Yesterday I was working with a student who was doing the “integer addition” activity. For the problem “9 + -5” the student would write 9 letter Bs and 5 letter Rs.

This is an extension of “adding with chips” such as is shown here: https://www.youtube.com/watch?v=7x7H09-Cca4 (I’m liking this tho’ I just posted it ’cause it was the first one). An even crazier version of this is Integer Eyes.

Usually the students just write the letters in a row. This student neatly wrote them in multiple rows.

At first I thought that the student had teh number sense to be doing some grouping but… the numbers in each row seemed to be random. They’d been shown that R & B added up to zero, & “zapped” each other (not as a “trick” but as a model)… but at first she was treating all the letters the same so if it were -3 + -4 the answer was -1.

She could get it on the number line, once she learned not to plop both numbers on the number line, but to pay attention to direction and change 😉

I think doing things in both formats was a benefit, though, because at the beginning of the exercise she was excising R… B R… B, one at a time (once she knew to check to make sure they weren’t the same letter). I suggested that she put the same number in a row (I couldn’t figure out a pattern; anywhere from 3-5 would go in a row and then she’d start over, and it would be different for the R’s and the B’s in the same problem).

The idea that she could just “cross out” five B’s and then 5 R’s … and then continue from there… was news. This is consistent with math ed development stages…

… and we can work with that, *without* going back to elementary math. Context is everything…

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howardat58

March 9, 2016

I give up with the teaching of “negative” numbers. I had a look at the Integer Eyes video. If teachers were not so obsessed with the idea that whole numbers were for counting they might give some thought to real applications of signed numbers such as temperature. The red and green dot thing is NOT going to help anybody understand the uses of signed numbers, and so can hardly be called a model.

xiousgeonz

March 10, 2016

This student still hadn’t gotten past “counting from one;” starting where students are is, in my opinion, pretty important.

It is a huge struggle to get students to recognize that -4 is, actually, different from 4.

NOw, I haven’t used the Integer EYes (I also think it crosses into “distracting”), but … I have seen the R’s and B’s help students understand the “opposite” nature of negative and positive. Happily, they didn’t know it wasn’t supposed to help them understand.

OH, and they’d already spent a fair amount of time working with thermometers and number lines.