Reasoning and Proof Standard


            Facility in math is recognized by educators as being key to later success in life. The National Council of Teachers of Mathematics (NCTM) has set ten content standards for the teaching and learning of mathematics from prekindergarten through twelfth grade.

            The standards in this series refer to the entire range of grades. Examples, however, are for prekindergarten to second grade, which includes the grade I teach.

            The NCTM publication Principles and Standards for School Mathematics has complete explanations of these. For more information, you may visit NCTM at

            Bullet points are quotations from the publication. Underneath them are my suggestions for parents.

Math principles and standards, part 7

Reasoning and Proof Standard

            The 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.

            The most important part of this standard is for a child to be able to explain the way she is thinking about something. The role of parents and teachers is to encourage each child to an understanding that what she sees makes sense. The family is nurturing by helping children to explain their perceptions.

            With younger children, this occurs most frequently when they recognize patterns and find ways to classify objects.

            When children are trying to group objects by similarities, the younger they are the more likely they are to focus on only one of the attributes of the objects. In school, we have an activity in which I ask each child to take off one shoe. Then we put them in the center of a circle so that we can find ways to put them into groups. Some of the kids are focused on the colors, some on the types of fastening devices (laces, buckles, Velcro), and some on the brand names of the shoes. Many of the kids see only one attribute.

            It takes a bit of doing to get them to sort and re-sort the same group of items using each of the attributes individually or more than one at the same time.

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