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Mathematics is just the extreme end of the two most fundamental concepts Abstraction and Generalisation. Start the intro to these concepts including showing how these concepts are useful and used by everyone in their day to day life in using natural language.

My wife has studied mathematics pedagogy, and one concept that really struck me from what she learned is compression. Put simply, you can't learn a new thing until you've compressed the old thing it builds on. If you have not compressed "addition" to the point that it requires little effort, you won't be able to learn "multiplication". Same holds for e.g. "derivatives" and "Taylor series", or "group theory" and "rings and fields".

(I think this was from Piaget, or maybe Brissiaud.)

I would guess Piaget, because it reminds of this quote from Papert (who drew heavily on Piaget):

> Slowly I began to formulate what I still consider the fundamental fact about learning: Anything is easy if you can assimilate it to your collection of models. If you can't, anything can be painfully difficult.

Could you expand on your second sentence, perhaps with an example or two and how you'd imagine they're be taught in class?

That is the best way to not learn mathematics.

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