Proportionally yours, ALEKS

Posted on January 16, 2014

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Students are learning about Pie Charts in Math LIteracy, including reading an article with a pie chart of the number of pizza stores by brand (lots of the big chains, and “independent”), and the sales $$. It’s fascinating watching most students make the connections between those formulae etc and … something with meaning. What *could* be the reasons that 59% of the *stores* are independent, but only 51% of the sales? Some leap to the conclusion that chains are more profitable… then we ask questions: what if an independent store is a lot smaller? Fewer workers… could be more profit for the owner… oh, and of course, there are franchise costs…
They also have some homework on ALEKS devoted to pies. ALEKS doesn’t teach; you get a problem and you can click “Worked example.” (In its “learnign” area, you’re given a problem and you can click “explain” and the programmers have plugged those numbers into the algorithms and you get to see it solved algorithmically.) For this homework problem, you’re told the equivalent of: Sue’s Bike Shop sold 150 bikes last year… and you get a chart by brand of how many of each type. Then, your job is to figure out how many degrees the angle will be of, say, the Trek 7.5FX piece of pie.
The “worked example,” however, asks you for the percent and gives you the angle.
There is no whisper of the faintest clue that these are all proportions. The student tells me that the worked example they did (either in class, or the “explain” option in the pie pieces) has the students calculate the percentage and multiply that in decimal form by 360. Another student had learned to “Multiply the percentage by 3.6.”
I am confident that the teachers are including that concept, but I have this funny attitude that if concepts are supposed to be important, they should get more instructional real estate, at every opportunity, instead of going back to the “algorithms R us” mode so quickly. When I showed the student the relationship between the parts and wholes of the bikes of Brand X vs. all the bikes, then “percents — as if it were how many out of a hundred,” that light bulb thing started happening… and he is doing his best to learn things proportionally.
I *love* that the Math Literacy finds it worthwhile to teach and reinforce proportional reasoning … now let’s get that idea infused into the “practice,” eh?
(It’s in the “Nix the Tricks” line of thinking, but I don’t think this is a “trick” common enough to add to the site…)

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Posted in: math