# Philosophy of Think Math!

This is a Think Math! feature or perspective

## What is special about Think Math!?

Think Math! is mathematically coherent and correct;

- it is comfortable for, accommodating to, and respectful of teachers with varied styles;
- it is sensible in the eyes of parents;
- it is aligned with state frameworks and tests;
- it has been tested thoroughly with students.

Think Math! develops very strong arithmetic skills and a confidence and ease with numbers;

- it is designed around how children learn and how teachers teach;
- it builds algebraic ideas while children learn what their parents expect;
- it uses children’s natural enjoyment of puzzling out the world;
- it teaches mathematical language in context, which is how children learn language best.

Successful mathematical problem-solvers need both understanding and skill. To develop skill and confidence, children need practice, and a lot of it. But when the practice becomes too mechanical, children’s minds turn off—they “sleepwalk” through the practice, and gain less from it.

One way to keep them mentally alert is to get them not only to produce an answer, but to notice how they got it, or what that answer is and how it relates to something else. Doing that through discussion is good, but discussions take time and therefore compete with practice, so one also wants to find other ways to design practice that helps children notice pattern and reasoning.

Children love to find order and regularity, to solve puzzles, and to make sense out of the world, and they feel (and are!) smart when they do figure things out. Think Math! takes advantage of (and fosters) this natural curiosity, building skills by embedding useful practice in puzzles, investigations, games, and, in fact, everything that the children do.

## Is the mathematics different from what we used to teach?

The mathematics we and our parents learned as children is still good mathematics, and even the arithmetic procedures we used are fine procedures. That mathematics helped our society excel in science and technology. (Only a small number of topics and ideas, now required by state tests and standards, were not taught when we were children. These, of course, are included in Think Math! )

What is new in Think Math! is an approach—based on the practical knowledge of teachers, grounded in the classroom, and supported by research—designed to help more children to learn and like more of that mathematics, and to be competent and confident at doing and understanding it.

## Why "philosophy" should be in quotation marks

In education, the word philosophy is sometimes (though incorrectly) used as if it were almost a synonym of faith. Statements like "we believe in direct instruction" or "we believe in constructivism" or "we believe in..." are not claims about science, but about belief.

The developers of Think Math! did not begin that way. The principles behind Think Math! are grounded in several fields of research, including developmental psycholinguistics, cognitive science, child development, and, of course, research on teaching and learning mathematics. We drew on traditional as well as progressive teaching ideas, asking not what "philosophy" they represented, but only whether they were mathematically sound, conformed with the best psychological research on learning available and the (empirically) best practice internationally, were useful for and usable by teachers, and worked with children.