It is difficult to understand mathematics, but it is one of the few ways students can see a large payoff from the struggle to understand. Using undefined variables as coordinates, displayed or not, is deception. Mathematics resides in the graph of the quantitative relation of measures of two fruit attributes, but I cannot see a way to measure or derive numbers for coordinates of undefined variables, and hence they are not quantitative. They are opinion.

Why do I think this is important?

Mathematics is a glimpse of both the difficulty and the possibility of understanding. Circumventing aspects that make it so leaves unique opportunities on the table. Students also need to see how the appearance of mathematics is used to lend undeserved weight to arguments.

I gave it a shot a long time in a lesson I regret for obvious reasons of sexism and objectifications, but I still like the illustration of the coordinate plane’s value. The dot plots don’t reveal anything all that interesting by themselves, but when you plot them *against* each other, the association *pops*.

*Exciting title!*

Now is a good time to think about graphical “tricks” with apparent mathematics in information display. For a good case study I suggest following the google trail of “Mathematics as Propaganda” by Neil Koblitz to Serge Lang and Samuel Huntington.

It takes you back to 60’s to see mathematics playing the star role in the real world. The issues it raises on the use of mathematics are still relevant in the application of social science to education.

]]>My initial idea for a revision would use one-dimensional lines. First I’d ask the students to place the fruits on a line to rank the tastiness of each fruit. I’d repeat the process, but this time I’d ask for the students to rank the difficulty of eating each fruit. Then the pivotal questions becomes, “Can we represent or communicate both pieces of information about the fruit in one image/representation?” My hope is that this would facilitate some thoughtful conversation and even allow the students to invent the idea of a plane. And after that, how natural is it for students to wonder, “What would a 3-dimensional system look like? 4-D? 5-D?”

Thanks for sharing all of this. Keep up the great work, Desmos!

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