I’m liking our new “math literacy” course. It’s still a challenge, though, when the student is presented with a problem and I want to shine a flashlight on the path to figuring out how to do it, not plop them in a motorized cognitive wheelchair and zip them to their “got the assignment done” destination.

They are to devise a spreadsheet to calculate teh amount in an account for which they start with 2000 dollars and add 175 per month, with the number of months in one column and the value of the account in the second.

Welp, since I hadn’t read ahead (which I couldn’t do for a while because I didn’t have the text), *I* got briefly stalled wondering whether or not they put in 175 on that first month, and thus whether there shoudl be a “zero” month, but let the students decide and it worked out.

Figuring out the formula was interesting… but what was effective for many was to ask how much money would be in the account in three months and/or five months…. most of them could do that and then we could work back from what they did to what that looked like as an expression. Not everybody, though: $2175 x 3 was one answer… I wish I’d had time to have her calculate that and see whether or not she realized that wasn’t consistent with adding 175 per month. Still, starting with a concrete, real example was useful in making the connection between the fixed and variable cost — and the fact that it took trial and error speaks to the likelihood that in the traditional course with a whole mess of problems to practice, they’re not making that cognitive connection either.

I have evidence that students *are* using their own number sense, though it’s not fun to watch. They’re to figure out via trial and error how many beers, sodas and hot dogs a guy sent his kid to buy (yes, the problem mentions that the guy gets arrested for sending his kid to buy beer) if he sent the kid with a hundred dollars, and he gets 25.50 in change, and there were 8 beverages purchased… Beer costs 8$, soda 5$, hot dogs $3.50…

…. so the scratch paper says 8 + 8 + 8 + 5 + 5 + 5 + 5 + 5 (calculator for calculations). I encouraged using the times key…I wonder if having visuals come up when you clicked that multiplication would be valuable.

And speaking of visuals, on the ride in through the sleet and rain (on the Xtracycle, since my studded-tyre bike flatted again last night coming back from the convent), I thought about showing fractions with the denominator a nice colored rectangle broken into as many pieces as the denominator indicted… perhaps with an animation shading the number of said pieces indicated by the numerator.

*math literacy, numeracy, visual math*

Opus the Poet

February 27, 2013

I had a flash of inspiration on that one: Start with a circle, then draw radials until there are as many wedges as the denominator, split the wedges apart than morph them into squares so that the student can see that fractions are a part of a whole, then shade the number of squares for the numerator.

And from the problem given above we can deduce that there were an odd number of hot dogs purchased, because hot dogs were the only item listed with $0.50 in the price and there being $0.50 in the change. That’s actually a difficult problem to answer because you have so many variables that trial and error won’t work without excessive recursion. the equation is simple enough 8x + 5y + 3.5z = 74.5 but that is about as far as you can simplify it because of a lack of common factors. You could multiply both sides of the equation by 2 to get rid of the fraction/decimal, but you still end up with a prime that isn’t a common factor to at least one other term. Not to mention that 149 (the result of 74.5*2) doesn’t have a whole lotta factors either.

Competent math teacher

March 4, 2013

You didn’t specify the grade level, but I hope it’s not later than fourth grade; otherwise, this would be a really dumbed down lesson (which needs work anyway).

xiousgeonz

March 4, 2013

Why do you think it is “dumbed down ” (brought ‘down’ from where?) ? How would you improve it? (No, it’s not my lesson and no, I’m not wedded to it… just curious about others’ perceptions.)

xiousgeonz

March 5, 2013

Could you elaborate?

One of the most serious issues my students have with math is that their instructors really, honestly have no idea how they think about math… and so they tend to assume reasoning that isn’t happening.