Addition Tally Marks

I was working with a 2nd grader yesterday on addition. Instead of having kids memorize the addition table, we encourage them to use number sense.  Example, most kids are good at adding doubles, 6 + 6, 4 + 4, etc.. (from playing Monopoly?).  So we encourage them to see 6 + 7 as 6 + 6 + 1, or 6 Double + 1 instead of memorizing 6 + 7 = 13.  Kids who learn addition this way still end up ‘memorizing’ the addition facts table, but along the way, build a stronger number sense and mental math skill.

So Christina, Grade 2, was practicing adding doubles plus 1: 5 + 6 = ____;  7 + 8 = _____; and so on.  I was observing her and noticed that she would pause first, look far into the distant blue yonder, then write down the answer.  It was slow, but the answers were accurate.  I was pleased with myself that she was applying this doubles plus 1 technique so well.  But after watching her do this gaze-into-the-blue yonder thing for every problem, I couldn’t resist asking her.

Me: “Christina, when you look up into the distance, what are you thinking?”
Christina: I am adding.

Me: And what are you saying to yourself or seeing in your mind when you are adding?

Christina: I see tally marks.  And I add them one by one.

Me: Does it give you a headache?  If I have to see more than 3 tally marks in my head, I get a all muddled up.

Christina: Not me.  I can see 20 tally marks, no problem.

Me: Wow, that’s quite a skill.  Hey, want to know how I do it since I’m so bad at seeing tally marks in my head?

And I proceeded to demonstrate the doubles + 1 technique, and have her mimick it a few times.  She finished the rest of the work sheet without the blue-yonder gaze.

This encounter made me realize that sometimes we explain a math concept, we think the child gets it because the answer looks right, but he/she really doesn’t.  Instead of telling you, this big know-it-all adult, that what you are saying doesn’t make sense to her, the child coninues to resort to old comfortable, though less-effective techniques of getting to the answer.  This may also be why in a big classroom setting of 20, 25 kids, children can fall behind without the teacher noticing.

How to avoid these situations? Simple, just ask the child to explain their steps back to you by asking questions like below:

Q. Nice job, how did you solve that?

Q. That answer is correct! How would you explain to a friend how you did that?

Q. What do you see in your head when you were thinking about that problem?

Q. Can you think aloud?  I’m interested to hear how you think about this.

Q. Pretend I’m your friend, and I just don’t get this.  Can you help me?