Educators and researchers have spent decades studying learners’ ideas, errors, and misconceptions, but the use of that knowledge has not yet permeated the classroom. Discovering learners’ conceptions and misconceptions can be a daunting activity for teachers, and today’s multiple-choice technology is not ready for analyzing networks of conceptual misconceptions.

How can we use all the research and knowledge on learners’ ideas, errors, and misconceptions to develop students’ mathematical thinking and increase math learning? How can the discovery of learners’ attempts to make sense of math lead us to better ways of thinking about and teaching math?

I have been passionate about the idea of misconceptions for ten years now. I used it to explain to learners the importance of reflecting in their process of learning and for them to see those misconceptions not as simple errors but as a natural part of building deeper understandings that need to be constantly thought of. I supported educators in using the MOZART project — a set of science tests to diagnose misconceptions — to learn how well students understand various concepts in science. Educators reported finding the MOZART project very useful, but I haven’t found a similar instrument for math.