M.W. Penn on Elementary Mathematics

Elementary Mathematics

NCTM President Henry Kepner in NCTM Summing Up, October 2009:

“When students connect mathematical concepts together and relate them to other subjects and their own interests and experiences, their understanding becomes deeper and more lasting, and they come to view mathematics as a coherent whole. Thus, through instruction that emphasizes the interrelatedness of mathematical ideas, students not only learn mathematics but also discover its utility.”


When you hear math mentioned in the context of elementary school, what comes to mind? Addition, subtraction, multiplication, division?

Fractions? Wait, decimals! No fun there.

Children are often introduced to math through hours of computation. Why? Computation isn’t fun and computation is only a small part of mathematics. Of course children must learn to compute. They also must learn to spell, but what if spelling were all we taught them of language?

When children study language arts we introduce enjoyable stories, and they understand that the ultimate goal of spelling and reading can be literature. When they memorize the multiplication facts, their ultimate goal is rarely explained.

What is mathematics if it isn’t computation? In truth, the seminal ideas of mathematics are varied and interesting: number; pattern; order; symmetry; measurement; data analysis; graphing; geometry; problem solving. Mathematics encompasses all of this and more, and we can make it fun.

Let’s just consider one idea: Two dimensional shapes – shapes in a plane, shapes that have no depth. They are easy to see and manipulate. Think of squares, triangles, circles and the fun involved in making pictures out of these shapes. Playing with flat shapes leads children to an understanding of two and, eventually, three dimensional geometry. Some children will search beyond, too, to a fourth dimension, stretching the limits of their understanding.

Will it lead there for every child? Of course not! Still, we teach every child to write; how many will become Shakespeare or Jane Austin? Every child deserves the chance to choose.

We often hear that America lags behind other nations in math and science. Did you know that India produces 15 engineers for one attorney, while we produce 15 attorneys for one engineer? How can we excel in the competitive international environment if we continue on this path?

And consider this. We live in a democracy where every citizen should be able to read and interpret a newspaper and express their own opinions. In the same vein, they should be able to gather data and interpret a graph. How can democracy survive without educated voters?

Over the past few decades, the NCTM has assembled the basic principles of mathematics into curriculum standards for each grade level. These standards encompass everything children should study in math class in a methodical and graduated program. The standards include computation, of course; but they also incorporate geometry and algebra, measurement and data analysis. We should present these concepts to every child, give each child the opportunity to understand them, and even let them have fun trying. Let’s look at just a few of these concepts.

Number: Number is an amazing concept. Where would we be if we couldn’t number – number just about everything?

How old are you? What time is it? Is the city far away? How much does gasoline cost? How many apples fit inside that box? How many rabbits does it take to destroy a garden? More or less?

Did you ever consider the amazingly clever way we number? We use only ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9), yet we can number the stars. You might think of it this way. We have 26 letters in the alphabet, but only those 10 digits in base 10. 26 versus 10? Number should be easy!

Pattern: Patterns are easily recognized in early childhood. Pattern recognition can be great fun, too, and it can lead children to grasp iterative functions.

Consider how often pattern occurs in nature and in the world that surrounds us. Even the pattern of metered poetry is math, after all.

Should I go on? A bit about symmetry, perhaps, the symmetry of a spider or an airplane? Can you imagine either of these being less than symmetric: a spider walking on seven legs; a plane flying with two wings on one side? Now there’s a fun idea! A teaching idea.

Mathematics: the study of number and pattern and order and symmetry and…
Math is poetry. Let’s make math fun!