Shelli Casler-Failing
Doctoral Portfolio

Department of Educational Theory and Practice
University at Albany

Introduction

After graduating from the Master’s program and beginning my career as a mathematics educator I realized that I wanted more; I wanted to use my knowledge to inform the practice of future mathematics educators.  I knew that in order to achieve this goal I would need to obtain my doctoral degree.  I contemplated this move very carefully as I was leery of performing research.  After a lot of thought, I felt confident in my ability to complete the doctoral requirements and applied to the program.

While studying for my Master’s Degree at the University at Albany I was instructed about “best practices” for teaching mathematics and introduced to theories to substantiate those practices.  It was through the required coursework that I became a fan of, and advocate for, the work of Lev Vygotsky, namely his constructivist theory of education.  Although I personally felt a connection to the underpinnings of this theory, it was through practice in my own mathematics classroom that I was able to substantiate the theory in my own mind.  I knew when I entered the doctoral program that Vygotsky would be an important part of my own theoretical and research foundation.

As I began my coursework in the doctoral program, I was able to delve deeply into many theories influencing today’s educational practices.  I looked upon these opportunities to not only expand the breadth of my knowledge, but to also deepen my knowledge of constructivist theories (e.g., Bruner). It was during my second semester in the program that I began to develop an interest in Math Anxiety.  While a student in Instructional Theory and Practice (ETAP720) I was required to write a literature review. After reflecting on a seminar I attended on Math Anxiety, I felt a literature review on this topic would provide me a great opportunity to examine it in more depth; I hoped to answer some lingering questions I possessed.  It was through this review that I discovered writing was one of many methods used to help students reduce their levels of math anxiety.  I also discovered that what many people were referencing as “anxiety” actually had more to do with attitude than with clinical anxiety.  Since I had found in the research that the more general ideas about math anxiety had already been sufficiently addressed, I began to look more deeply into the researchable variables and the theories related to attitude and mathematics. Since writing was one method used to help alleviate anxiety I was left wondering if it could also effect change in students’ attitudes.  Once I chose to travel the path of investigating theories focused on writing and student attitudes, namely how/if one’s attitude effects his/her performance, I knew that I had found an area of extreme interest as well as an area in need of further research. 

However, choosing a topic to investigate in more depth was just the beginning.  In order to properly investigate writing and its possible effects on students’ attitudes I also needed a theoretical framework to guide my research interests.  I knew that constructivism would be a part of the framework, but I did not feel it would substantiate everything I was hoping to encompass in my own future research endeavors.  This led me to search much deeper into other theories that have helped to shape education.

During this time I gave a lot of thought and attention to various theories as they related to: attitude, self-efficacy, self-perception, writing (in general as well as writing in mathematics), assimilation, social constructivism, cognitive constructivism, apprenticeship, and learning. This was not an easy, nor a quick, process as I felt that portions of each of these theories could influence my research.  After reading, and re-reading, many articles and books I was able to create a theoretical framework that I felt best represented my interests.  My theoretical framework evolved through a mix of Vygotsky’s Constructivist Theory, Connelly’s Writing Theory, Bem’s Self-Perception Theory, and Katz’s Functional Theory of Attitude.

As I investigated the above-referenced topics I found that I could not solely investigate writing as there are many different forms of writing in the educational setting (e.g., free writing, journal writing, and term paper writing).  I needed to continue to investigate writing theory and writing to learn theory in order to focus my research on a particular aspect of writing in mathematics.  As I read through numerous articles and books I felt that transactional writing should be the method of writing implemented in my research because it relates to student responses given to a particular question or problem.

Once I had chosen a topic to investigate and developed a theoretical framework, I still needed to determine the type of research I would implement.  My doctoral coursework allowed me to investigate many different research designs, but I had difficulty choosing between a quantitative and qualitative study. I knew that a quantitative study would be generalizable to a large population with statistics to substantiate any improvement in student performance.  However, attitudes could not be reflected through statistics as they are an innate characteristic a person possesses.  For this reason, I chose to use a mixed methods framework – I could substantiate improved student performance with statistics and document students’ attitudes through pre- and post-attitude surveys as well as interviews throughout the research process.  As far as the qualitative research design of my study, I was leaning towards a case study, but felt I needed more information on the method.  A scholarly piece I have included in this portfolio Case Studies: Why should I use this design? allowed me to gain a deeper understanding of the methodology.  This deeper understanding guided the development of my pilot study proposal, Transactional Writing and its Effect on Student Attitudes and Understanding in the Middle School Mathematics Classroom, which I have included as an artifact to substantiate my research abilities.

Although I was able to write a research proposal I knew that experience performing research would be invaluable to my overall doctoral studies, however, being a full-time educator prevented me from becoming involved in the many studies being conducted in the education department by my colleagues and professors.  In the fall of 2011 I enrolled in Seminar in Technology and Education (ETAP 723) with Dr. Carla Meskill and was pleased to find that this course would provide me the experience I desired.  I was able to participate in a research project through collaboration with Dr. Meskill and three other graduate students to design, implement, code, evaluate, and disseminate the findings of a research study.  The paper I have included substantiating my research abilities, Models of Mind in YouTube How-to Videos, was the final product of our research.  Although I have not yet been able to follow through with my pilot study, this research project allowed me to experience the realm of research first-hand and has provided me with the confidence and experience I need to move forward with my own research. 

Throughout this program I have had the opportunity to collaborate with many fellow graduate students; these were priceless experiences as each opportunity allowed me to strengthen my understanding and further develop my research, scholarly, and collaborative abilities.  I am a huge advocate for working with others, whether it is at my current teaching position being a team member, while working with a group of fellow students to determine the significant findings of a journal article, or working with fellow educators to create mathematics curricula.  

It is through my studies and experiences in this program I feel I am a well-informed and knowledgeable researcher; informative writer; and eager, knowledgeable collaborator.  I have transformed from a student-learner to a researcher-educator.  I look forward to designing, implementing, analyzing, and reporting findings from my own research on writing in mathematics and its effect on student attitudes.  I feel confident and capable of being a contributor to the field of education, namely mathematics education.

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