Saturday, November 15, 2014

Counting Backward...and Why It Matters

By this time in the school year, many of my first grade friends are pretty comfortable with counting forward. Sometimes it sounds like this, in warp speed:


But ask them to start with a number other than one and everything changes:

Count from 5 to 13.

Count from 18 to 25.

Count from 23 to 31.

Suddenly, student comfort levels become more apparent.

But if you really want to know how fluent students are with number sequence, ask them to count BACKWARD.

Quite a few will rattle off 10 - 1. But ask them for other sequences and you'll soon discover things you might not have known.

Count backward from 13 to 5.

Count backward from 17 to 9.

Count backward from 27 to 19.

I've recently been doing some intervention work in first grade. Some students can slowly and methodically count back. Others really struggle. In a few cases, I would never know about their lack of confidence with number sequencing if I had only asked them to count forward.

It's interesting to see what strategies they use. Today I watched one little boy do this:

17, um...

(whisper counts on his fingers, 1, 2, 3, 4, 5, 6, 7...6),


(whisper counts on his fingers, 1, 2, 3, 4, 5, 6,...5),

15, etc...

Based on his whispers, it appears that he understands that the order of numbers repeats in the teens, but he must go back through the single digit numerals to figure out which ten & something digit comes next.

Some kids need written support to count backward. If they ask for help, I write their responses in a double ten frame as they count:

27, um..., 26

I continue writing, recording each number as they say it:

After working with a hundreds grid for quite a while, the double ten frames look pretty familiar and they can usually relate to the decade numbers being on the far right.

Robert Wright's (et al) book, Teaching Number in the Classroom with 4-8 year-olds, has many ideas about the relevance of backward number sequences in mathematics. Here's a sample:
"Children might omit a word in the backward sequence which they do not omit in the forward sequence, for example, sixteen, fifteen, thirteen, twelve, and so on. This error can be persistent and can result in errors when using the backward sequence for subtraction, for example, 17-4 as sixteen, fifteen, thirteen, twelve!." (p. 35)
 What insights have you gained from asking students to count backward?

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