Math is active. Children should learn how to predict and estimate. They need time for discovering that there is often more than one way to find an answer. In the elementary grades, math activities should include working with real materials such as buttons, counting rods, leaves, coins, paper clips, and etc. Interest in math and self-confidence can be developed by using numbers in games, in conversations, in questions.
Students do problem-solving.
We used to think that children had to know all their number facts before they could work on more complicated problems. But most children can problem-solve whether or not they have mastered all their facts and tables. In fact, interesting problems often keep children liking math even when learning number facts is hard. They can then report the results of their survey by making a graph that they use to report their study. Middle school students can solve harder problems.