The dispute focuses on differences in ideology about how mathematics should be taught in the lower grades. The folks from "Mathematically Correct" insist that direct instruction that emphasizes the individual mastery of computational skills such as addition, subtraction, multiplication and division is the most appropriate approach. On the other side the NCMT standards emphasize collaborative learning and group problem solving experiences, estimation, and the use of calculators to carry out numerical computations. In many respects these "math wars" resemble the "reading wars" where the battle lines are drawn between "phonics" and "whole language" approaches to reading.
To a large extent the Irascible Professor finds the ideological warfare issues silly. Based on his more than thirty years in the classroom, he knows that there are positive and negative aspects in both approaches. Some students respond better to direct instruction, while others respond better to group learning experiences. Some material lends itself better to direct instruction, while other material is best taught through collaborative experiences. The real problem is that mathematics is difficult to teach. There are at least three issues involved: the acquisition of basic skills, the development of an understanding of the logical structure of basic mathematics, and the need for students to apply both numerical skills and logical structure to the solution of every day problems. A skilled math teacher needs to use all the techniques available to him or her to help students develop their numerical skills, their basic understanding of the logical structure of mathematics, and their ability to put this knowledge to work.
The real problem is that most K-8 teachers don't have the background to teach math effectively. Unfortunately, most new elementary school teachers simply are themselves not proficient in mathematics. In fact, many of them are scared witless at the prospect of having to teach the subject, because they have no confidence in their own mathematical knowledge and skills. Here at Krispy Kreme U we offer a one-year course in the fundamentals of arithmetic for prospective elementary school teachers. It is a serious course that addresses the logical structure of basic mathematics, as well as problem solving issues. It is offered by our math department, not by our education people. Some of the best instructors in the math department work in this course. Nevertheless, they can only do so much with students who have no idea how to carry out such simple operations as the addition of fractions.
What can be done under such circumstances? The Irascible Professor has a radical idea. Let's surrender! Let's declare that we have lost the war. Let's admit that we have very little hope of improving the ability of the average grade school teacher to teach mathematics no matter which pedagogy we prefer or what techniques we use. At the same time, let's take the primary responsibility for teaching math in the grade schools away from the classroom teacher.
Instead let's concentrate our efforts on math specialists who would provide the majority of math instruction in the grade schools, and who would work with regular grade school teachers to help them provide supplementary instruction. Math specialists could be recruited from the minority of current and prospective grade school teachers who are good at mathematics and who like to teach it (perhaps some 10 or 15% of all grade school teachers). A single math specialist working with the regular teachers should be able to serve several grade school classes. Unlike the regular teachers, the math specialist would have a better grasp of both the fundamentals of the subject and the various pedagogies that could be used under different circumstances. He or she ought to be able to do a far better job of teaching math than a regular teacher, who must teach all subjects.
Now to get this
idea to work in the "real world" we would have to be willing to pay for
this extra expertise. But, if we pay a premium for a grade school
math specialist that should help with recruiting efforts. In any
case, we couldn't do worse than we are doing now! It's worth a try.....
The
Irascible
Professor invites your comments.
©1999
Dr. Mark H. Shapiro - All rights reserved.