Math: Process Matters

Math probably causes more apprehension among students and parents than any other subject.

What if you (and your teachers) are doing it wrong?

Take a bird’s eye of Monday’s “speed test” of multiplication facts: In a class of 30 students, one or two wunderkinder speed through the trial; others lag behind; the bottom ten or fifteen are in despair. These children, under stress, are forgetful. They grow up to fear and hate math. As adults, they may have trouble computing a 10% tip; a 15% tip will confound them.

It need not be this way.

Way back in the day, when writing out my multiplication tables, I observed many patterns. For example, do I need to memorize that 7*5=35? Why bother, when I know the general pattern: to multiply by 5, first multiply by 10, then divide by two. Add a zero and divide by 2. Half of 70 is 35. Boom, next problem. Do I always do it this way? No, but I can – and that gives me a great deal of power when solving many problems.

How about multiplying by nine? Multiply by ten and subtract the number. 9*7? 70-7=63. Boom. Done. As a side benefit, note that the digits add to nine.

Methods such as these cannot be taught, they must be discovered. The child, discovering them, owns them; she keeps them as valuable treasures.

If multiplication “facts” were just arbitrary random syllables, rote memorization would be the only method. But they’re not; these “facts” arise from the properties of numbers – properties which are discoverable and useful. To build a structure of “facts,” without excavating and laying a sound foundation, is to build something which will only need to be rebuilt in later years.

When my peers first confronted the associative, distributive, and commutative properties, it was as if they had met incomprehensible aliens from space. To me, these “alien” properties were familiar friends of long acquaintance; we scampered off and played together. I had been using these ideas all along, as I learned to appreciate and apply the properties of numbers.

The math “facts” are not the “basics” of multiplication; they are the products (excuse my pun) of a simple, easily understood process. That which makes sense is easy to remember – or to recreate.

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