Symbols and Meanings in School Mathematics

"Symbols and Meanings in School Mathematics" by David Pimm

Think, write, pair share.

Practice is necessary to review that you have understood the problem and have found a way at arriving at a solution. It is necessary to see that your understanding of the math problem and your solution work under many situations.

Practice makes perfect, or better yet; perfect practice makes perfect answers are cliches, that we need to test what we have read or learned to see that we understand how to use it to solve additional problems.

If the problems are all the same in a textbook in a section this is because each individual may require a different amount of practice to achieve understanding.

It is then up to the teacher to make increasingly difficult questions as the number within a section increases and harder in increasing sections. All questions should challenge the student to recall prior knowledge and to learn to use it.