Making sense of their world is a natural characteristic of young children. Making sense of mathematics through the use of logical thinking is the foundation of the Reasoning and Proof Standard. Being able to reason is essential to understanding mathematics. Reasoning is a way both to use mathematical knowledge and to generate and solidify mathematical ideas that are new to us.

How do we help students reason mathematically? In this session, we will look at various examples of mathematical reasoning typical of early childhood. We will observe students' thinking about mathematical ideas and their efforts to draw conclusions and make generalizations about those ideas. We will talk about how reasoning is an integral part of mathematical experiences in the early grades and how we can help students connect their own reasoning processes with the mathematics work they do in school. Finally, we will reflect on the teacher's role in helping students develop habits of making, testing, and refining conjectures.

This session shows you how to help students do the following:

• Use logical thinking to make sense of mathematical ideas
• Use patterns and relationships to analyze mathematical situations
• Draw conclusions as they do mathematics
• Use models, known facts, properties, and relationships to extend their thinking
• Justify their answers and solution processes

Instructional programs . . . should enable all students to --

• Recognize reasoning and proof as fundamental aspects of mathematics
• Make and investigate mathematical conjectures
• Develop and evaluate mathematical arguments and proofs
• Select and use various types of reasoning and methods of proof

Principles and Standards of School Mathematics (NCTM, 2000). For more information on this Process Standard, see the NCTM Web site

  Observe a math problem