Math principles and standards, part 2  


           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 2

Algebra Standard

    The instructional programs should enable all students to:

  • Understand patterns, relations, and functions.

  • Represent and analyze mathematical situations and structures using algebraic symbols.

  • Use mathematical models to represent and understand quantitative relationships.

  • Analyze change in various contexts.

            They can use properties such as size, color, and shape to sort, classify, and order objects. Ask them to tell you, when they are grouping things, why they belong together.

            They can also recognize patterns that they see, describe what they see, and extend the patterns. If you count, “One, two, three, four,” they can continue. As they get older, they can continue when you count, “Two, four, six...”

            They can analyze how the pattern was created by saying, “I skip a number and then I say a number, then I skip one, then I say one, etc.”

            Any child who has learned to count to 100 has internalized this because she has recognized the way the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 repeat themselves and make a pattern.

            At this age, we don’t use terminology associated with high school algebra, but children do learn that certain of these operations are in place. For example, they begin to understand that whether they add 2 + 4 or 4 + 2, the order doesn’t matter: the sum will be the same. In the same way, they understand that if 3 + 4 = 7, then they can also break down that 7 by saying that not only is 10 + 7 equal to 17, but 10 + 3 + 4 is also equal to 17.

            The most helpful way to do this with most children is to encourage them to draw or write examples that show the situation being depicted. When five children each has three cookies, this can be drawn by showing all five children, each of whom has three cookies in front of her.

            Many changes in children’s lives can be described in mathematical terms: they grow taller, they get heavier, they get older. In the world around them, the temperature gets colder or warmer as seasons change.


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