What happens when teachers anticipate and respond to student misconceptions in mathematics?
True Understanding through MisconceptionsThe focus of my inquiry is to critically analyze what happens when teachers anticipate and respond to student misconceptions in mathematics. These misconceptions can take the form of gaps in computational, procedural, or conceptual understanding. I explored the potential value of mistakes as insight into student thinking and also as an integral component of the learning process. I noticed a strong interplay between students expressing their thinking through mathematical misconceptions and teachers anticipating and reacting to them. The central realization that I am coming away with is that all of these elements—errors/misconceptions, responding, and anticipating—can work in conjunction with each other towards the goal of guiding students to the development of true understanding. Navigation Note: These interweaving exchanges are illustrated in the flow diagram on the left. You may explore in any order. Each individual site page focuses on the specific idea at hand, but the other ideas will also surface throughout. |
The Story and Development of the Inquiry
When I began my student teaching, I found myself being caught off guard, but intrigued, by the misconceptions that my students were having about math. My students would raise their hands and explain how they got their answer. Sometimes their reasoning would be incorrect but would have some logic to it. I often did not know how to respond to these misunderstandings. Simply responding with “I can see how you got that, but that’s not quite right” seemed unhelpful, and possibly even detrimental, to student learning. Listening during class and looking at written work appear to be authentic ways to formatively assess my students' developing understanding and how they are processing the material. Whether correct or incorrect, these expressions of student thinking help me as a teacher to view the material from their perspective- the perspective of a novice. |
In instances where misunderstandings presented themselves, I struggled to find ways to still value my students’ thinking and not dismiss how they were making sense of the math. Unfortunately, failing to acknowledge students’ voices, even when they are wrong, can negatively impact students’ confidence in their own abilities and willingness to contribute again in the future.
I began to think about how I could appropriately and effectively anticipate and respond to student gaps in understanding. Thinking through during the lesson planning stage about the possible student misconceptions could improve my ability to react in the case that one or more of my students actually does have one of those confusions. By utilizing, rather than skimming over, student misconceptions as starting points toward understanding, I was curious to see the impact on my students’ learning. |