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.
principles and standards, part 7
and Proof Standard
The instructional programs should enable all students to:
reasoning and proof as fundamental aspects of mathematics.
and investigate mathematical conjectures.
and evaluate mathematical arguments and proofs.
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