We like games at our house, but there are rules that one has to follow when using them. And the rules are not just for playing the games (those we actually often modify at will), but there are also rules for putting it away (which are stricter).

One of the rules when putting away the game BLOKUS (a favorite) is that you have to count the pieces and make sure that there are 21 of each color. Today, after playing with the game, Zoe (4.5 yo) diligently picked up a bag and started putting blue pieces into it. She counted normally until 7, but then she put in the next piece and said “nine”.

I naturally thought that she just forgot about 8 and pointed out to her that she skipped it.

“I’m counting by 2’s now,” she said.

“But you put in only one piece,” I countered.

Zoe looked at me with surprise. Without any words, her look said it all: “Yes. And?”

“When you count by 2’s,” I explained, “you have to put in two pieces.”

“Oh,” said Zoe, and took out the piece that she had just put in. Without any questions, she picked up a second piece, put them both into the bag and triumphantly said “nine” one more time.

Zoe then proceeded to count the remaining pieces by 2’s, making sure to put in two pieces each time.

I was surprised that Zoe didn’t ask me why she had to put in 2 pieces at a time. It must have made sense to her. And yet, she was perfectly happy counting by 2’s and putting in one piece before I pointed this out.

I have actually seen this phenomena before. Kids understand the concept of counting by 2’s and are good at figuring out the sequence of words, but then when it comes to counting physical objects they don’t connect it to counting 2 of them at a time.

I think that Zoe understood the connection this time, but I won’t be surprised if she makes the mistake again before fully internalizing it.

What similar misconceptions have you noticed children having?

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## About aofradkin

I enjoy thinking about presenting mathematical concepts to young children in exciting and engaging ways.

I’ve seen it with older kids with fractions. They learn what 1/3 is or 1/2 but then when faced with actually using those measurements in the kitchen, they aren’t sure what to do. For example, a recipe may ask for 1 1/2 cups and they read it as 11 cups or divide 11 by 2, or ask how to measure it if they read it correctly

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I believe the way to avoid confusion between 11/2 and 1 1/2 is always to write a fraction in a proper way, with horizontal division line. As for the second case that you described, it takes time and is similar to what is described in the post. It requires a psychological extra step and comes with a practical use on a regular basis.

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I think you need to work with manipulatives from the day one of using skip counting.

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I was going to comment on this when I found this recent post:

https://discoveryandconjecture.wordpress.com/2017/06/27/unit-switch/comment-page-1/#comment-38

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Misconceptions are such wonderful opportunities. They are so often based in solid, though mathematically faulty, reasoning. Acknowledge the solid – correct the faulty!

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