Defining Reasoning and Proof
 Introduction | Pattern Recognition | Repeating Patterns | Reasoning About Repeating Patterns | Growing Patterns | Classification | Your Journal

Let's think about what happens as students develop reasoning skills with repeating patterns. At a very young age, children can copy a pattern provided by the teacher. They can use a variety of materials to represent the pattern, draw it, act it out, or make sounds. Having children describe the pattern enables them to hear as well as see the repetitive nature of the series of objects. Once children begin to recognize patterns, they should have opportunities to extend patterns and to create and describe their own patterns, using various representations. Then, as children begin to recognize similarities among different patterns, they can begin to translate the patterns to different representations, as in the student work below.

 After several days of working on an AABBB pattern in the second grade, one student notices the similarity among the following representations:

Marc: Hey, these patterns are the same.
Teacher: Tell me what you mean.

Marc: Well, there's a triangle triangle square square square and a smiley smiley heart heart heart.
Teacher: How are they the same pattern?

Marc: There are two things the same and three things the same, and two things the same and then three things the same.
Teacher: Can you show this pattern another way?

Marc: Yeah -- I can do it with the color tiles:

Marc has recognized the AABBB pattern. He is able to describe his reasoning using his own words. He has also translated and represented the pattern in another way.

These actions do not usually take place without specific attention being paid to them. The mathematical tasks being posed and the teacher's questions help students focus their thinking. If we are aware of what we want students to experience, we can formulate our activities and questions around the reasoning we want to occur.

When children are given a variety of opportunities to copy, explore, describe, and extend repeating patterns, they will begin to use reasoning skills to generalize about and make predictions involving patterns. This does not occur in just one lesson or even one unit. Reasoning with patterns should be an integral part of students' mathematical experiences throughout the early grades.

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