Student thinking as a source of insight.

One powerful lens that I find fascinating and incredibly rich is to take the stance of a student. Based on interacting with a student–listening to what they say, watching intently as the do, draw, or create something–and ultimately wondering, based on what I know about this student (history), the context we are in (situation), what might this student be thinking?

In a recent research report by Amy Ellis and Rob Ely, they shared findings of their sense-making of student’ thinking. Early in the talk they gave at RUME 2018, Amy said:

I believe student thinking can give us insight into our own mathematical ideas.

– Amy Ellis

From this lens, they continued by sharing a context for learning they designed with their research team (a dynamic paint roller), and the design principles and mathematical goals that formed a foundation for asking questions and designing new tasks.

This sketchnote captures my take of their research reported at the RUME 2018 conference:

IMG_4283Sketchnote Art by Nicole L. Fonger @nmlfonger

For me, the big take aways for practice (and for research!) are:

  • Adopting a theoretical perspective, like quantitative reasoning, or covariation, can form a strong basis for designing tasks. In a practical sense, this might mean moving from an instructional goal of “teaching topic/standard X, Y, or Z” to an instructional goal of “supporting students to reason about continuous covariation in linked quantities of area of a painted region and length of a painted region.” This shift puts students’ thinking front and center in instructional design.
  • As researchers, and as teachers, we operate in our world with different understandings than students. Celebrate this difference by becoming curious about the ways students understand the world through close listening, records of practice, and conversations with others. When Amy heard a student say “I think a curve is a lot of lines” she reflected later that it is “poetry that moves my heart.” We learn more by listening to students.

Read more about this research project here:

Scaling-Continuous Variation: A Productive Foundation for Calculus Reasoning View free PDF of Paper here!


See Amy’s research site here


Tell me — What are you noticing? What are you wondering?

3 thoughts on “Student thinking as a source of insight.

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