counting: Is accumulation a visual way for counting?

[shahar]

Is accumulation a visual way for counting?

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[Dr.Peterson]

What it says is:

Addition is simple, yet it can mean several things:

• Accumulate: Count up similar quantities (often for tangible items).
• Slide: Shifting a number along a scale (for less tangible things, like temperature).
• Combine: Make a new quantity out of two different ones (like notes in a music chord).

These are different ways to apply addition. They are not intended as methods for doing addition, though they can sometimes help to think about it. (For instance, accumulation can be the basis for the method of "counting on", where we might add 3 to 4 by counting "5, 6, 7".)

Accumulation, here, refers to putting together groups of items -- 4 apples, and 3 more apples, and 5 more apples, and so on. ("Accumulation" literally means "piling up".)

Note that the author says, "A single operation (addition) can take on several intuitive meanings. This list isn’t exhaustive — they are the interactions I’ve noticed, and I’m sure you have others." That is, this is not a set of technical, formal categories that mathematicians recognize, but just an informal attempt to help people realize that one model of an operation is not all there is.