Philosophy of Mathematics Education
Three things are essential in a good math classroom:
Counter Intuitive Thinking
Students need experience with counter-intuitive problems to develop logical thinking skills.
Manipulatives not only help students understand concepts more clearly, they also give concrete examples of how mathematics surrounds us. For instance, baby toys can teach integral calculus, a Slinky demonstrates geometry formulas, sewing patterns are derived from statistics, M&Ms follow patterns of probability, applesauce teaches about similar figures, fingerprints coincide with the binary system used by computers.... Fun examples are everywhere.
Calculators and computers allow students the freedom to explore the beauty of mathematics without the time consuming calculations. Children can understand complicated mathematical ideas even though they cannot yet perform the cumbersome arithmetic that makes those concepts possible.