Last week I offered some review each day on coordinate skills, as we have ACT coming up next month.
Rather than posting 2 points and the midpoint formula, I only wrote the word midpoint and 2 points, then asked for a point they knew was NOT the midpoint.
As they responded with wrong answers, I asked them to convince me (ode to @steveleinwand) -how did they KNOW it wasn’t the midpoint? And their responses were varied from number sense to a graphical picture, always referring to betweeness, not exactly in the middle. I cheered them on-that their reasoning here could help them eliminate wrong answers on ACT.
Someone asked, isn’t there a formula? Me: Yes. Do you know the formula? … well. Does anyone KNOW the formula? …. silence… finally, a student asked, Is it something like x1-x2 divided by 2? And y1-y2 divided by 2?
Hmmm. I wrote it down and said, let’s try it. The result, students quickly said, no, that doesn’t work, explaining why.
My issue with giving a formula and working multiple problems…about 60-70% (my guesstimate) forget the formula, not because they can’t use it, but because they never move it from their working memory to long term, it’s not internalized. They use it for an upcoming test, then trash it and move on to something else.
In both classes, students intuitively found the distance between the coordinates, divided by 2, then counted that many units from either endpoint.
As I asked my students why so many were not math fans, one student stated – because there’s only 1 way to do the problem and if you don’t get it, you’re doomed.
I said to her, you are exactly right. And you are exactly wrong.
There’s never just 1 way to solve a problem. But often times, students are only presented with 1 way. So when they don’t get it, they give up.
In the end we had multiple ways suggested to find the coordinates of the midpoint, and they were all correct. Similar to these…
It continues to make me sad that students think there is exactly one way to do every problem. I am slowly trying to change their mindset.