Thursday, October 29, 2015
3 x 5

Supposedly the purpose of the Web is to have LINKS that lead you to a deeper or more original source. This story about an overly literal math teacher fails the Web standard. Every iteration of the story includes this bit:
The National Council of Teachers of Mathematics (NCTM) in the US defended how the paper was marked, saying it gives students a better understanding of the problems they are solving. "Part of what we are trying to teach children is to become problem solvers and thinkers," said Diane Briars, president of the NCTM. "We want students to understand what they're doing, not just get the right answer."
but no iteration includes a link to the NCTM's actual statement. Google doesn't get there by any keyword I can think of.

If this is ALL Briars said, she's flat wrong. I doubt that this is ALL she said, but I can't find the rest of it or the context.

There's nothing new about using rectangular arrays to show addition and multiplication. Normally the WHOLE POINT of doing the array thing is to give the student a strong visual feel for the commutative property, the idea that 3 x 5 and 5 x 3 are always going to give you 15. It doesn't matter if you see the array as 3 groups of 5 or 5 groups of 3. It's 15.

The teacher is blowing the WHOLE POINT of the array method by marking the kid wrong for switching the rows and columns. Switching the rows and columns is EXACTLY WHY YOU DO THIS EXERCISE.

= = = = =

Footnote for clarity: I'm not intending to bash the teacher. I suspect she's inexperienced and overwhelmed by CC. She may have made a simple mistake. I'm bashing Briars of NCTM, who has issued an authoritative message approving this mistake on behalf of all math teachers. Not in my name, Briars!

= = = = =

Few days later: Some tech-tyrant asshole tried to defend the bad marking. He cited two vague connections: (1) Equal isn't the same thing as Equivalent in Javascript. Huh? That has nothing at all to do with math. It's solely about Javascript's peculiar and inconsistent ways of converting strings to numbers. (2) Matrix multiplication is not commutative. Valid in itself, but irrelevant for a 3rd grade class. At this stage you need to get a FIRM GRASP on the commutative property, because it's crucially necessary for all sorts of algebraic manipulations. If part of your mind is thinking non-commutative, you'll be lost in algebra.

I've been programming about graphics and waves for 30 years, and I've NEVER had to use matrix multiplication. I use the basic properties of sin, cos, tan, and polar-to-rect conversion every day. You could say those are closely related to matrices, but I've never felt the need to do actual matrix ops.

Nearly all the commenters soundly lashed the tech-tyrant asshole from a wide variety of angles. Refreshing and reassuring.

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Polistra was named after the original townsite of Manhattan (the one in Kansas). When I was growing up in Manhattan, I spent a lot of time exploring by foot, bike, and car. I discovered the ruins of an old mill along Wildcat Creek, and decided (inaccurately) that it was the remains of the original site of Polistra. Accurate or not, I've always liked the name, with its echoes of Poland (an under-appreciated friend of freedom) and stars. ==== The title icon is explained here. ==== Switchover: This 2007 entry marks a sharp change in worldview from neocon to pure populist. ===== The long illustrated story of Polistra's Dream is a time-travel fable, attempting to answer the dangerous revision of New Deal history propagated by Amity Shlaes. The Dream has 8 episodes, linked in a chain from the first. This entry explains the Shlaes connection.

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