Intuitional Math

Frustrated Father made some news when he wrote a letter to a teacher expressing frustration over the new style of teaching math:

I have a bachelor of science degree in electronics engineering which included extensive study in differential equations and other higher math applications,” he wrote. “Even I cannot explain the Common Core mathematics approach, nor get the answer correct.

Mindful Mathematician responded:

The “new” methods you’re seeing are not being taught. They are methods that students naturally invent. Just the way that mathematicians invented them before our formal mathematics system existed. Believe it or not, simplicity and efficiency are at the forefront of our classroom discussions EVERY day. We are guiding students through their own sense making methods not only to understand numbers and operations but to find the most efficient methods for each problem.

I was first confronted with the brave new world of math teaching when I was doing sub-work. I ended up writing a post about it. The method taught in Arapaho schools, “Cluster Math” appears to be mildly different from the worksheet, but the thought behind it seems to be the same. Old Math was strictly algorithmic. As MM says, you didn’t always know why you were doing what you were doing. You just learned how to do it. It’s not quite rote memorization as MM suggests, but unlike the new stuff it is fixated more on getting the right answer than understanding why it’s the right answer.

The algorithmic method is still what I prefer. That’s not mutually exclusive with other ways of getting the answer and indeed, sometimes the math I do in my head actually more closely resembles what is being taught. I do think, though, that it was best for me that I went through algorithmic and came out the other side.

A few people scoffed at Frustrated Farent for making a mistake in his own work. The Frustrated Parent actually sees it as a sign that the new way is deficient, which isn’t quite right. Critics of FF suggest that he shouldn’t be saying much since he himself is prone to error. The thing is, though, my somewhat limited experience in Arapaho demonstrated to me that error-proneness is precisely the problem with the new method. As I previously described it:

Kids try it out one way, hit a wall, then start over. Before you know it, they have multipliers or 38 written down all over the place and when it comes time for the final addition, they don’t know which counts. In the above case (38×27), his answer was over 2,000.

Maybe the new new math isn’t prone to this sort of error. I do know that for me, knowing the best and quickest way to get the right answer helped me figure out other ways to get to that answer. Perhaps that’s redundant in the Age of the Calculator (on your phone, which you have on you at all times). For my own part, since I am very much the sort of person that forgets which 38 gets applied to which problem, I am not at all optimistic that any method other than the one I was taught would have worked as well (though the Lattice Method, which I was also taught, was fun).

For other kids? I don’t know. I do know that I am a bit disturbed by the Culture War aspect of this. That includes parents high-fiving FF for the wrong reasons (and I do think some are) but also those scoffing at any skepticism towards the new teaching as being anti-math or anti-education. And/or making fun of their computational errors.