David Pimm: understanding ----------- fluency
In-depth understanding ------------ procedural algorithm
Go straight 100 meters, turn right and walk 200 meters, then .....
Go to book store, go to the village, go to the bank, etc.
Square x, square y, plus them together, then take the square root, then that is the length of the hypothenuse of a right triangle.
Consider the right triangle, use Pythagorean theorem.
Multi step algorithm....... Need explanation
Students get the first few rules, but the rest......
Teachers can't fully explain why to to these steps......
Some cases are instrumental friendly as long as students can SEE the reasons.
Basically connect what is learnt to things students are familiar with
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