This is the first in a series of letters that desribe a research-based approach to teaching children mathematics. The aim of the instruction is to help children develop understanding of mathematically important ideas about space and number. Teaching for understanding involves building upon children's knowledge and experiences so that mathematical ideas take root and grow. We would like to develop a partnership with you so that teachers and parents work together to build on children's thinking about mathematical ideas.

Although learning number facts and practice both contibute to understanding mathematics, inventing solutions to problems and communicating about one's discoveries are far more important ingredients. For too long, many children weren't "getting" math, starting a cycle of frustration, dislike, and avoidance of math. A small number of children appeared to be learning mathematics in that they could calculate rapidly. Unfortunately, most of these children could not apply their knowledge in new situations. Both of these problems are avoided when children learn with understanding.

We will be sending home letters that describe how your child might be thinking about an important mathematical idea, like measurement or addition. Each letter will also contain suggestions for homework. We can only tell you about general patterns--you will have to find out about your child. We will help by suggesting some ways to discover what your child is thinking. We believe that this information gives parents a good idea about what children may already know and what they will be learning next. By building on their knowledge and guiding them to the next step, parents help children feel successful and confident in math. Because parents are such important role models and coaches to their children, every effort will be made to keep you informed and involved. In the weeks to follow, we will talk about:

- Learning by Solving Problems. Children learn the most about mathematics when they solve problems. We will talk about different types of problems.
- Learning to Solve Problems in Multiple Ways Children learn the most when they can develop several different ways to solve problems. Then, if one way doesn't work, another usually will. We will talk about how children approach different types of problems and how their ways of solving change with experience.
- Learning to Communicate Communication is an important part of mathematics. Children learn to reason mathematically by talking about their ideas and solutions. The best way for parents to learn how children figure out problems is to ask them to explain their solution to you. Children learn about math- ematical reasoning by talking about their solutions.