Mathematics in the Primary Grades: Communicating with Numbers and Shapes

Mathematical thinking is organizing information, comparing quantities, and seeing relationships. Learning the concepts and language of mathematics--more, less, equal, a fraction of, multiples of, and so on--helps children to plan, calculate, reason, and communicate solutions to problems. To think mathematically, children need to go well beyond basic computation skills. They need opportunities in school to develop a real understanding of mathematics by applying skills to real problems.

When you were in elementary school, the focus of the math curriculum probably was not "mathematical thinking" but rather "arithmetic." Students who knew their facts and could add, subtract, multiply, and divide quickly were successful in math. The world our children are growing up in places greater emphasis on knowing how to apply mathematical concepts to new problems. As a result, children must learn to think mathematically. Children still need to learn arithmetic. It's just that now they need to learn much more.

The skills your child should be learning

A balanced math program

Questions to ask your child's teacher

The Skills Your Child Should be Learning

According to the National Council of Teachers of Mathematics, to become effective mathematical thinkers, students must learn about:

• patterns and relationships
• number concepts and operations
• estimation
• geometry and spatial relationships
• measurement
• probability and statistics

These components form the basis for mathematics instruction. In every grade, your children should have opportunities to work in each of these areas.

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A Balanced Math Program

Problem solving is the core of mathematical thinking. However, correct (accurate) answers to problems are equally important, so learning to calculate is necessary. As children learn computational skills, they also need opportunities to solve mathematical problems and develop strategies for reaching and evaluating solutions. Among these problem-solving strategies children should learn are

• stating a problem in their own words
• identifying what information is needed to solve the problem
• trying out different methods
• recalling similar problems and using familiar skills
• asking themselves if their answers make sense, and--if necessary--trying again

The key to a good math program for your child is finding the right balance. A program can emphasize problem solving while children still learn computation skills. For example, if a child gets the wrong answer to a problem and there is no discussion of how he or she approached the problem, then there is too much focus on answers alone. However, a program where process is emphasized but accuracy of answers is ignored is also out of balance. In addition, programs have to recognize that children approach learning in different ways. One child may memorize math facts easily and compute quickly. Another child may never achieve quick recall or may consistently rely on slow, deliberate calculations to find answers. Both children can become mathematical thinkers.

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Questions to Ask Your Child's Teacher

• What are your goals for my child this year in math?
• How will I know she is making progress?
• How does he approach new or unfamiliar types of problems?
• Can you show me some examples of how she goes about solving problems?
• What strategies does he use to add or subtract large numbers?
• Can you tell me about his progress in learning basic number facts?
• What can I do to help?

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