Reasoning and proof are included as an NCTM Process Standard because they should be an integral part of the process of learning and using mathematics. Similar to problem solving and communication, reasoning should not be isolated from everyday mathematics lessons. It is important for the teacher to form goals, develop investigations of problems, and prepare probing questions related to reasoning and proof that are appropriate for students throughout their mathematical work.

When upper elementary students engage in reasoning and justify their solutions and ideas, they have opportunities to reflect on their understanding and to make mathematical connections. They are also learning that mathematics makes sense and that people, including themselves, can make sense of mathematics. In addition, they learn the value of collaboration.

Let's look at the role of conjectures and a variety of types of reasoning and proof that may be encountered in the upper elementary classroom.

  Investigating conjectures