**UPDATE: **With a tip of the cap to Mathalicious for pointing this out to me, here’s a link to a lovely related Radiolab episode.

Having seen her brother count to 120, Tabitha (just barely 4 years old at the time) was eager for her turn.

### tabitha counts

Those familiar with the development of counting in young children should have some strong instincts about answers to the following questions:

- How far will she get?
- Will she make any errors along the way?
- What do the answers to these questions tell us about English number language?

I’ll use this task in my math content course for future elementary teachers next fall. If you teach such a course, by all means use it and report back on what kinds of discussion it generated from your students.

Question for you:

Why did I “know” she would not get further than the 20s?

One should also let students know that there is a wide range of counting skills at that age, from those who can’t make it to 10 through those who can count accurately into the 100s and do addition and skip counting. That was about the age that my son learned to count on his fingers in binary (I may be off by as much as a year, since it was over a decade ago now).

A lot depends on how much counting the kids have seen modeled at home, and how much numbers appeal to them.

Mary:

I don’t know. You tell me. What knowledge

didyou draw on ?gasstation:

Agreed.

But whatever age they hit it, this is a very typical stage of development that demonstrates an awful lot about what it means to learn number.

My father asked me when Griffy was about three,

Does he know how to count?This video demonstrates that this isn’t really a yes/no question. Does Tabitha know how to count? We can see from the video that she knows most English number words up to twenty-nine, and she knows some of the patterns inherent in those number words. We cannot see whether she connects those number words to quantity (i.e. cardinality); we cannot see whether she understands that there must be a one-to-one correspondence between number words and objects when counting a set, etc.Yes, I’ll issue the appropriate caveats. But the video really is a way of making

learning to countproblematic for future teachers-to help them understand in a visceral way that this is worth studying.This is interesting. My daughter is two and turns three this week. Maybe I’ll watch and listen carefully next time she counts and try to make some observations.

I read One Fish Two Fish by Dr. Seuss with my three year old, Tatiana. There is one character in the book who has eleven fingers (seven on one hand, four on the other.) Tatiana had no problem counting seven fingers on one hand, and pointed to each finger as she counted it. The weird thing is that when she got to the four-fingered hand, she kept counting “one, two, three, four” for the four fingers as she pointed to them and then “five” , pointing to the hand where a fifth finger should be even though there was no fifth finger on that hand, no matter how many times we counted the fingers. It was as if she could no comprehend that a hand could exist without a fifth finger (although a few extra fingers didn’t seem to bother her!) Is there any mathematical reason for this?

Alex:What an interesting story!

My gut instinct would be to say that she has probably had lots of experience counting fingers on real hands. And that she associates very strongly this experience with the sequence “one, two, three, four, five”. Hence the continued counting-it’s part of what you do. But the fact that the counting

stops at fiveis less salient to her. Perhaps because the counting doesn’t always stop at five. Sometimes, we count the fingers on both hands and plow right past five. But we never stop at four.Evidence to collect to test this theory includes having her count other sets of four. Four toes on an imaginary creature? Four legs on a cat? Four wheels on a car? Does she continue on to five in those cases, too? I’m guessing “no”. But I’m curious about the toes.

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