Having an almost three year old daughter leads me into deep philosophical questions about mathematics. :-) Really, I am concerned about the concept of "being able to count". People ask me if my daughter can count and I can't avoid giving long answers people were not expecting. Firstly, my daughter is very good in "how many" questions when the things to count are one, two or three, and sometimes gives that kind of information without being asked. But she doesn't really count them, she just "sees" that there are three, two or one of these things and she tells it. Once in a while she does the same in relation to four things, but that's rare. Secondly, she can reproduce the series of the names of numbers from 1 to 12. (Then she jumps to the word for "fourteen" in our language, and that's it.) But I don't think she can count to 12. Thirdly, she is usually very exact in counting to four, five or six, but she makes some surprising mistakes. Yesterday, she was counting the legs of a (plastic) donkey (in natural size), and she had to move around to see all of them: she managed to come to the conclusion that the donkey had six legs. Fourthly, she usually forgets one of the things or counts one of them twice when she is counting to seven, eight or nine. Finally, she never asked her parents what is the number "next" to some other number (say, the numbem "next" to twelve). Now, do you think that she can count? And to how many things can she count?
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