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Wednesday, March 30, 2011

About Homework (with bonus lesson on area of a circle)

In the midst of extreme busyness, I left a short, hurried post nearly four weeks ago about how I recently became the temporary legal guardian of a sixth grader. Now it is spring break and I am even busier, but I have managed to carve out half an hour to write. I do not remember being so busy with the demands of a child when I was raising my own kids.

Attitudes of School Officials

Although I have teaching experience in elementary and even preschool, I spent most of my thirty-five-year career in secondary school settings. Suddenly, I have been spending a lot of time interacting with an elementary school. The classroom teacher and the school secretary do not know I am a teacher. The way they choose to interact with me is quite interesting, if somewhat condescending. I can only surmise that school people, intentionally or not, treat parents as if parents are basically ignorant. I apologize if this observation offends some. I completely understand that some parents are difficult, but it was disconcerting to have the teacher or secretary dispute with me almost from the get-go as if I knew nothing about the child.


Homework? What homework? In spite of the (shall we say) whining that kids these days are overly burdened with homework, I am just not seeing it. My ward brings very little homework home. Alfie Kohn, an educator with whom I am generally on the same page, has been crusading against homework for years. Just a few weeks ago, he sounded similar alarms, making it sound as if any and all homework is bad, bad, bad.

Funny thing I actually agree with most of his points. I absolutely detest homework as busy work. I remember when my own third-grade child came home with an assignment to write out the sevens ten times. His teacher knew that he could recite the times tables on demand, so the assignment was a complete waste of his time. In an effort to salvage some usefulness, he decided to type it in order to he could use the assignment as an excuse to practice the ten-key pad on the right side of his keyboard. His teacher gave him an “F” and scolded him for shortcutting the assignment. “You could have written it once,” she said, “and then simply copied and pasted.”

Nevertheless, homework does have a useful place, especially when used to generate fodder for idea generation during class discussion, as when the student measures the circumference, diameter and radius of ten round things. Or perhaps the student writes up a report of an experiment done in class in order to prepare to discuss the findings with the rest of the class the next day. The homework my ward brought home was generally useless, but certainly not time consuming. The teacher says she is only allowed to give 20 minutes of language arts and twenty minutes of math per day. The teacher does not even expect sixth graders to write their last name on their papers.

Homework as Practice

Normally, if a student has acquired the concept, it does not take a lot of practice to reinforce it. In my experience, homework as practice often means the student has not acquired the concept. The younger the student, the more control the teacher has over acquisition (but it must always be remembered that the teacher does not have total control). Anyway, homework as practice at the elementary level is worse than useless if the student has not acquired the underlying concept. Such students spend the twenty minutes reinforcing the wrong learning. It would also be helpful if elementary math teachers actually had what Liping Ma calls the “profound understanding of fundamental mathematics.”

Area of a Circle

My ward brought home a worksheet to practice finding the area of a circle. From her point of view, it was nothing but plug and chug. She asked me what “pi” meant. We spent a little time developing the concept of pi. Then we cut up a paper plate into pie slivers and arranged them, point up point down, into a sort of parallelogram with scalloped edges. I asked her what shape it reminded her of. Not surprisingly, she answered, “Rectangle.”

I asked her how to find the area of a rectangle. “Length times width” she replied.

“Right. So what part of the circle is the width of this rectangle?”

“The radius.”

“Right. What part of the circle is the length?”

She thought a bit and offered, “Half the circumference?”

“Exactly so. Then instead of length times width, what can we write?”

I began writing “A = r,” whereupon she shouted, “times 1/2C.”

We continued along these lines until we had written A = r X ½ X ∏ X 2 X r. Then r times r equals r squared. ½ times 2 equals 1. When she was done substituting, she had A = ∏r^2.

“Okay,” I said, “Look at your worksheet.”

To her amazement, the formula for the area of a circle was exactly what she had written. She had figured it out herself. That is the sort of success that builds genuine self-esteem. My disappointment came when I described this experience to her math teacher. He had no idea what I was talking about.


  1. That is wonderful! So concrete, and gives students something they can do. I'm a math teacher and *I* appreciate that! (in fact, I'll probably use it) ^_^

  2. Beautifully explained and instructed lesson on how to use the formula to find the area of a circle. So simple to follow and to do homework on circle geometry.