Conceptual Understanding in Mathematics

If you are following principalaim, I have shared some of my favorite educators, innovators, and creative thinkers. Among my favorites is Grant Wiggins, co-author of Understanding by Design. An authority on subjects dealing with assessment, student engagement, and the Common Core, Wiggins is constantly being sought to answer questions concerning the best practices in education. In Wiggin’s latest blog, he asked us to think about “what conceptual understanding in mathematics means and how best to use it to help students understand which ideas are key (relevant).” Ultimately, it is critical that we understand how best to prepare our students to become avid readers, mathematical thinkers, independent, and innovative creators. tlb

Granted, and...

The Common Core Standards in Mathematics stress the importance of conceptual understanding as a key component of mathematical expertise. Alas, in my experience, many math teachers do not understand conceptual understanding. Far too many think that if students know all the definitions and rules, then they possess such understanding.

The Standards themselves arguably offer too little for confused educators. The document merely states that “understanding” means being able to justify procedures used or state why a process works:

But what does mathematical understanding look like? One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from. There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b)(x + y) and a student who can explain…

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