Reinforcing Tricks

Posted on December 2, 2014

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Students are doing conversions.  Conversions, I am thinking (as of this very second so I may change my mind), are an interesting diagnostic tool.   Some students are all about “what’s the formula???” and are likely to confound and conflate proportions and conversion factors without serious, repeated guidance as to the meaning of the equals sign and the meaning of a conversion factor, and… argh, it’s still hard.   Student today was utterly frustrated and confounded with changing meters per second to miles per hour *because* of competent reliance on  basic number sense for familiar units.   It was one of those cases where I had to begrudgingly acknowledge a benefit to “show your work, THIS WAY.”  The teacher of the other to students at the table was of the “show it!” school, and… this student would have had to translate the familiar into the mathematicl language.   Seeing something that already made sense in mathematical terms and learning to say familiar things would have been at least a partial bridge over today’s “but how do I know when to divide and when to multiply?”     When I asked what half of 100 was, it was 50, but 100 divided by 2 would have taken pencil and paper; the student didn’t know.   However, this was a student who had noticed, when discussing the two “different” equations for converting Fahrenheit to Celsius, that it made sense when the roles were switched that the fraction should be the reciprocal, and she used the word before I did.  Lots of really good stuff in the foundation — but lots of things unconnected and therefore fragmented and not strong enough to sustain complex conversions.  (That said, I have to wonder whether visuals would help…)

Explaining that multiplying things together to find the whole and if you had the whole, you divided to find the parts was enlightening — but more important was the encouragement and testimony of the two other students who’ve made this place their second home (and have the teacher who insists on the details) because yes, the frustration factor was the bigger barrier.

Then there’s the other student who’s kinda sorta got it.   LIke most of ’em, though, that Celsius to Fahrenheit and vice versa thing is overwhelming.

… “Celsius:  subtraction first.   Fahrenheit:  Fraction first.”   Then I explain the order of operations reasons why… today another student did it wrong first, and when I said those words, she then proceeded to figure out how that was applying the order of operations (‘the subtraction is in parentheses so you do it first’).

I’m positive this could be classified as “a trick” — and if I stopped at the phrase, it would be… but it has been serving rather nicely as a way to avoid tossing monkey wrenches into the working memory…

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