Middle childhood, (seven to 12 years old) or “latency,” was once thought to be uneventful in a child’s life. They were the “calm years” before the “storm” of adolescence.

Recently, middle childhood years are proven to be not so uneventful. In fact, the seven to 12 years span is considered critical in cognitive development. Cognition is “knowing” and the process of thinking. Psychologists cite important factors and critical structures in the thinking processes of the brain, which need to be developed in middle childhood. Unless these so-called “mental structures” are developed, the child cannot go to the next stage of higher-level thinking—or what they call formal thought.

Many adults are still stuck in the thinking level of middle childhood. Many do not achieve high-level thought.

How does one get stuck?

Telling or lecturing is one of the most inefficient ways of teaching. Ralph Nickols (University of Minnesota) shows that people forget 50 percent of what they hear in the first two minutes. A United States Department of Health Education study reports that people retain only 10-25 percent of what they hear in a 30-day period.

What are the implications then to the seven-year-old when most of what he learns is told to him—especially in school? How effective is that learning?

A second grader was being tested to know how well he knew numbers. When asked which was greater, three or seven, he answered “Seven, of course.” When prodded, he was asked, if seven is bigger than three, which is bigger, 1/3 or 1/7? He hesitated. In school, he was taught that 1/3 was bigger. Then he said, “I guess 1/7 is bigger than 1/3.”

Giving examples

A wise teacher once said, “My tests are all simple. I only have one question: Give me an example.”

The middle child should do precisely this in his learning. Give examples. Show me. Show me that 1/3 is indeed bigger than 1/7. In cognitive psychology, it is called concrete operations.

Telling and further drilling is precisely just that. Drilling. There is nothing wrong with drilling. In fact, many tutoring schools are based on that. Drilling develops greater facility in computations. Computation, however, is one of the lower forms of mathematical operations.

When a child gives examples—using concrete objects, popsicle sticks, stones, marbles—he not only begins to fully comprehend but can also begin to extend and expand his understanding. Number seven cannot be defined. It has to be experienced in many different ways—seven stones, seven candies, seven steps to my room, etc. But when I have to divide my pizza into seven pieces, my spaghetti into seven plates, I know I will get less than if there were only three pieces or three plates.

It will not serve the middle child well to learn to memorize multiplication tables and division tables and not fully understand basic number concepts. Memorization is just that. Memorization.

Comprehension is more important. And more lasting.

Concretizing logical mathematical concepts is what middle childhood is all about.

When your child has a number problem, ask him or her to show it to you. No need for fancy math toys—just everyday objects that are readily available.

Crucial to all this is one basic ingredient: enjoyment. Enjoy your child as you are working out numbers. Enjoy his or her answers as he or she is trying to work it out, even the wrong answers. Wrong answers are springboard for better understanding. Work out the problem together. This is not “tutoring.” This is discovering life together. And being the wiser and smarter for it.

Author is lecturer at Miriam College and consultant to Bridge School and Learning Tree.

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