehri and Ellington reinforce my beliefs and vision about teaching and learning mathematics but how does one go about promoting and encouraging teachers to take the leap to change the way they approach teaching and students. Boaler has some wonderful ideas regarding student-centered learning but again how does one go about getting teacher buy-in is the big concern. My enthusiasm for mathematics teaching and learning does help. Some teachers have even stated that it has encouraged them to take that step to approaching the classroom using student centered lessons. Currently I have been working on professional development content for our county that will engage teachers, facilitating lessons they might employ with their students. The general format in the past for professional development has been fifteen hours during the summer and 2-two hour follow up sessions during the school year but they have become a check off session. Teachers go to the workshop, check it off, they are done for the year. Many do not even attend the follow up as they just take sick leave for the four missed hours. For the school year 2009-2010 I am approaching the professional development sessions three different ways: three summer days and two follow up sessions, two summer days and four follow up sessions, and six-three hour sessions during the school year. I am curious to see which type of  session will be more fulfilling for the participants. The objective would be that more sessions offered during the school year will enable teachers to work on, practice, and reflect on lessons that exhibit best practices and meet student needs in the classroom. Could I have gathered some type of data to analyze my approaches more fully? Yes, but what kind of research, questions, and methodologies would be best? Change does takes time and patience.

Original Goal Statement

            My name is Pamela Bailey and I am applying for admission into the doctoral program in education.  While teaching mathematics for twelve years in Westmoreland and Stafford Counties I have mentored and trained teachers with regard to methodologies, classroom management, and correct usage of technology within the classroom.  In both counties I actively participated and lead in planning and sequencing the curriculum to meet local and state standards.  This has led to my current position as the Mathematics Coordinator for Spotsylvania County with a focus on the secondary level.

            At the beginning of my first year of teaching I was told by my mentor to start on page one of the first chapter of the text and keep going.  This did not work as the students were frustrated and so was I.  As a parent of two sons, one with a learning disability and one that was gifted, I was concerned with the level of knowledge that the students possessed and the methodologies employed.  After talking with my Principal, and with his encouragement, I sat down with all the standards to align them for understanding, scoped out the year and more specifically the first quarter, assessed where my students were at that time, planned active lessons to increase involvement, and used the text as only a resource.  I continually searched the Internet for ideas on methodologies that would help to encourage my students to do their best and to love mathematics.  Always in the back of my mind were my own children and their needs when learning mathematics.  My journey had begun as my research on the constructivist approach to teaching and to the correct usage of graphing calculators in the classroom blossomed.

            My belief is that all students can learn and love mathematics; it was my job to find methods so that all could be successful.  Taking courses at Rappahannock Community College, Virginia Commonwealth University, and eventually my master’s degree at the University of Phoenix aided in my search of knowledge.  I studied diversity in teaching, learning, and curriculum for all individuals that included special education to gifted students and from small children to the elderly.  Through out my educational experiences I have learned that I’ll never stop learning, researching, mentoring, and modeling so that students and teachers will be successful. 

            From early in my teaching career it has been my overall goal to obtain a position that would include the time to train and mentor teachers and work with the mathematics curriculum so that all students can learn, understand, and feel successful mathematically.  My master’s degree, as well as becoming a regional trainer for Texas Instrument technology, is a step in the right direction.  As a regional instructor, my training experience has broadened to working with teachers on the local, regional, and international levels.  Introducing technology into the classroom so that it’s usage is an aid in discovering the mathematical concepts has been my goal as a trainer when using the graphing calculators or the Navigator system.  When I was teaching I attempted to use a multi-modality approach so that I might reach as many students as possible.  The more I searched for ideas to aid my teaching methods and therefore student learning the more I realized I had only just begun.  Developing new activities so that my students would become actively involved in their learning had become a goal. 

Since I was a high school teacher my current position as a coordinator is broadening my knowledge on teaching and curriculum on the K-8 level.  I have always been curious about how an elementary or middle school teacher presents lessons on mathematics and why students are so involved in mathematics on the elementary level but by the time they get through middle school and into high school one begins hearing how much they hate mathematics.  One of the big questions I have asked myself is why a high school mathematics teacher does not use centers in the classroom in order to aid in differentiation.  A concept I explored intermittently through out my teaching years with a desire to observe elementary teachers in action.

While teaching I shared my research findings, activities, and student results with my peers to encourage them to become student centered.  This involved many working lunches, after school training sessions, and professional development courses, all with my time being donated.  The opportunity to work as the Mathematics Coordinator is the beginning of a more formal journey of working with the teachers to encourage them to employ student-centered activities in their lessons, to search for methods so that all student may learn and appreciate mathematics.  This has proven to be a challenge as the teachers in general are not willing to modify their current teaching practices.  Some will agree that students learn best when actively involved but still are not willing to change while others do not feel that the methodologies they currently employ have any effect on student performance.  It is the student’s fault if they do not understand the concepts according to some teachers.  Now not only a new journey is beginning but also a new goal has developed.  The search and inquiry into methods to bring the teachers on board to be open to become student centered teachers.  

In the future I would eventually like to obtain a supervisory position in mathematics, continue working on methodologies to encourage teachers to use student centered activities to teach mathematics, and to develop activities in which the students are involved and developing ownership in the mathematical concepts they are learning.  After researching institutions on the Internet and then talking with others who are attending George Mason University I was pleased to find that within the Education PhD program a focus on mathematics leadership and a minor that involves technology was offered.  Each day I am currently learning about being a “leader” and feel that the program will fit my needs and future aspirations.

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