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The whole point of math is to learn about abstraction. How to solve problems you've never encountered. Mat is about dealing with what you have left when you strip away everything concrete. It is not, as some people imagine, about number. That's arithmetic. But you could teach by example. You would still be dealing in abstraction, but it would be the raw, subconscious, neural abstraction that exists in the human brain and allows it to learn new skills. It would not be the formal, symbol abstraction which is necessary for solving more complex problems. The ability to solve simple numerical problems is not the primary reason you are in math class. It is important to be able to look at new problems and analyze what are the important parts and how they interact with each other.
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