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:
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
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 they’ve 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 student’s 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.