"The Knowledge of Theories in Mathematics Education is Important for All Teachers of Mathematics, at All levels, and for All Mathematics Education Researchers."Tonight the MAT 403 class had a formal debate for the above proposition. The class is taught by Dr. Ken Clements, a mathematics education professor at ISU. He ALWAYS has interesting projects for his classes that change every time he teaches. He sent out an open invitation for people who wanted to watch the debate. I decided to go and watch the debate. The graduate students sat in two opposing groups, the affirmative and the negative. They faced each other and took formal turns. They were only allowed to address each other at specific times with questions. Dr. Clements served as the moderator. I have to admit it was extremely hard not to say anything... which is probably why I am blogging about it tonight. :) Affirmative or Negative?I feel a bit like a politician trying to make everyone happy; however, if forced to debate I do not not be able to comfortably pick either side with extremism. I will provide an anecdotal story as support to why I fall somewhere in the middle. On the Negative Side ... Upon entering my first year of teaching, I knew about constructivism and Piaget. I read about Gardner and multiple intelligences. I even memorized Bloom's taxonomy. I also participated in a three week intensive professional development during the summer before my first year of teaching that promoted using experiments and integrating science and mathematics into the classroom. Yet, there I stood in front of my class my first year lecturing and lecturing. Cognitive emptying upon cognitive emptying. Writing example upon example on the board. Occasionally, I would do a group activity or a game. Every chapter, I attempted a project where I didn't tell my students what to do, to help my students "think." During this first year, I made little conscious reference and reflection to the theories that I had learned. As a second and third year teacher, I started meeting other teachers and networking. I learned about collaboration and my ideas about instruction began to significantly change. By my third year, I started my masters, where I met many inspirational teachers. Through conferences and networking with these teachers, I really blossomed as a teacher and my classroom was drastically different than my first year. Entering my fourth and fifth years of teaching, I had evolved into a teacher that valued student thinking and I was a teacher that didn't want to think for my students. My pedagogy evolved each day, each week, each year. It was a beautiful experience watching the growth, learning from my mistakes, and embracing a philosophy to continuously improve. This was, in fact, what let me to the PhD program here at ISU. Theory did not directly make me a better teacher, even though my pedagogy clearly aligned with theoretical approaches and philosophies of teaching. It was my personal beliefs and experiences with students and other teachers that directly impacted my practice. On the Affirmative Side ... After my fifth year of teaching in the public school system, I became a fulltime mathematics professor at a small private university. While teaching fulltime, I took three graduate courses here at ISU. This particular coursework was a gamechanger for me. I learned about theories of student thinking about rational number in a rational number class. I learned about CGI in a seminar. I took MAT 403 where I learned about many theories in mathematics education. I was completely hooked on research, particularly theories that involved student thinking. What surprised me at the time, was how this knowledge directly impacted how I taught all of my classes, even in courses for math majors like Calculus I and Calculus II where it is almost expected for the professor to lecture. Suddenly, I only wanted to pose questions and listen. I never wanted to talk, I wanted my students to talk. I wanted to challenge them and facilitate their sense making. It is with strong confidence that I can say that it was the theories in mathematics education that have eventually influenced who I am as a student, a teacher, a researcher, and even a PERSON. Without the knowledge that I now possess of these theories, I don't think I could make informed decisions as an educator and researcher. For better or for worse, I am more informed about the Common Core initiatives because of theories about learning progressions. I am more informed about gender issues and races issues because of critical race theories. I am more informed about the strategies that my students will pose in class because of theories about student thinking. Sure, my students sometimes use a strategy I wasn't expecting. But, because I was expecting the other strategies, I was better prepared to make sense of the strange ones. Theories about noticing, questioning, and mathematical discourse, have directly influenced my pedagogy and I even think about them consciously in class sometimes. I am now a beautiful product of experiences, failures, successes, relationships, mathematical knowledge, and, of course, theories. As Mathematics Education Researchers ...As mathematics education researchers, we are in the business of theorymaking. Even if we utilize grounded theory, that is a theory that promotes theorybuilding. We are theorygenerating, theorybuilding, theoryrefining, theorycritiquing researchers. Admittedly, I do think that the use of theory can both restrict and promote creativity. If one holds to tightly to a theory and tries to pigeonhole everything into the descriptive categories of a theory, even when it doesn't fit neatly, this can be restricting. However, if one uses a theory to help make sense of a phenomena in a way that furthers what we know in a productive way, this is creative and important for the field in connecting and extending the research. In conclusion, as a mathematics education researchers, we can not deny the role and importance of mathematics education theories. Theories help us make sense of the complex phenomena we encounter. We will never be able to fully describe the phenomena with any one grand theory. Different theories give us different perspectives into the same phenomena. For the interested reader, I would like to recommend reading the 2008 JRME monograph 14. Each chapter of this monograph shows an analysis of the same 5 minutes of classroom discourse using a different theoretical approach. Each chapter of the monograph sheds light on a different aspect of the classroom phenomena.
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Nicole M.

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