This topic for my blog came to me during a three day professional development in mathematics. How do we get students to be Mathematicians? Its simple! Its about getting students to invent strategies that they have discovered while solving a series of problems. But how do we get students to invent these strategies? For a long time now, the way we tell students to multiply fractions together is straight across the top and straight across the bottom. But WHY does this work? Many students do not know the answer to this question. If we are not letting students explore and discover these strategies to solve problems are they really learning math or are they just applying what they were told.
If you want your students to learn about area, perimeter, and volume, how would we do this? Give them the formulas of each and let them solve problems on paper? But what happens when they ask where did the formula come from. Why not give them a problem with numbers and tell them that we want to find the area, perimeter or volume and let them explore inventing the formula for each. This would give them more ownership over using the formulas in the future and have an understanding of why the formulas work the way that they do. Students should be able to answer the question why in mathematics!
I agree completely. As a homeschool parent and someone who runs a math club, I can see how many students don't really understand what they are doing. And many local schools emphasize rote learning and speed tests - not mastery of concepts. Ugh!
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