As I watched my children play at the park one day this summer, my attention quickly focused on a small voice saying, “one, two, three, four, five…” I looked over and observed a game of hide-and-seek in progress. Even my youngest is self-motivated to recite the number sequence more accurately when she is playing. This, again, is a testament to the value of learning through play, which I’ve written about previously.
However, in this post I want to attend to number words. During hide-and-seek the number word sequence is not being used to count. Instead, use of the sequence seems to measure an amount of time and manifests the multilayers of meaning that number words contain. Vocabulary is an interesting topic overall, but this segment of mathematics vocabulary is especially interesting when we consider the meaning of the words.
Putting aside technical words that are specific to mathematics, let’s just consider the number words. For example, when we say “three,” we are speaking of two aspects: a group of 3 items, and the single items that make up the group of 3. Without even realizing, we use the word “three” with this dual layered meaning. Through meaningful experiences we have learned to use number words accurately. These experiences may have been a variety of actions such as:
- Hearing the word “three” associated with the symbol 3
- Counting 3 items
- Hearing the word “three” associated with the dot pattern of 3 like on dice, domino, or playing cards
- Hearing the word “three” associated with the written word “three”
- Hearing the word “three” associated with the finger pattern of 3
- Creating three items from a pile
- Assigning three items to the symbol for 3 (like the photo above)
I’m sure you can think of many more similar examples. When each of these experiences happen connections in the brain are made and become stronger around what will become the concept of the number 3.
When you magnify the process you began to see just how complicated a system the idea of number proves to be. At the age of 42, it is easy for me to assume that such a concept of threeness is trivial and to forget just how many experiences are behind my assumption. The researcher Ernst Von Glaserfeld said, “ …when children are taught arithmetic they are expected to ‘abstract’ the meaning of number words from the perceptual situations in which we ordinarily use them” (The Role of Figurative Patterns, 1982). We err in this expectation as adults and unwittingly fall into minimizing the importance and intricate construction that is occurring during these valuable mathematical situations. Perhaps this expectation is in part why we see so many with math anxiety and math phobia. Math needs to shed this idea of performance and become an operation that feeds our curiosity. In these last days of summer, play math. Ask questions like, “How many jelly beans would fit inside this jar?” “How many licks would it take to eat a scoop of ice cream?” Or “How many strokes does it take to get across the pool?” And next time you hear a child count, think about the complexities of what is happening and how moments like those are precious and invaluable.