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The Teacher Tip

Use Contexts to Build Mathematical Understanding

January 3, 2018

Adapted from Comprehending Problem Solving by Arthur Hyde 

For students to succeed in developing a real conceptual understanding of mathematics, they need ways to organize their new learning and connect it to the knowledge they already have. One way to help them do this is to introduce a concept multiple times, using different contexts. 

Try this: discuss negative numbers in the context of temperature, altitude above and below sea level, and so on. Students represent each of these ideas in multiple ways, and then as a group, debrief the problem and discuss the ideas in it. Guiding students to compare and contrast these different representations and contexts can help them build generalized understanding as they identify the commonalities behind them. As they tease out these commonalities, they can begin to use more abstract representation that are less concerned with the particular features of each context and more widely applicable to other contexts.

To learn more about Comprehending Problem Solving and download a sample chapter, visit

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