Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

 Defining Reasoning and Proof
 Introduction | Pattern Recognition | Repeating Patterns | Reasoning About Repeating Patterns | Growing Patterns | Classification | Your Journal
"The ability to reason systematically and carefully develops when students are encouraged to make conjectures, are given time to search for evidence to prove or disprove them, and are expected to explain and justify their ideas."

## (NCTM, 2000, p. 122)

Simply defined, reasoning is the use of logical thinking to make sense of a situation or idea. Reasoning is a natural part of childhood. Young children use reasoning when they play games, classify items, solve problems, observe their surroundings, and listen to others.

Reasoning skills develop at a rapid pace in early childhood. Even before they enter school, children have many experiences with refining their thinking as their reasoning skills advance. For example, when young children first learn the word "ball," anything in their environment that is round is called a ball: The moon is a ball. A watermelon is a ball. But as children begin to identify additional characteristics of a ball (round, spherical, a toy), they refine their thinking about the items that do not fit this more sophisticated understanding. New words become part of their vocabulary to describe the items that were once known as "ball."

Reasoning with mathematical concepts follows a similar pattern. Children begin to reason about big mathematical ideas, and, as they mature, they refine or expand their ideas with the use of logical thinking. By making conjectures -- guesses made on the basis of experience or information -- and testing those conjectures, students make sense of the mathematics they are learning.

In this section, we will take a closer look at the use of patterns and classification in the early grades to help children reason about mathematical concepts.

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