If you asked your students what the purpose of math is, what do you think they’d say?

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I’m currently rereading Jo Boaler’s book, Mathematical Mindsets, which was recently released in its second edition. Chapter 3 is titled The Creativity and Beauty in Mathematics. Does that strike you as odd? Do you think your students would describe math in that way? The main point of this particular chapter is that there is a huge disconnect between the way we teach math in our schools and the way math is actually used in the real world. Our instruction largely centers on performance—performing calculations or answering questions. Yet, Boaler refers to Conrad Wolfram’s four stages of math:

1. Posing a question
2. Going from the real world to a mathematical model
3. Performing a calculation
4. Going from the model back to the real world, to see if the original question was answered

Unfortunately, Wolfram states that 80% of the instructional time in our mathematics classrooms is focused on Step 3, performing a calculation.

Something that Boaler goes on to discuss is the importance of having students explain their thinking:

Many parents ask me: What is the point of my child explaining their work if they can get the answer right? My answer is always the same: Explaining your work is what, in mathematics, we call reasoning, and reasoning is central to the discipline of mathematics.

So how can we shift the emphasis away from calculations? It will require a hard and honest look at the types of tasks we give students to do. Consider long division. How do students benefit from a page with 30 long division problems? Either they know how to do it, and they’ll get them all right, or they don’t know how to do it, and they’ll get them all wrong. We need to move toward more thinking and reasoning-type tasks.

Consider this long division choice board.

Yes, there are problems that require only calculation, but there are more thinking/reasoning-type problems. It’s used like a tic-tac-toe board, with students choosing the three problems they want to solve. I would suggest telling them that the only option they can’t choose is diagonal from the top left to the bottom right because that would result in them only performing calculations. Every other option presents them with one calculation problem and two thinking/reasoning problems.

Click here to grab a copy of the long division choice board.