Balancing ‘conceptual’ and ‘procedural’ understanding in math
By Tyler on June 28th, 2012
This is one in a series of posts examining the Common Core State Standards and the conversation surrounding their impact on teaching and learning.
A quick math quiz for you (no paper and pencil or calculator allowed!):
Tell me an example of a number that is greater than 1/5 and less than 1/4.
Is that easy for you?
I heard a presentation today from Jason Zimba, one of the lead authors of the Common Core State Standards for Math, where he put this question up on a slide. (I didn’t copy down the exact wording, so I’m sure I phrased it differently than he did.)
One of the key points he made today was about the importance (as outlined in the Common Core) of students mastering “conceptual understanding” of math in addition to “procedural understanding.” Too often, he said, students memorize the procedures of math without actually understanding the concepts. And asking students carefully-selected questions like this can get to heart of whether they actually understand fractions.
Marilyn Burns of Math Solutions often makes a similar point, saying that students need “math reasoning skills” in addition to learning the algorithms of math. She’s made sensational videos of students being interviewed by teachers where the students are asked questions (say, 1,000 – 998) and asked to calculate that without paper and pencil and then explain HOW they got the answer. Easy, right? Well, not for a huge number of students. A lot of students will use their finger as an imaginary pencil and pretend to write out the calculation on the desk, writing 1,000 and then 998 under it and then subtracting one column at a time. Students like this have learned the algorithms, and in some circumstances can “get the answer right.” But they lack conceptual math understanding, which is key to making connections to the real world and to higher order math.
The Common Core standards say children should build fluency with math facts, but they should also be taught math reasoning skills.
(Flickr photo by alancleaver)
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