Note: The views and opinions expressed in this document are solely those of its author. The contents of this document have not been reviewed or approved by the University of Minnesota. This is a slightly modified version of the statement that was delivered on January 25, 2001 to members of the Higher Education and Education Policy Joint Committee of the Minnesota State Legislature.

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. I am well informed about recent trends in math education.

Why I have become involved:

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. I can help the local school districts by letting them know what kind of expectations we have for students entering our classes. It is important that the viewpoint of the math department at the U have a representative, and I have been assigned (by my chairman) to fill that role.
5 of my concerns:
  1. In our haste to reform math instruction in the public schools, we risk the 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 doesnít need fixing. And in spite of what you may have heard, there is no reliable data to support completely eliminating the traditional high school math track for these students. Can we afford to throw out something that has been successful with precisely the students who are inclined to enter scientific and technological fields?
  2. 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 with their children in the evenings, trying to help them get through math. I have talked to dozens of parents whose children are in "integrated" or "reform math" classes. The overwhelming majority of them report that their children are having 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. 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?
  3. 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 scientists, engineers, and mathematicians badly misinformed about what is important their our own fields? Should their input be ignored?
  4. 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. Letís not ignore those weaknesses.
  5. The new texts contain many errors. If you want to know more about this point, please contact me. For a sample list of errors in Core+ texts, see

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
Traditional math instruction Reform math instruction
High school math divided into four separate classes: Algebra I, Geometry, Algebra II, and Precalculus (which includes trig and possibly other topics like statistics) Several simultaneous "threads": Algebra, Geometry, Trigonometry, Probability and Statistics, Discrete math, Math modeling, often mixed within single units of text
Lectures and teacher-led discussions, with individual or group practice; a few enrichment projects Mostly group work, with teacher as "facilitator"
Mathematical rules, procedures, and definitions always presented early in chapters that have been organized by different mathematical topics. Concepts reinforced first by drill-type exercises, then by word problems. Section and chapter summaries usually given. Everything presented "in context", in the form of exploratory word problems and projects, with very few rules, definitions, summaries, or drill-type exercises. Students discover rules and procedures for themselves, making a journal or "toolkit" to keep track of what theyíve learned.
Students learn to solve problems with pencil and paper, w/ emphasis on speed, accuracy, "computational fluency". Students learn to use calculators and other technology, w/ emphasis on understanding, problem-solving, estimation.

Traditional instruction at its worst: Interest in mathematics is killed by tedious drill that has little relationship to reality. Students might be able to solve routine problems, but they have no idea what the point is. Because algebra and geometry are separated, students see no relationship between them. Geometry and algebra require different skills, so many students do poorly in one of the first two years of high school and then quit.

Traditional instruction at its best:

Students have a sense of accomplishment as they gain computational fluency. As a result, they can confidently tackle interesting word problems and "enrichment" modules. Advanced math courses (like calculus) are easy for students that have a solid foundation of computational skills, without over-dependence on the calculator. Mathematical formulas and rules become powerful tools, applicable to a wide variety of situations. The emphasis on accuracy and precision benefits all parts of the studentís education. Material is organized efficiently, so it can be covered quickly (as in college).

Reform instruction:

Good news: Some teachers report that more students stick with math through high school in the reform approach than they do in the traditional approach. And students who simultaneously take both traditional and reform classes seem to do quite well. In one pilot study carried out by the developers of reform textbooks, reform students seemed to do slightly better on college placement exams than traditional students. Bad news: Pilot studies are notoriously unreliable. I have received widespread reports of serious problems from parents and teachers alike. In fact, all of the direct evidence that I have is negative. Please consult my list of concerns about math reform. Bottom line: No one knows what the long-term effects will be. This is still an experiment. My best guess is that it will be 5-10 years before reliable results will be available.