Where on this graph would you find the best sprinter of all time?
In class today, a bunch of kids said that the best ever would be at the top of the graph. It took a few seconds before a wise soul pointed out that the best would be at the bottom of the graph. But at first, that’s hard to see!
The hardness of this has to do with an idea that’s pervasive in our culture: up is better. In Metaphors We Live By, Lakoff and Johnson argue that status, virtue, wealth and many other positive attributes get an “up” orientation in our language.
After a student makes a point, I sometimes ask them “What’s the ‘therefore’?” In this case, the ‘therefore’ is just about awareness. To understand that “down is better” in this graph, we have to go against our conceptual tendencies. Students are going to make this mistake, but maybe we can help by pointing out that graphs often go against the “more is better” metaphor.
Or maybe something else entirely is going on here? What do you think is happening? Where else do you see issues like these arising in understanding math?