Math principles and standards, part 3


           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 3

Geometry Standard

            The instructional programs should enable all students to:

  • Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

  • Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

  • Apply transformations and use symmetry to analyze mathematical situations.

  • Use visualization, spatial reasoning, and geometric modeling to solve problems.

            Early experience in this area lays the groundwork for formal learning that will come later. At this age, children learn the names of shapes, compare them to objects they see around them, and describe which ones are similar and how.

            Children who recognize landmarks on a route that you regularly take are already showing this ability. Terminology to use with youngsters to build this type of relationship will be in the areas of direction (which way?), distance (how far?), location (where?), and representation (what objects?).

            They use these techniques already when they try to solve jigsaw puzzles, as they turn pieces around to try to get them to fit into the given areas. You can look for symmetrical designs around you: when you are standing in front of a car, you draw an imaginary vertical line down the middle to see that each side is symmetrical. However, when you view the car from the side, the front and back are not symmetrical.

            One of our favorite dinnertime games in our family was a help in reinforcing this skill. A member of the family closed her eyes while another person changed something that was on the table. We called this game “What’s different?” and it was a challenge to determine what had changed on the table.


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