Searching for purpose: mathematics and teaching.

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.

“…we need to …

“…we need to encourage people to become less productive. Make time to not work. Make time to think. Make time simply to be.”

Read more:
Inside Higher Ed

Why I am I scholar.

I am a scholar to change the world. 

Be the change you wish to see in the word, is a motto that is akin to that of my alma mater (challenge yourself change the world). These sayings resonate with me in a powerful way. To me they are motivators to act, to be, to lead. To innovate. This is somehow related to the mantra of my current institution: Think and Do. And as a colleague of mine might add, And Be.

Leadership is an essential quality of a scholar. That leadership can be conveyed in writing, and speaking, and in acting. There is always more to write. This is something that I do not allow enough time for. 

What does it mean to change the world? To empower others. To break the mold. To connect communities. To translate and link ideas. In my world, this means “linking research and practice,” an important part of NCTM’s research agenda conference report, and part of my own agenda as well.

One unknowable plan is in relation to being versus becoming. Is it one’s claim that they are a scholar, or is it in one’s being (thinking and doing) that one is a scholar. It is unknowable in that who decides. Like a proclamation that “this is art” — says who (Julia Roberts?)? Who decides who is a scholar? Maybe it is my own decision. Yet that decision is always judged by others.

I am a scholar to learn. To challenge myself. It is the pursuit I have chosen and in the thralls of.

Living and learning.

Every day is a new day. Today, and lately, I’ve been learning about living. Learning about living a fuller more complete life. I find learning about living to be challenging and tiring. Caught in seemingly disparate worlds as tumultuous as a bubbling ocean busying itself during a  a storm.  I tire my eyes, body, and soul with deep questions that do not have answers. Yet at the same time, catch-y phrases are catching my attention such as “Fight the Impostor Syndrome!”  “80 hour a week academic jobs” (are not real–it’s more like 50-60 hours) “Just do it!” “That’s the million dollar question” and hey, what about “Emotional Intelligence?” Is there a pattern in the randomness? What is the Signal in the Noise? My million dollar question right now is what do you want to do? To be? To aspire to?

I realized that my sticking point is no different than a perspective or theory on living–why should there be some pre-determined endpoint that I aspire to achieve? I prefer to think more organically about life, especially in regards to opportunities to learn, live, and grow. Yet at the same time, I know that I aspire to lead, to motivate, and to contribute to the growing and budding field of mathematics education research. One does not reach the stars in a day night or a week, but over a life time of work and dedication.

Some quandaries that stop me in my tracks deal with the contradictions and seeming inconsistencies between learning trajectories and curriculum development. If a learning trajectory, by definition, involves predictions about students’ processes on a task or instructional activity, then a problem or task necessarily exists that can be expressed in written form from which one could identify some gain size of curriculum. Does the reverse hold? If one has some gain size of a curriculum, say a task or activity, and if there is some sequence of tasks or activities that comprise a meaningful ordering of lesser to more sophisticated reasoning of the child, student, or learner, then these tasks can be taken as signposts of a learning trajectory. Now this is not to say that “curriculum” and “learning trajectories” are one in the same. The only case in point made here is the conceptually  linked nature of these constructs.

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