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Why Models Matter

Why Models Matter

We have all seen this happen in our math classes at some time: students learn the basics in our lessons, but then struggle when those concepts are extended in just a small way. Students cheerfully recite their basic addition facts, but have no idea how to solve 7 = ? + 4. And story problems? Yikes. Quantities and operations get buried in language and contexts that bring anxiety and confusion to all involved.


We know from evidence that visual math, and the use of manipulatives, have an important place in learning. Yet many people consider these tools just for very young children.

But new brain research tells us that visual mathematics encourages more brain activity that promotes greater understanding, and also allows more opportunities for conversation and reflection as students build to mastery.

Watch this video from Jo Boaler's excellent (and free!) online course that discusses the idea of 'brain crossing':

What if you tried this?

Visual mathematics and well-chosen manipulatives aid students of ALL ages. They promote deeper understanding and increased activity in the learning center of our brains.

For one class period, choose a challenging problem from your curriculum. The Symphony Guided Practice Materials can provide a nice starting point for suggested word problems and/or other modeling tasks. Give students manipulatives and have them construct models as part of their solution. You can use unifix cubes, counters, or even paper and pencil to contstruct grids or number lines.

After students have time to talk, build, and explore, discuss their models and conclusions with the class. We recommend you model this activity first, relying on Symphony Math examples, with your whole class.

Change Isn't Easy

Manipulatives have an important place in learning and their use is excellent for highlighting the mathematics inside a problem. Yes, older students may impatient at first. But with a positive presentation by you, highlgihting the fact that mathematicians engage almost entirely with visual mathematics and models, you can win over your class. The payoff is clear: you will witness a more robust understanding of mathematical quantities and relationships.

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