Spelling and Math

Last night, as part of our learning-play, I asked my five-year-old son how to spell “night”. He told me “nitk”. That got me thinking about math education.

English spelling is notorious for its quirks and oddities. In the case of “nitk”, my son told me it was because he knew a “k” went in there somewhere, but wasn’t sure where. It’s possible he was thinking of “knight”, but at the time I interpreted him to be thinking about the “gh” in “night”.

Either way, it supports my argument. It seems to me that while learning English orthography involves a complex interchange of phonics and memorization, there are three basic stages for most exceptionally spelled words: Guessing, memorization, and understanding. Also, most readers who are fluent but non-reflective stay at the memorization phase for most exceptionally spelled words.

This came to my mind recently while teaching, when I was discussing the word “rectangle”. “Rectangle” is so-called because all of its angles are right angles, and while “rectangle” follows basic English phonetic rules (that is, it can be successfully sounded out by someone who’s never seen it before), “right” contains the silent cluster <gh> and has a “long I” sound. Its homophone, “rite”, has far more predictable spelling.

At first, my students didn’t seem to believe me that “right” and “rectangle” are related, so I gave them a quick review of German. The German word for “right” is “recht”, which is pronounced as spelled (roughly “rekt”); the German words for “night” and “knight” are “Nacht” (“nakt”) and “Knecht” (“k-nekt”, respectively. I went on to explain that the <gh> in those English words are the remnant of a sound in an earlier version of our language, related to the <ch> in German. We got rid of the sound but not the letters.

After this explanation, I did seem to get a lot more buy in to my claim that a rectangle is called that because of its “recht” angles.

Last night, reflecting on this and my interpretation of my son’s error, I thought about my students and the way it feels like they often write numbers and operators down in a haphazard way. They know that certain elements are supposed to be in there “somewhere”, but because they lack understanding, they’re not quite sure where.

Through spelling bees, as in math class, we tend to put a lot of emphasis on memorization. We teach sets like “right”, “might”, and “plight” as rhyming groups. Would it help second graders to know that the <gh> is a remnant of a once-pronounced sound analogous to German <ch>? Probably not, frankly. It would confuse them more than it would clarify. But what about high schoolers? At one point should we make this transition?

I was helping a student in after school tutoring yesterday to work problems involving tangents. The details will be a separate post, but the upshoot was on manipulating the Pythagorean Theorem in order to make solving a particular problem more efficient. When formulas are taught as fossilized objects to be memorized, students are resistant to modifying them. Memorization is not understanding.

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