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• Eileen Horng

# Mathematical Conceptual Foundation

## What does that mean?

In my last post, I talked about giving a child a firm, comprehensive mathematical conceptual foundation - one that would support a lifetime of math learning if the child so desired. But what exactly is a “mathematical conceptual foundation”?

For starters, it is NOT memorizing math facts and formulas and being able to recite them with speed and accuracy.

## Beware of Party Trick Math

I was spending time with friends when one of their four year olds asked me, “Do you know what 145 plus 231 equals?” and proceeded to tell me the answer. I was astonished and impressed. And no, it was not that he had memorized just this one random equation - he could indeed add two three-digit numbers together. This actually makes for a very entertaining party trick - the little magician awes the audience when he calls out, “Give me a 3 digit number, any 3 digit number…” But in the end, this is little more than an entertaining gimmick. Upon closer examination, I noticed what might seem like a trivial quirk. When he asked me the original question, he actually said, “Do you know what one-four-five plus two-three-one equals?” rather than “Do you know what one hundred forty five plus two hundred thirty one equals?” I understood what he meant, so no big deal, right? Perhaps. Or perhaps this was revealing a gap in his mathematical conceptual foundation. Did he think that the 1 in 145 was equivalent to the 1 in 231? In his math trick, he could treat them the same way to get the right answer, but does he really understand place value? And does it matter?

Yes, it matters tremendously. It of course matters in a very practical sense. For example, if someone gave you a bill with handwriting that was difficult to discern a 1 from a 7, as is often the case, the difference between \$231 and \$237 is very different than the difference between \$145 and \$745. But even more, understanding place value matters when developing the foundation for learning more complex math concepts. I would argue that understanding place value is much more important than memorizing addition facts like 4+3=7.