The lock-step approach of algebra, geometry, and then more algebra (but rarely any statistics) is still dominant in U. S. schools, but hardly anywhere else. This fragmented approach yields effective mathematics education not for the many but for the few primarily those who are independently motivated and who will learn under any conditions.

The lock-step approach of algebra, geometry, and then more algebra (but rarely any statistics) is still dominant in U. S. schools, but hardly anywhere else. This fragmented approach yields effective mathematics education not for the many but for the few primarily those who are independently motivated and who will learn under any conditions.

For most problems found in mathematics textbooks, mathematical reasoning is quite useful. But how often do people find textbook problems in real life? At work or in daily life, factors other than strict reasoning are often more important. Sometimes intuition and instinct provide better guides; sometimes computer simulations are more convenient or more reliable; sometimes rules of thumb or back-of-the-envelope estimates are all that is needed.

Philosophically, mathematics is not a part of science. Mathematics studies patterns, science studies nature

Mathematics is the science of patterns.

What humans do with the language of mathematics is to describe patterns... To grow mathematically children must be exposed to a rich variety of patterns appropriate to their own lives through which they can see variety, regularity, and interconnections.

Mathematics is often defined as the science of space and number . . . it was not until the recent resonance of computers and mathematics that a more apt definition became fully evident: mathematics is the science of patterns.