When I entered the field of mathematics education, it was first through mathematics. I happened upon mathematics in somewhat of a magical way. That magic can best be described by enjoyment and a sense of accomplishment and empowerment. I was good at it, and competed with others (mainly those of the opposite sex). I continued enjoying and excelling, seeing the connections to art and music and engineering, and architecture more saliently as I continued to study. My motivations to continue studying mathematics were firmly rooted in the desire to be challenged. Mathematics, it’s complexity, beauty, structure, and utility is challenging, yet reachable by those who are interested. I continued my studies of mathematics, not initially seeing the need to study the education of mathematics. If I worked hard, studied hard, collaborated with others, talked openly with my professors, read my books, took notes, and persisted, I could accomplish it. In education, I did not initially understand why it was a discipline to be studied.
I can teach mathematics if I know mathematics.
Maybe this is an impression or belief that I surmised based on my experiences as a student of mathematicians for so many years. When I taught mathematics for the first time, two classes of summer school geometry, I approached it the way I knew best.
I taught mathematics the way I was taught mathematics.
These students should be able to learn and master the art, beauty, and complexity of high school geometry the same way that I did. This was a fallacy. While teaching, I was also searching for ways to continue my education. I was fortunate to be offered a position as a research assistant at Western Michigan University. As my primary mentor, I learned from a lifetime achievement award winner, Dr. Christian Hirsch. He taught me about curriculum development, careful reading and writing, patience, and humility. He trusted me, gave me room to grown and learn, and together with his colleagues, provided opportunities that were aimed at building the capacity of researchers and scholars of curriculum. Along this journey of becoming a scholar, I continued to study mathematics. I learned to question my professors, to think actively during lecture, to read, and re-read, and write, and re-write, to persist, and to ask for help. I learned about friendship, family, and love. I learned to prove. I learned about different structures in a variety of branches of mathematics including algebra, topology, graph theory, geometry, and real analysis (advanced calculus).
I love being a learner and consider life-long learning to be an important part of my identity.
Beyond my studies in mathematics and my work as a research assistant, I learned about education. I was not ~the same~ as other mathematics educators who had years and years of teaching experience in the classroom. I had a summer of teaching experience, and several semesters of shared teaching experience at a local school in which I was invited to teach some algebra and geometry classes as my schedule allowed it.
The fire in my belly was not sparked by teaching, but rather by the pursuit of knowledge.
Something did change in me, though. And it is important to note here, in contrast to the statements made above about teaching. I was fortunate to be a student of Jon D. Davis. He taught me about the beauty of creating a classroom environment that was sensitive to the ebbs and flows of student reasoning, yet with a clear, directed purpose. He crafted this balance in such a masterful way, and I worked to adopt that teaching philosophy in my own practice as a teacher educator.
Teaching mathematics is a craft and art form.
The practice of teaching mathematics weaves together innovative thinking that is informed by research and theory on student learning, curriculum and curricular resources, mathematical reasoning, habits of mind (e.g., pattern searching; cf. Cuoco, Goldenberg, & Mark, 1996), and technology. My goal as a teacher is to provide opportunities that challenge yet support students as they grow in their own quests, and to negotiate productive social and sociomathematical norms (cf. Cobb & Yackel, 1996) within the classroom community. For example, for a lesson on compound interest, I create a sequence of tasks that are set of to engage the community of learners, giving them access at multiple entry points with multiple possible solutions. With students sitting next to one another at tables or desks, I ask them to interact with each other as they work on a problem set. A student might ask me “Did I do this correctly?” Before I assert mathematical authority to answer that question, I might ask “Can you explain to your neighbor why it makes sense?” The authority to judge “correctness” is shared among community members; a mathematical explanation is judged by the persuasiveness of the argument.
The best way to learn is to teach. – Frank Oppenheimer
Maybe this is next.