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I am a volunteer math tutor. My student is in fifth grade. He was evaluated in August and found to be at the first grade level in math. (His reading is very close to grade level.)

He has epilepsy, memory problems and ADD, and has made slow but good progress.

This week I discovered he has a right-left problem that I wasn't aware of before. We were doing some color coding and there was a need to write the word "Red" on the board to label something. He wrote a backwards R, crossed it out, and said he couldn't do that. I asked if he'd like to write it lower case, and then he did, more happily. That was the first time I observed a left-right reversal.

The next day we were working on a multiplication activity, laying out chips in an array to model multiplication. We rolled the dice and got 7 * 3. He arranged the chips on the table in a 7 by 3 grid. Then I said, let's imagine that this shows us the apple trees a farmer planted. Let's say the farmer planted three rows of seven apple trees. He said, "There are 21 trees." (He's very proud of having learned how to multiply -- which we accomplished by skip-counting.)

I wrote the number 21 on a piece of paper, and asked him to multiply by 100. I reminded him of the shortcut we had done the day before, drawing two zeros after the number. He did that fine. I asked if he wanted to put the comma in, and he placed it wrong initially, so I helped him with that. Here's what the final result looked like:

2,100

Then I asked him to read the number out loud. He made two attempts:

"One thousand, two hundred

"One hundred, two thousand

I checked to make sure he wasn't trying to be funny -- he wasn't.

Then I wrote a number in words, and asked him to write the number. The text number was

Thirty-two thousand, six hundred forty-seven

Here's what he wrote:

000,032,647

When I suggested that the leading zeros aren't needed, and that erasing them wouldn't change how big the number is, he said, "No, don't erase them, I need them or I'll feel very confused."

Now, we did similar exercises about a month ago without any trouble. He was okay with numbers below a million. I noticed that past a million, all the digits started to swim around in his visual field.

It seems the right-left reversal is a symptom that comes and goes. But I need to find a way he can remind himself that numbers get bigger to the left. But without using the word "left," and remembering that anything involving right and left is liable to get confused.

I think I need a simple graphic mnemonic he can use to remind himself which side the ones column goes on, and which direction we go in order to get bigger numbers.

Suggestions? Please, nothing too fancy. This is a student who needs simple procedures. When his working memory was measured, it was found to be at the 6th percentile for boys his age.

What he can reliably do now: he can add one, two or three digit numbers together vertically with pencil and paper. He can carry reliably. He can add two digit numbers mentally in the context of the game, as long as there's no carrying. If there's carrying, he usually prefers to use pencil and paper.

He can also plot a number up to one thousand fairly reliably on a number line, and also go the other direction. It seems that once we get over three digits, things start to go haywire for him.

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    $\begingroup$ Just want to mention that I think this is a really good and important question. $\endgroup$
    – mweiss
    Dec 17, 2015 at 20:40
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    $\begingroup$ Is he strongly right- or left-handed, or is he somewhat ambidextrous or indifferent about which hand holds the pencil? If he is strongly one-handed, you could possibly use that as a guide to which side is the ones column (and decimal point), either the side closest to his writing hand or the side farthest away from his writing hand. $\endgroup$
    – shoover
    Dec 17, 2015 at 23:55
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    $\begingroup$ @aparente001: Especially if his mother has similar issues, you should consider the possibility that there's an underlying neurological phenomenon---dyslexia or something similar. That's not to see a mnemonic isn't useful, but identifying the issue and consulting specialists in that issue may be the most helpful thing. $\endgroup$
    – Henry Towsner
    Dec 18, 2015 at 2:27
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    $\begingroup$ Unfortunately, just pinning a dyscalculia label on the child doesn't bring a special magic wand to the problem. However, I can share some good news: when we started working together in late July, he could not add 8+2. Now he is solid with all addition and multiplication. We are making real progress and I am very proud of him. $\endgroup$
    – aparente001
    Dec 18, 2015 at 2:39
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    $\begingroup$ I am not a tutor. This question opened my eyes to what I hardly would have considered existing. Left-right reversal. Got me reading about it, made me understand your question better. Good question. $\endgroup$
    – KhoPhi
    Dec 18, 2015 at 9:07

1 Answer 1

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I think I need a simple graphic mnemonic he can use to remind himself which side the ones column goes on, and which direction we go in order to get bigger numbers.

Suggestion: Start making routine use of the decimal point, and perhaps instruct the student to always write that as a guidepost; note that it always goes at the end of an integer (to the right), in the same place as a period in an English sentence (thereby leveraging his intuition in that realm).

This has the advantage that it's not too distracting to other readers if he does it all the time (e.g., many calculators do this; as opposed to the lead zeroes thing). He can use this as a flag about where the "ones" place is (immediately next to it). If commas are desired, he can be instructed to always count from this anchor point. And then hopefully later on he'll have a head start in learning about decimal fractions that come after the point, if need be.

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    $\begingroup$ This is a brilliant suggestion, and just the sort of thing I was looking for. I had the feeling there was something simple, if I could only think of it -- and this is it. I am going to draw the parallel between the decimal point and the period at the end of the sentence, as you suggested. I'll exploit the symmetry around the decimal point. I have started doing tenths and hundredths with him. I'll make some place value cards, shuffle them, and ask him to arrange them on the table in a V formation, with the decimal point at the bottom. Thank you very much I will post next week with an update. $\endgroup$
    – aparente001
    Dec 18, 2015 at 1:37
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    $\begingroup$ Problem solved. We did a dice-rolling game with a 12-sided die, where he would write down the digit that he rolled, and keep going until he rolled an 11 or a 12, at which point he would write the period (decimal point). Then it was my turn, and I rolled and wrote, in this way, until I rolled an 11 or 12 and wrote my decimal point. If his number was bigger, he won. He enjoyed the game very much and it only took two sessions of this and the left-right reversal problem was resolved. $\endgroup$
    – aparente001
    Jan 29, 2016 at 18:20
  • $\begingroup$ @aparente001: Fantastic! $\endgroup$
    – Daniel R. Collins
    Jan 29, 2016 at 18:53

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