Saturday, December 21, 2013

Favorite comments of '13 continued: Julie in GA and Auntie Ann

on Conceptual understanding under Everyday Math

Julie in GA said...

My 2nd grader's school supposedly uses a "balanced" approach. ThinkMath and Harcourt materials for math. I think they use ThinkMath's instruction, but send home Harcourt pages for homework.

His math homework for this week is a single worksheet on 2-digit addition with regrouping, but the teacher attached a note with a copy of a hundreds chart, with instructions to use the hundreds chart or partial sums to solve the 14 problems.
From the weekly newsletter:

"We will continue to add 2 digit numbers. We will work with base ten blocks in small groups for adding. For their homework, I have attached a hundreds board for them to use. Please do not teach them the algorithim. We haven't gotten there yet. Right now, they have learned to use the number line to skip count by tens and ones, to use the hundreds board, and to add using the break apart strategy with place value (example: 56 + 23 they would do 50 + 20, then 6 + 3, then 70+9= 79)"

So I asked my son to show me the partial sums method she wants them to use. I never learned it, so I had no idea what it was...and yet I can easily add 2 digit numbers (imagine that). He didn't seem to know how to perform partial sums either. So he defaulted to the hundreds chart to add. 46+38 37+39 etc.

Bad parent that I am, I showed him how to solve the problems with regrouping. It clicked. What would have taken him forever to do on a hundreds chart, took him 5 minutes.

I am so sick of the word "strategies." They spend lots of time discussing strategies and very little time on anything else.

Auntie Ann said...
What I don't understand about many of these methods, is that they require the students to write many more things down and do many more calculations. Each of those extra pieces is a place where errors can creep in. At an age when kids' handwriting can often be illegible, having them write down more numbers is just opening up the door to error.

Here's another article relating fluency of math abilities to chemistry ed: 
In addition, we argue that these results indicate an inadequate degree of mathematics fluency for the majority of the students tested, which can seriously impede their abilities to develop a firm conceptual understanding of quantitative introductory chemistry.

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