# Elementary School Mathematics Education Mysteries

Since these two problems are really the exact same problem, in two different forms, why not just use “x” to teach it, from the beginning, in elementary school, instead of using the little box? The two symbols have the exact same meaning!

To the possible answer, “We use an ‘x’ for multiplication, instead, so doing this would be confusing,” I have a response: why? Using “x” for multiplication is a bad idea, because then students have to unlearn it later. In algebra, it’s better to write (7)(5) = 35, instead of 7×5 = 35, for obvious reasons — we use “x” as a variable, instead, almost constantly. This wouldn’t be as much trouble for students taking algebra if they had never been taught, in the first place, that “x” means “multiply.” It’s already a letter of the alphabet and a variable, plus it marks spots. It doesn’t need to also mean “multiply.”

Why are we doing things in a way that causes more confusion than is necessary? Should we, as teachers, not try to minimize confusion? We certainly shouldn’t create it, without a good reason for doing so, and these current practices do create it.

These things may not be mysteries to others, but they certainly are to me.

[Note: for those who do not already know, I am a teacher of mathematics. However, I do not have any experience teaching anything at the elementary level. For this particular post, that’s certainly relevant information.]

# A Polyhedral Demonstration of the Fact That Nine Times Thirty Equals 270, Along with Its Interesting Dual

It would really be a pain to count the faces of this polyhedron, in order to verify that there are 270 of them. Fortunately, it isn’t necessary to do so. The polyhedron above is made of rhombus-shaped panels which correspond to the thirty faces of the rhombic triacontahedron. Each of these panels contains nine faces: one square, surrounded by eight triangles. Since (9)(30) = 270, it is therefore possible to see that this polyehdron has 270 faces, without actually going to the trouble to count them, one at a time.

The software I used to make this polyhedron may be found at http://www.software3d.com/Stella.php, and is called Stella 4d. With Stella 4d, a single mouse-click will let you see the dual of a polyhedron. Here’s the dual of the one above.

This polyhedron is unusual, in that it has faces with nine sides (enneagons, or nonagons), as well as fifteen sides (pentadecagons). However, these enneagons and pentadecagons aren’t regular — yet — but they will be in the next post.