Spiraling (out of control) math
Day 5 of third grade saw "expanded notation" come round again. That's where kids have to write a number as an addition problem. 45,100 becomes, for example, 40,000 + 5,000 + 100.
"This is stupid!" Big Guy complained. "I don't see why we have to do this."
Neither did I until I googled. I knew enough to know it's part of the "spiraling math" concept in vogue, but I wasn't sure what taking the long way to write a number is eventually supposed to spiral into.
As it turns out, it's algebra. It seems that writing 40,000 + 5,000 + 100 prepares them for the idea of writing (4 x 10,000) + (5 x 1,000) + (1 x 100). That, in turn, gets them ready for ax2 + bx + c=0.
"Understanding expanded notation may be the single most important thing to understanding how our (and other) base systems work, and is the basic building block of understanding numbers and how to use them," one enthusiast wrote. He also claims that he can calculate faster using expanded notation, but I'm not convinced.
I'm not really convinced about the whole "spiraling math" concept. The idea is to touch lightly on subjects in the early grades so that when the time comes for higher math students will have the background.
Very soon in Big Guy's class that will lead to lessons in Chapter 2 of their math book on the various properties of addition. I need to bone up right now on commutative, associative, etc., because those definitions flew out of my head years ago.
The hope is that it will stick in Big Guy's head until he gets to eighth grade, but I have my doubts.
Start with the sample questions in the lessons about the properties of addition. They're written at an 11th-grade reading level, which means the good readers are going to need serious parental intervention to even understand what they're supposed to solve, and the weaker readers are going to be lost.
Add to that his confusion this week on expanded notation. They'd "touched lightly" on that concept in second grade, but didn't spend enough time that it stuck in his brain until this fall. So much for the "spiral toward mastery" theory. Yes, he remembered it after I reminded him, even though he still thought it was stupid.
I doubt he'll remember mean, mode and range when it spirals around again either. He regarded last year's whole experience with it as a nightmare best obliterated from his memory.
Ay, but when they finally get to multiplication in Chapter 4, the lessons are actually too easy. The focus on one quiz I found online was on "repeated addition." I suppose that's because they spent so little time last year learning multiplication tables because "drill and kill" is bad.
While I mostly agree with that - books, not sight words, teach reading - there are some things that you just have to go through the drill to learn. Multiplication is one of them.
You could dismiss this all as just the gripe of a mom frustrated with re-learning math to help her frustrated kid understand it. Except I'm not the only one exasperated by spiraling math. So are some professionals. They see what happens in the classroom - and on the tests - and they don't like it.
Unfortunately, I'm stuck with it. That's why, if you need me when Big Guy's class gets to Chapter 2, you'll find me crawling into a closet in hopes that commutative and associative properties can't find me there and hurt me.
Copyright 2011 Debra Legg. All rights reserved.