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Posted: Wednesday, February 20, 2002 12:00 am | Updated: 7:46 am, Thu Mar 24, 2011.

iddle school math teacher. I have been teaching in the same school district and school building throughout my ca-reer, which began 20 years ago.

When I first started teaching, our district utilized a fairly traditional mathematics curriculum. Computation was emphasized, and calculators were not yet used in our middle school math classrooms.

How times have changed. The mathematics curriculum in our school district is totally dominated by the guidelines and beliefs of the NCTM [National Council of Teachers of Mathematics]. Anything that is put out by the NCTM is regarded as the gospel. To question the NCTM is regarded as blasphemy. Here is what our mathematics curriculum supervisor has been telling us each and every year, for at least the past five years, during our orientation meeting which is held in August:

"You know not the hour or the time when I will enter your classroom. And when I do, I had better see three things: Calculators, manipulatives, and cooperative learning. The last thing I want to see are your students doing worksheets by themselves in nice, neat, rows."

Here's another directive that has been specifically issued to the 7th grade teachers: "If your students have not yet learned how to add, subtract, multiply, or divide, forget it. Give them a calculator."

All of the above is anathema to my personal beliefs about the teaching of 7th grade math. I am a traditionalist. I believe in computation, paper and pencil drill, and students working in nice, neat rows.

Also, commencing with this year, all math teachers in my school district have to submit in their lesson plans a detailed description of how they are using manipulatives [blocks, beans, counters, anything you handle] with their objectives each and every week. In other words, we are now required to submit evidence of our use of manipulatives each week.

It is this type of "gestapo" tactic that has been increasing in my school district. As a result, I am looking elsewhere for a teaching job, preferably in a school district with a more traditional orientation to the teaching of middle school mathematics.

Recently, as a result of several observations, my principal has been hounding me about the "lack of manipulatives" present in my classroom. She has been preaching to me how absolutely vital manipulatives are for middle school students, so that they will bridge that gap between the concrete and the abstract, and how "all the research" supports the overwhelming efficacy and vital importance of using manipulatives in the middle school mathematics classroom.

What I would like to do is investigate the so called "research" my principal is always claiming that shows the tremendous efficacy of manipulatives. Here is my question: What is the status of the research on the efficacy of manipulatives in the middle school mathematics classroom?

The following question keeps nagging at me. If manipulatives are so vital, then how did our generation, our parents, our grandparents, our great grandparents, our great-great grandparents, and so on and so on, learn math without them? I asked a similar question to a math consultant a number of years ago. His reply went something like this: "We finally realized that the old methods were no longer working. Therefore, we had to start looking at some new methods."

Immediately, I wondered if it was not the old methods which were "no longer working", but rather, if it was the students who were "no longer working" and the parents of these students who were "no longer working" to see that their children were "working."

When I was in elementary school, I once brought a note home from my teacher after school on Friday, saying that I had not yet learned all of my multiplication tables. As a result, I was grounded the entire weekend, until I knew each of them by heart.

I remember pitching a fit, but I finally got so mad that I sat down and learned them. Finally, I got to go outside late Sunday afternoon. Unfortunately, I don't think we have enough parents like that today.

Any information and leads on this issue would be greatly appreciated. What I would like to do is develop a repertoire of counter arguments to offer to my principal when she lectures me on the value of manipulatives.

Your question is a lengthy one, but it is a perfect example of the frustration and anger that good teachers feel when forced to adopt untested curricula and methods. You have my sympathy. All you want to do is teach math and you're being forced to play with blocks in 7th grade.

The situation you describe is happening in hundreds of school districts around the country. In some of them, parents are organizing to protest. Often, the parents who are getting organized are scientists, mathematicians, and others who use mathematics in their professional lives. These highly knowledgeable parents are appalled at the trend and are asking the same questions you have asked. Where's the research?

Educators dance around the issue, throw the smoke screens, and in one instance which was reported to me very recently outright lie. It's amazing to me the lengths some educators will go to protect their right to make bad decisions. Readers might be interested in visiting a web site ( to find out more about the problem around the country.

Here's the answer to your question about research. A number of years ago when California was making decisions at the state level about math they commissioned a report to investigate research in mathematics. The authors of the report found only four studies that were of sufficient quality to even consider the results. Three of those studies--all conducted in elementary schools--found no benefit to learning when manipulatives were used. One study, conducted with middle school students studying fractions and ratios, did find some positive benefits (Harrison, et al., 1989). But, one study with a few positive benefits is hardly enough to force middle school teachers to include manipulatives in their lessons. Your poor principal is misguided and is following the party line of the National Council of Teachers of Mathematics who are also misguided. All of the research does not support the overwhelming efficacy and vital importance of using manipulatives in the middle school mathematics classroom. There are only four experimental studies and 3 of the 4 do not support the efficacy of manipulatives.

The same is true of calculators. In Japan, one of the higher achieving countries on international tests of mathematics and science, calculators are not used before the 5th grade. Calculators are not the "magic bullet" for higher achievement if we look at practices in the high achieving TIMSS countries. The Third International Mathematics and Science Study done in 1999 found that "many of the higher achieving countries both had less technology [calculators and computers] available and made less use of technology than did the United States. The case of the efficacy of using technology must remain at best 'not proven'."

Elaine is a former teacher, librarian, principal, and district administrator. She has an Ed.D. in educational administration and is the author of more than two dozen books for parents and educators. You can visit her web site at

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