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May 24

A Constructivist Journey

Posted by Bank Street in Math Leadership on May 24, 2017

NoneBy Katie Pitz
Graduate Student, Math Leadership Program



My math experiences as a student and as a teacher had always been very traditional. As a student, I’d taken timed tests, memorized algorithms, and generally not enjoyed math. As a teacher, I used workbooks and tried to teach my students basic math skills without really understanding what I was doing. Math was a struggle and I didn’t like it. I hoped there was something more to teaching math that I just hadn’t learned yet.

In the Math Leadership program at Bank Street, I discovered a whole new approach to learning math. Constructivism, a philosophy of learning, made so much sense to me. And I saw action research as a perfect pathway to learning more about constructivism and how I could embrace this philosophy in my own learning and in my own classroom. With guidance from my cohort and my professor, I narrowed my focus to asking open-ended questions in math as a way to experiment with developing more student-centered math lessons.

Through the research process, I experienced a huge shift in not only my practice but in my beliefs about how students learn math. A few of my most important discoveries:

  • To think about connections across mathematical content and what these connections mean in terms of student learning when planning. As I planned open-ended questions, I began to make connections across mathematical concepts that I hadn’t noticed before. I realized that my students needed to make these connections as well, and I had to consider how to help my students make those connections themselves (Burns, 2015).
  • To foster an environment of discourse in math, instead of an environment where I hold all of the knowledge and my students expect me to confirm right or wrong answers. During one lesson I was using for data in my research, I noticed that I had been interpreting my students’ comments out loud to the class. I wondered how I could encourage them to further clarify their own and their peers’ thinking. Clements and Battista (1990) describe the constructivist classroom as, “a culture in which students are involved not only in discovery and invention but in a social discourse involving explanation, negotiation, sharing, and evaluation” (p.6).
  • To monitor the manner in which I respond to students in order to create a safe and inquisitive learning environment. Math can feel very scary, and when students do not feel safe in sharing their mathematical thinking, it becomes even scarier. I wanted my students to be deeply involved in the learning process (Sullivan & Lilburn, 2005) and take risks as they solved open-ended math problems. This meant I had to learn to monitor my tone, my language, and my facial expressions as I facilitated lessons, so that students would feel safe to explore and make mathematical discoveries.
  • To consider multiple lesson formats, such as the Launch-Explore-Discuss model which helps a synthesis of the learning take place at the end and gives students ownership over their learning. Placing my students mathematical ideas at the center of the learning (Clements & Battista, 1990) became extremely important as my practice shifted. By restructuring the format of my lessons, I was able to create more space for student construction of ideas and student dialogue, shifting the focus away from myself as the teacher and onto my students as the learners.

The research I conducted this year took me places I never expected to go. I have a completely different approach to teaching mathematics because I understand the math I’m teaching. I love teaching math. I also believe that many of my students now love a subject that they previously approached with dislike and fear.

I’m wondering, for the teachers out there who don’t enjoy teaching math, what is it they need to make this shift in their own practice?

 

References

Burns, M. (2015). About teaching mathematics. Sausalito, CA: Math Solutions

Clements, D. H., & Battista, M. T. (1990). Constructivist learning and teaching. Arithmetic Teacher38(1), 34-35.

Sullivan, P., & Lilburn P. (2005) Good questions for math teaching: Why ask them and what to ask, grades K-6. Sausalito, CA: Math Solutions.

tagged action research, math, math leadership, teaching math
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