There has been a war in the mathematics education world for the past few decades about whether students should master basic skills, or whether they should use calculators or software for basic skills to save time and energy for higher-level thinking. More and more people nowadays are seeing this for what it is: a false dichotomy. It’s quite possible, and indeed very helpful to students who are learning mathematics, to emphasize both. Mastering basic skills makes it much easier for a student to successfully devote thought to higher-level conceptual development. Anyone who has watched while a student suffers through the struggle of learning calculus when he has difficulty adding two fractions can empathize.
In my experience, one of the most effective methods for teaching mathematics involves helping students to make connections. This can be done in many ways, by connecting ideas that appear different initially, by connecting mathematics to science or to applications, by connecting examples to theorems, and so on. An important example of making connections is to connect abstract, symbolic formulations of an idea with concrete, especially visual, instances. Another way to say this is connecting the algebraic with the geometric.
I’ve written some notes on helping students to learn the multiplication table, where I have attempted to implement some of these ideas:
I’d love to hear feedback from anyone who uses the notes, or who has experience teaching elementary school students.
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Earlier posts in this series:
How Much Mathematics Should a Student Memorize? (Part 1, Trigonometric Identities)