Quiz: Describe How and Why Math Works
Math test today. I'm tired. We were quizzed on solving systems of linear equations. A lot of the test focused on using matrices. We were allowed to use calculators for part of the test.
I think I understand pretty well how to add, subtract, and multiply matrices as well as how to divide matrices by multiplying a matrix by its inverse. (We'll see how well I understand when I get the test back!)
But I have been a little confused about why some of the math works. In particular, I'm not entirely solid on the process for finding inverse matrices. Without getting too much in the weeds, to figure out the inverse of a matrix you have to find something called a determinant and then plug it into a formula that involves changing the position or the negative signs within the matrix. Forgive the oversimplification. (Or feel free to put it in words better than I just did!)
It's difficult to describe how or why math works. It's easier to just write the formula and say, "Do this." Several readers have commented on this blog that what's often missing from math education is more of a focus on why certain applications work. I agree. It's harder to remember what to do, if you don't have some sense of why it works.
A worksheet that the teacher, Tricia Colclaser, handed out after the test came close to addressing this. Titled "Math Journal," it asked us to explain how to determine whether two matrices can be added or subtracted or multiplied. Colclaser asked the class to "explain in a sentence, a full complete sentence."
Here's a primer on inverse matrices and a look at the formula for finding them - if you want to review.
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