At first, numbering seems to require fingers and toes
Counting is one of the earliest forms of abstract thinking that we teach pre-schoolers. To really get this technique, it seems, the young have to encounter it in many different circumstances until they are able to extract this technique from its contexts and understand they can use it anywhere — to count trees, say, or apples or babies. At first, of course, numbering seems to require fingers and toes. About this time, numbers are also encountered in nursery rhymes:
“One, two, buckle my shoe,” “This old man, he played one,” “Five little Indians jumping on the bed.”
Taking this development a little bit further, books can be useful. In that regard, I like Leo and Diane Dillon’s Mother Goose Numbers on the Loose because it’s a handy collection of nursery rhymes that involve counting (you will remember, for example, “One Potato, Two Potato” and “Baa, Baa Black Sheep”). I also like 1 2 3 4 U by David Horvath and Sun-Min Kim but for different reasons: because it is a board book (perhaps the most appropriate format for hands-on or teeth-on learning at this age) and because it’s zany.
Books about counting divide into two kinds: there are those where each page is (more or less) its own thing though often sequential, and there are those which endeavor to tell a continuing story as we move from one number to the next. In this latter category, my favorite is Maurice Sendak’s One Was Johnny which tells the growing complications faced by our young cowboy hero and how he gradually undoes a Cat-in-the-Hat-like mess that grows up around him.
These are my favorites, but I also asked others about theirs. My local children’s librarian took me to find Olivia Counts and Anno’s Counting Book; but because they were so popular, the place where they would have been was vacant.
My favorite first-grade teacher, my daughter, had one answer: “Hands down, Ellen Stoll Walsh’s Mouse Count — which is available in a bilingual edition.”
It goes without saying, then, that it is still a long way from here to figuring out a restaurant tip as a percentage of the bill. But, remember, the journey of a thousand miles begins with — well, one or two or three or 3.5 steps. Expose the young to enough and varied examples of counting and, eventually, they will be able to abstract this skill and apply it where they like — for example, in the delighted enumeration of cookies on a plate, or in the more annoying habit of counting cars that pass by.
At this point, however, it should be admitted that math education can only go so far. The young can answer many, many questions of their own by making use of acquired measuring skills. But as near as can be determined, they will forever be unable to use those same skills to answer two eternal questions: “Are we there yet?” and “How many days until Christmas?”
A version of this essay originally appeared in Parents’ Choice (November 2009).
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