Not all math classes are the same even in the same school

Researcher William H. Schmidt believes education has become a game of chance in which the odds of success are predicated on factors outside the control of the students, including where they live, the schools they attend, the teachers they have and the textbooks they use.

An internationally recognized researcher on effective math education, Schmidt says that U.S. students lack equal opportunities to learn math, something he saw firsthand when he took sabbatical from Michigan State University to spend a year at the University of Virginia.

As an author of Michigan’s math standards, Schmidt knew his second grader would have been learning multiplication tables up to the number five back home in East Lansing. In Virginia, multiplication was not taught at all in second grade, reinforcing what Schmidt already realized from his international comparisons: All math classes are not equal and students do not have the same opportunities to learn math.

In his new book “Inequality for All: The Challenge of Unequal Opportunity in American Schools,” co-written with mathematician Curtis C. McKnight, Schmidt documents in great detail the variations in not only how math is taught across districts, but within schools. The variances occur in affluent and poor districts. In fact, they found the greatest variation in content coverage in schools that serve middle-class children.

“A topic can be covered or not covered,” he says. “Topics can be covered within different sequences, some of which may not make any sense from the point of view of the content itself. Students can receive more or less time for instruction, depending on the teacher’s decision.”

Schmidt also found that textbooks had a far greater influence in U.S. classrooms on what is taught. That’s a problem because he also found that we don’t have particularly effective textbooks.

In coding 353 math and 150 science textbooks, Schmidt found great variances in what was covered and at what depth. His conclusion: U.S. textbooks offer the worst of all worlds in that they are often more complex and less coherent than books used in other countries.

“We have to break the notion that that the textbook is the curriculum,” he says.

Speaking from his home in Michigan, Schmidt cited several factors for the wide array in math instruction, from lackluster teacher training to phone book- sized textbooks that go wide but not deep. (He notes that U.S. fourth grade math textbooks can run 500 pages, compared to the 150-page books used elsewhere in the world.) And teachers often confront contradictory marching orders from state standards, district pacing guides, textbooks and test content.

In surveys of teachers, Schmidt found that many don’t feel prepared to teach the more rigorous math standards. Despite the push to introduce algebra in middle school, only half the teachers felt academically well-prepared to teach expression and simple equations, fundamental algebraic concepts.

“We put teachers in totally impossible positions,” he says.

Consider that when Georgia introduced its integrated math eight years ago, half of the middle school teachers who responded to a state survey expressed doubts they could teach to the elevated bar because their own math content wasn’t deep enough.

(Although Georgia is backing away from its integrated math in which elements of algebra, geometry and statistics are interwoven with increasing difficulty over time into single classes, Schmidt notes integrated math “is more consistent with what is done everywhere in the rest of the world.”)

Schmidt blames teacher prep programs and state certification for gaps in teacher skills in teaching math. “States set up their own certification requirements and universities implement those requirements. Teachers were told what to take and they did it, and it was just not adequate.”

Another factor undermining math education is ability tracking, which he proclaims “a dumb idea. It is like a race. Kids go faster and faster and not deeper. In the rest of the world, there is almost no tracking. They take the brightest kids in the class and allow those kids to go deeper.”

In this high school math arms race, Schmidt says conceptual depth emerges the loser. He cites the surge in high schools students taking calculus, only to arrive at college with procedural skills but a weak grasp of the deeper substance.

He also expresses skepticism at the drive to make math “fun” through video games and other online platforms, pointing out an essential truth to which any Georgia Tech student will attest: Math is tough.

Schmidt has studied international math instruction and is aware of the extra classes that kids take in other countries, including the “juku” schools in Japan. While he recognizes the value of online tutorials as adjuncts to traditional math preparation, he says, “I don’t think as they now sit, they would be a total replacement for in-class instruction for the kids.”

“What I learned from all the international research, from kids all around the world who are doing the best on the tests, is that they don’t like math particularly and they find it hard. We just keep believing in a magic grail, a magic bullet, that will somehow make it easy,” he says.

Schmidt believes that we ought to find ways to help students understand math connections to the real world and to their futures. He says other countries have proven that all students can be taught math essentials, contending that the new Common Core state standards adopted by most states, including Georgia, are the first step to finally laying out the math reasoning skills that we expect all American kids to attain.

But he says, “I have a degree in mathematics. I never really found it fun. I was always nervous when I had a test because I knew it would not be easy. Math is hard; it’s hard for the teachers and it’s hard for the kids.”

Schmidt does not argue that schools can eliminate all achievement gaps among students, noting,  “When they are left free to achieve in comparable circumstances, unequal results will likely follow.”

But, he says, we do not have comparable circumstances now in U.S. schools. “Schools must provide equal content coverage for children of all backgrounds at least through the first eight years of schooling,” he says.

Denied that, Schmidt cautions, “Even the most motivated and striving student in those circumstances will achieve less, likely even less than other students in different circumstances who are not as motivated or do not work as hard. This situation fundamentally violates another American value — that of fairness.”

–From Maureen Downey for the AJC Get Schooled blog