What is conceptual understanding?
Mathematics educators talk endlessly about conceptual understanding, how important it is (or isn’t) for effective math learning (depends what you classify as effective), and how best to achieve it in learners (if you want them to have it). Conceptual understanding is one of the five strands of mathematical proficiency, the overall goal of K-12 mathematics education as set out by the National Research Council’s 1999-2000 Mathematics Learning Study Committee in their report titled Adding It Up: Helping Children Learn Mathematics, published by the National Academy Press in 2001. I’m a great fan of that book, so let me say up front that I think achieving conceptual understanding is an important component of mathematics education. That appears to pit me against one of the two opposing camps in the math wars – the skills brigade – so let me even things up a bit by adding that I think many mathematical concepts can be understood only after the learner has acquired procedural skill in using th
