The U.S. has long been pouring resources into K-12 education. Yet American students do not shine in mathematics. For years, their performance been at best mediocre when compared with students in other, poorer countries. (Evidence of our mediocrity is found in the Trends in Mathematics and Science Study and the Programme for International Student Assessment.
It isn’t that students in the U.S. are less intelligent than are students in such countries as Singapore, Japan, and Latvia, all of which had higher average scores. Instead, the problem seems to lie in the way we teach math.
That is exactly the conclusion reached by the prestigious group of mathematicians who have studied how math is taught in America’s schools of education. Their report, “No Common Denominator – The Preparation of Elementary Teachers in Mathematics by America’s Education Schools.” was released in June. It probes the way we prepare teachers who will be responsible for teaching mathematics and finds that many education schools are not doing a good job.
Professor Kenneth Gross of the University of Vermont has written, “All of mathematics depends on what kids do in the elementary grades. If you don’t do it right, you’re doing remedial work all the way up to college.” Unfortunately, we aren’t doing it right. That means that we waste a lot of resources in trying to make up for the inadequate instruction many students receive in the early grades.
Even then, we wind up with a lot of young people who are permanently handicapped in math. If you’ve ever encountered a young cashier who is stumped when you plunk down $1.04 for an item costing 79 cents, you know what I mean.
The root of the problem, according to the report, is that actual mathematicians have very little input on the mathematics education of new teachers:
The administrators of the education school, not mathematicians in the mathematics department, generally determine what mathematics courses will be required and how many. While many academic mathematicians have little direct interest in teacher preparation, those who do often stand frustrated on the sidelines, feeling strongly that prospective teachers need more preparation in mathematics content.
Consequently, many teachers in elementary and middle school are lacking depth of comprehension in math. We wind up with second grade teachers who can just barely do third grade math, which makes it difficult if not impossible for them to really explain math concepts to their students. Quite a few teachers are math-phobic themselves and are therefore apt to convey to students the idea that math doesn’t have to be taken seriously. (After all, we have calculators, don’t we?)
The report set forth five standards for education school math preparation, then surveyed a sample of education schools to see how well they met the standards.
Here are the five standards:
• Aspiring elementary teachers must acquire deep conceptual knowledge of the math they will need to teach, focusing on four key areas: numbers and operations, algebra, geometry and measurement, and data analysis.
• Education schools should insist on higher admission standards, with candidates able to show that they have at least a sound knowledge of high school mathematics.
• Prospective teachers seeking licensure must be able to demonstrate that they have sufficient competence in math.
• Math content courses should be taught in close coordination with a methods course that gives students numerous opportunities for practice teaching.
• The job of teaching math content to prospective elementary teachers should be within the purview of the mathematics department.
With those criteria in mind, the report analyzed the programs at 77 colleges and universities. The only North Carolina school included was Greensboro College, so we don’t know how well the education schools in the UNC system would fare. Only the program at the University of Georgia was regarded as exemplary. Several others that received good marks were the University of Maryland, the University of Michigan, Boston College, and the University of Montana.
The report also finds that only one state – Massachusetts – has taken the necessary steps toward upgrading the preparation of teachers. Regulations there state:
Candidates shall demonstrate that they possess both fundamental computational skills and comprehensive, in-depth understanding of K-8 mathematics. They must demonstrate not only that they know how to do elementary mathematics, but that they understand and can explain to students, in multiple ways, why it makes sense.
That’s good, but such stringent standards will run into a problem – they will weed out many prospective teachers at a time when we are looking to increase the number of teachers.
That is a short-run problem that we’ll have to accept in order to solve the long-run problem of weak math instruction. People who want to get into teaching but are math-phobic will have to bite the bullet and learn math well enough to pass the exam. My guess is that in Massachusetts or any other state that requires serious math competency, something akin to bar review courses for new law school graduates will spring up, giving those who are weak in math a crash course. It’s better to set the standards high and require people to meet them than to keep them low so no one is too uncomfortable.
The study has drawn support from quarters where you might have expected defensiveness. For example, Donald Langenberg, Chancellor Emeritus of the University of Maryland, praises the report, saying, “Our education schools urgently need to ensure that our elementary teachers do not represent in the classroom the substantial portion of our citizenry that is mathematically disabled. We must not have the mathematically blind leading the blind.” And that’s precisely the problem. As things now stand, teachers who are “mathematically blind” can end up trying to teach math to their students.
There is no reason why Americans should tolerate that.
The way our colleges and universities train future teachers is extremely important. A recent Pope Center paper found that North Carolina’s education schools are largely committed to dubious theories of education. Now we have reason to question how well they prepare teachers to teach math. We urge elected officials in North Carolina, UNC system administrators, and decision-makers at the private colleges and universities with education schools to scrutinize the study and then act on it.