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January 25, 2001
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Math Instruction
Written testimony of Dr. Lawrence Gray

to members of Minnesota's
Higher Education and Education Policy Joint Committee

Who I am:

My name is Lawrence Gray. I am a Full Professor and Director of Undergraduate Studies in the School of Mathematics at the University of Minnesota. As such, I am responsible for the math instruction of the roughly 11,000 undergraduates that enroll in math classes at the U each year. In particular, I am in charge of our undergraduate math curriculum, and I meet regularly with faculty in many other departments to try to ensure that our courses meet their needs.

I am a research mathematician (currently working on the mathematics of traffic jams), so my field is not Math Ed. But I have taught math at the U since 1977, everything from College Algebra to graduate courses in Probability Theory. I have co-authored two texts. I have taught courses using a variety of methods, including the exploratory group-learning approach common to some of the latest K-12 math curricula. I helped design a sophomore calculus course that makes extensive use of computer technology.

I have also spent considerable time reviewing high school math texts, particularly the Core+ material. So I am well-informed about recent trends in math education.

In certain respects, I consider our math students at the U to be my customers. I decide on the content of their courses, I teach some of them in the classroom, and I handle their complaints. One of the most important factors in their level of satisfaction is the level of mathematical preparation that they have when they graduate from high school. I am interested both personally and professionally in anything that impacts on that level of preparation.

Little by little, I have been increasing my involvement in math instruction in the public schools. I feel that I can be useful to them, because I am the authority on the expectations that we have at the U for high school graduates, in so far as math is concerned. For example, I am currently working with the Roseville schools, to help them with their math skills assessment tests, and also to consult with them about their recently approved two-track math curriculum, in which parents and students can choose between traditional math content and the new Core+ curriculum. My chairman and I both feel that this kind of outreach is an important part of my job.

In our haste to reform math instruction in the public schools, we risk a real danger of turning our backs on our prior successes. By using traditional high school math courses, we have done quite well with those students who are inclined to go into technological or scientific fields. Over 90% of the students who enter IT (Institute of Technology) are ready to take Calculus I (or higher) during their first semester at the U, and of those, well over 90% pass their first math course. These are all students who had four years of traditional high school math. But now, many school districts have decided to force all of their high school students to take the recently introduced "reform" or "integrated" math (such as Core+). Even Steven Leinwand, who is one of the leading advocates of the recent math reforms, has admitted that for what he calls the "top 20%", our math instruction in K-12 doesn’t need fixing. And in spite of what you may have heard, there is no reliable data to support completely eliminating traditional high school math. Can we afford to throw out something that has been successful with precisely the students who are inclined to enter scientific and technological fields?

I put a great deal of stock in the concerns raised by parents about recent reforms in math instruction at the K-12 level. They are the ones who sit at the kitchen table in the evenings, trying to help their children get through math. I have talked to dozens of parents whose children are in "integrated math" classes. The overwhelming majority of them report that their children have serious difficulties with "basic skills", and they report that it is very tough to help their children once they fall behind (for example, due to illness). Because of the way in which some of the new texts are written (no worked out examples, very few summaries of basic math facts, rules, or formulae, and much skipping around of topics), they seem almost designed to alienate parents who try to help their children. Perhaps this explains why so many of them are organizing themselves to demand the traditional math option for their children. This is what happened in the Roseville School District, where I am involved. Parents are a critical part of the K-12 educational process, and they are the ones who will likely pay for extra math classes in college if their children are not sufficiently prepared. Can we afford to ignore their concerns?

While the content and emphasis found in "integrated math" courses have almost universal support within the Math Education academic community, they are viewed with widespread suspicion among scientists, research mathematicians, and engineers. In our disciplines, we expect our students to be comfortable with basic mathematical skills, both with and without calculators. Indeed, we find that the students that have the most difficulty in our courses are typically those that are weak in this area. But recent trends in K-12 math education put low priorities on these kinds of skills. Are we scientists, engineers, and mathematicians badly misinformed about what is important in our own fields? Should our input be ignored?

According to advisers that I have talked to in the IT Lower Division Advising Office, the most common reason given by students for failure in our math classes is that they had become too dependent on their calculators in high school. Yet many math educators say that we need to give the calculator and other such technology an even bigger role in math classes. There are definite strengths and weaknesses in using calculators and computers in math classes. Let’s not ignore those weaknesses.

I do not want to be misunderstood when I express these concerns. I am supportive of most of the goals of the "reform" movement. We can and should improve math instruction in K-12. We can and should train our math teachers in a variety of pedagogical approaches. We can and should reach out to students who have traditionally been left out of effective math instruction. The traditional math content and emphasis is not for all students. But it is dangerous to radically eliminate something that has proven effective for an important segment of our student population. And it is equally dangerous to ignore the concerns of the parents, and of the professionals in scientific and technological fields. I can be contacted at gray@math.umn.edu

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