That said I found out almost immediately that there are many students who feel that math is “not for me,” and become increasingly helpless when they are faced with learning new math operations or skills. Regardless of when these students come to us there is one common factor. They do not know basic math facts, and consequently they do not feel that math is an achievable or enjoyable skill. These feelings are not surprising, since math does require early and intensive work to develop mastery – and with mastery comes confidence.
The problem with Everyday Mathematics is that it is not based on the premise that intensive work is worth doing. Here’s a quote from the teacher’s manual about division:
“The authors of Everyday Mathematics do not believe it is worth student’s time and effort to fully develop highly efficient paper and pencil algorithms for all possible whole number, fraction and decimal division problems…The mathematical payoff is not worth the cost, particularly because quotients can be found quickly and accurately with a calculator.”
Consequently many pages of the Everyday Math fourth and fifth grade texts are devoted to calculator use. So many of the students we see are baffled when they must do simple math facts. One young student, now a senior at Notre Dame Academy, could only do a very few division facts in a minute when we met her. She was terrified of fractions, and as an eighth-grader was struggling with Algebra 1. When we had her work in carefully chosen steps on her division and fraction skills, she suddenly took off. On her first attempt she converted four fractions into decimals in a minute, but she rapidly accelerated her performance. Two weeks later she could convert 50 fractions to decimals – and I thought that would be plenty. However she insisted on continuing. By the fourth week, in a total of 10 minutes of practice, she was converting an entire sheet, 104 fractions, to decimals in one minute. Then she decided that was enough!
Her ability as an algebra student climbed rapidly. In fact, after about six weeks she was getting all A’s and we didn’t see her again for another year, when she was worrying about geometry. After an hour or two she was sailing through that too. This girl is an extreme case, because she developed marvelous skills and a real passion for math. But the tools for becoming so wonderful and passionate at math were denied to her by Everyday Mathematics, and she hated and feared math when we first began working with her. Her ability to perform with excellence would not have been discovered without focus on foundation skills that are neglected in Everyday Mathematics.
The approach that the dominant American math texts use is called “constructivism.” Basically the approach is predicated on the idea that kids will learn and retain information better if they construct the approach themselves. Some readers may have gotten the alarming letter that the schools send out to parents of fourth grade students saying that their sons or daughters will be “inventing” their own approach to division. “Instead of requiring all students to learn the same computation procedure, by rote, at the same time, Everyday Mathematics aims to make students active participants in the development of algorithms.”
This means that each fourth-grader will be using various experiments to re-invent division, rather than learning to divide. Wouldn’t it be wiser to build upon the existing knowledge base – and learn to extend it – rather than ignoring or downplaying it? Moreover, while the authors of Everyday Mathematics want students to learn math facts, these are not taught or practiced extensively as part of that curriculum. In Hingham an exercise called the “Mad Minute” has been added to the math curriculum. The “Mad Minute” is really 5 minutes long, and once a student passes the criterion of 100 problems in 5 minutes, he or she does not have to do it again. This practice is better than the Everyday Mathematics approach, but does not build high speed responding – which is the hallmark of mastery of a subject.
I asked a fourth-grade teacher who had two students at The Fluency Factory, neither of whom had good math facts, about why that was happening. “Those parents are just letting down,” she said. “I don’t have time to work on math facts, I am teaching concepts.” I was surprised, but now I know this is routine. Instead of math facts, students will learn a little algebra, a little geometry, a little data analysis, and how to answer open-ended questions about math problems, in which the student must explain why their answer is what it is. Writing an essay about math is not mastery – and leaves students without mastery or confidence.
Richard McManus is a Hingham resident and is founder and director of The Fluency Factory and Beal Street Academy. He can be reached at: email@example.com