I read somewhere recently the words, Math is literally a code.

I won’t link to the author, their words, or the context because I have zero interest in engaging directly with online argumentation right now. But I do think it’s important for people doing the work of helping children make sense of math to have coherent perspectives available to them. So here goes…

The writer of those words offered the plus sign (+) as an example—it has a meaning that you cannot guess or intuit.

That last part is absolutely true. None of the symbols used in mathematical writing are guessable without either being told their meaning or having a tremendous amount of exposure from which to draw inferences.

In this way, mathematics is very much like language. The alphabet is also a thing you cannot guess at. There is no inherent connection between the form and the sound of the letter B (and indeed the letter B may take on different sounds in different contexts—more like a V in Spanish, indicating a high tone in Hmong.

But in the cases of both mathematical and linguistic symbols, thinking of them as codes means that they encode something.

What does the plus sign encode?

It turns out to encode a wide range of ideas that all share a structure we call addition. Having some and buying more, you’ll need a plus sign to encode that situation. You have five blue things and seven red things? Use the plus sign to notate that, even though there’s no action that makes anything bigger. Do you have money in the bank, and also owe somebody else some money? Oddly enough, the plus sign is useful there too, even though the sum is smaller than one of the addends, and even though you’re never planning to combine those into a single account.

If you’re saying math is literally a code, then you’re saying that only the symbols are math, not those underlying ideas above.

But then what do we call the ideas that the symbols encode? What do we call it when a child is counting out loud? Or when a child notices that there are ten radishes because they can match up one radish per finger twice, what do we call that? Surely we don’t we don’t wait for it to be encoded as 5 + 5 to call it math.

So no, math is not literally a code. There are aspects of mathematical work and practice that involve encoding and decoding, but those aspects are a fraction of what math really is. Just like children have ideas about words, language, and human relations that come from their experience and that precede their ability to decode words on a page, so too do they have ideas about numbers, patterns, and shapes that precede learning to decode the corresponding symbols.