Our Teaching Is Based On How Kids Really Learn Logic, Skills

We have been teaching mathematics in the public education system for 33 years, collectively. Reading the July 19 Opinion commentary by Andrew Bernstein left us deeply concerned that the public may be misled.

In our not-so-distant past, intelligence was measured by the size of one’s skull. Using the science of the time we had the ability to make external skull measurements. Larger skulls could hold larger brains and larger brains could hold more knowledge. At the time, this argument made sense. Advances in the biological sciences have given us the ability to map the human brain, to see how learning actually takes place and to refine the way we educate children.

Research conducted by well-respected scientists from around the world (Piaget, Kamii, Bovet, Mohseni) have given us a clear picture of how the human brain learns. From the moment a child is born the process of learning is taking place. When children construct their own learning by reasoning their way through activities such as folding paper strips and bending straws they are developing high-level logic and reasoning skills. This constructivist view of learning has been supported in several reports in Educational Psychologist and the Journal for Research in Mathematics Education. It was cited in a recent publication by the State Superintendent of Public Instruction, Teaching and Learning Mathematics, OSPI, March 2000.

The recent test Bernstein referred to was the Third International Mathematics and Science Study, or TIMSS. The United States did rank low in this study. The high-scoring nations have redefined what they consider basic mathematics. Similar to the process Washington state is going through now, problem solving and logical reasoning are emphasized in classrooms. TIMSS found the content of U.S. mathematics classes requires less high-level mathematical thought than classes in Germany and Japan. (http://www.timss.enc.org)

In Japan, where students scored very high, a teacher might get in front of the class, offer a problem verbally, then ask students how they could go about solving it. They would exchange ideas for a while before the teacher, if necessary, guided them to the answer. It boils down to this: If you can’t talk about math, you are unlikely to do it well. (Newsweek, Dec 2, 1996, page 96.)

Bernstein describes mathematics reform as dumbing down mathematics. We are in fact expanding the field in both depth and breadth. Research shows that early work with mental computation rather than paper and pencil exercises builds a deeper level of understanding. Traditional algorithms such as carrying and borrowing are not the traditional algorithms taught in all countries. In fact, the teaching of these algorithms can actually unteach the very essential concept of place value. (Young Children Reinvent Arithmetic, C. Kamii, Teachers College Press, 2000)

Bernstein states the idea that a math problem has an objectively right answer has now been discarded. This is nonsense. Two plus two is still equal to four and always will be.

However, Bernstein is addressing only the conventions of mathematics. True learning includes not only knowing the facts of a particular discipline but also understanding the relationships between the structures and functions of a discipline. (How People Learn, National Research Council, National Academy Press 1999, page 11) Mathematics is not just computation. Our fourth-, seventh- and 10th-graders are currently having to solve more-sophisticated, higher-level math problems for our state’s new standards. Students are not told how to solve the problem or what computation to use. They have to read the problem, decide what step or steps are needed to solve the problem and then communicate, and justify, their thinking in writing.

Bernstein sums up his thoughts on reformed mathematics education with the statement, “A student will be unable to think, he is not qualified for college, for a demanding career - or even to make change at the checkout counter.” Employers today are looking for problem solvers. Someone who can see a problem, define it, go about solving the problem and clearly communicate their process. These are the basic math skills, the thinking skills, that our children will take with them into the future. As educators, we do not view our responsibility as one of training the mind as Bernstein states but of empowering every child to develop as an individual thinker.