SPECIAL SERIES: TEACHING MATH
Elite math classes show big increase
For all the students who are struggling with even the most basic math concepts, there is a corps that is taking advanced classes, such as calculus, at an earlier age than ever before. Such courses are now seen as critical for students to thrive.

Bottom line for math students: Good teaching is what counts

By ALAN J. BORSUK
aborsuk@journalsentinel.com
Oct. 6, 2003

Second of four parts

Teaching Math: No Simple Formula

Quotable
You can give a great program to a lousy teacher, and it won't go anywhere.

- Diana Kasbaum, math specialist with the Wisconsin Department of Public Instruction

Math Facts
Some experts worry that U.S. math teachers don't know enough basic math. To test this, a University of Wisconsin-Madison education professor who taught a class for prospective elementary school math teachers gave them an eighth-grade-level problem to gauge their expertise. The problem:Divide 25.56 by 0.004 Fewer than half of them got the right answer, 6,390.

MORE MATH FACTS

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Section: More education news, features

The Series
SUNDAY: Despite the importance of a future work force that can cope with the everyday demand for math proficiency, students across the United States are not doing very well. And there is no consensus on how to respond.
MONDAY: Despite waves of change in math education, quality teachers - more than the choice of a curriculum - continue to spell the difference between success and failure. One problem: There aren't enough of them.
TUESDAY: Some high school students are taking advanced math classes earlier than ever before. And then there are those headed for remedial classes in college.
WEDNESDAY: Competence in math enhances quality of life, can create a more disciplined mind and can open the door to better jobs. But most math competency exams offer mixed news, at best.

A national commission on how to teach mathematics in school reached this conclusion:

"The greater part of the failure of mathematics is due to poor teaching. Good teachers have in the past succeeded, and will continue to succeed, in achieving highly satisfactory results with the traditional material; poor teachers will not succeed even with the newer and better material."
That was in 1923.

Richard Askey, a University of Wisconsin-Madison math professor, quoted from the report during a 1999 conference at Harvard University on the controversies surrounding how to teach math. Askey has become a prominent figure in arguing that the biggest problem with how math is taught isn't the choice of curriculum. It's whether the teachers are able to do their jobs effectively.

Through multiple waves of math reform, through dramatic changes in technology, culture and schools themselves, what was true in 1923 is true in 2003: Teachers matter.

As Johnny Lott, president of the National Council of Teachers of Mathematics, put it: "The value of the good teacher is almost immeasurable. . . . The good teachers are probably going to outweigh, in many instances, the material."

Or as Diana Kasbaum, a math specialist with the Wisconsin Department of Public Instruction put it, "You can give a great program to a lousy teacher, and it won't go anywhere."

Recent research supports that thought.

Horizon Research, a private firm based in Chapel Hill, N.C., analyzed more than 300 math and science classes in 31 school districts across the United States. Using trained observers, it rated 59% of the classroom sessions as low in quality, 27% as medium-quality and 15% as high-quality. (A minor math lesson: When you round percentages, they can come out to 101% sometimes.) The study was funded by the National Science Foundation.

Iris R. Weiss, president of Horizon and the lead researcher, said researchers concluded that teachers can use either constructivist or traditionalist approaches to teach math effectively - or ineffectively - and there was no correlation between that choice and whether a class was of high quality. The constructivist approach focuses on teaching kids to solve problems on their own; the traditionalist approach focuses on teaching them basic math fundamentals. The best thing, Weiss said, might well be to use elements of both.

The key issues, the study concluded, were running classes in which students are challenged, their performance is monitored and they are helped to grasp both concepts and skills.

Ways to improve teaching

Improving the quality of work that teachers do in math classes, from kindergarten through high school, is a subject that comes in a variety of flavors. Some focus on better preparing teachers while they are in college; others on offering more chances for teachers to improve their skills on the job; still others on addressing the frequently low grasp of basic math knowledge of many teachers.

The new federal education law, known as No Child Left Behind, calls for all teachers to be "highly qualified" in their subjects by the end of the 2005-'06 school year. Math will be on the front lines of that effort.

That will be all the more true in Milwaukee, where work on improving teacher quality recently received a huge boost. The National Science Foundation announced Sept. 26 it would provide $20 million over five years for efforts that include a fresh push to improve how people studying to be math teachers in local universities are prepared for the job, and creation of broader opportunities for current teachers to work together and increase their effectiveness.

Critics say such grants have often been ineffective nationally, but educators involved in the local grant say they are confident the money will help across the spectrum of math programs practiced in Milwaukee.

"We're going to see those math scores go up," said DeAnn Huinker, director of the Center for Science and Mathematics Research at the University of Wisconsin-Milwaukee.

But it won't be easy, either in Milwaukee or anywhere else.

U.S. Department of Education officials say fewer than 50% of math teachers have a major or minor in math, and many education schools say their classes for preparing teachers to deal with math have had low enrollment.

Some associated with the Bush administration have pushed to make it easier for people with strong backgrounds in math to get licensed as teachers through alternatives to the standard ways of training and licensing teachers. So far, there does not seem to be a major national change in that direction. But there is a general shift toward requiring new teachers going into subjects such as math to have more background in math classes, prodded in large part by the new law.

In-service training

Once teachers are in the classroom, the amount and quality of the training they get vary widely and often end up being fairly sparse. Many education advocates say that in other developed countries, teachers are given far more time to prepare for classes and to work individually and in groups on raising the level of what they do in class.

There are efforts under way nationwide to improve "professional development" for teachers - it is one of the stated goals under the No Child Left Behind law. In Wisconsin, there is also a new licensing system being implemented for teachers that raises the requirements for continuing development of skills. But many such efforts in the past have hit up against budget and time pressures.

Then there is the issue of performance in the classroom.

In too many American schools, some experts contend, math is taught through a teacher lecturing, the students following (or not), a lot of repetition of material and the slow introduction of new ideas.

A commission headed by former astronaut and Sen. John Glenn told the U.S. Department of Education in a report in 2000: "The basic teaching style in too many mathematics and science classrooms today remains essentially what it was two generations ago. By contrast, teaching innovation and higher student performances are well documented in other countries, where students' improvements are anchored to an insistence on strong professional development of teachers."

The Glenn Commission said, "We are of one mind in our belief that the way to interest children in mathematics and science is through teachers who are not only enthusiastic about their subjects, but who are also steeped in their disciplines and who have the training - as teachers - to teach these subjects well."

Knowing one's subject

For experts such as Askey, the phrase "steeped in their disciplines" is critical. Their concern is: Do many teachers themselves know basic math very well?

Askey started teaching a course four years ago in Madison for prospective elementary school math teachers. One of the things he did was ask them a question from an eighth-grade math test that was used in an international study several years ago: Divide 25.56 by 0.004. Fewer than half got the right answer (which is 6,390).

It was another piece of evidence, in his view, that far too many math teachers don't have a strong grasp of the basics of what they're aiming to teach.

A study this year conducted by RAND, the widely known California-based research organization, said, "Numerous studies show that many teachers in the United States lack adequate knowledge of mathematics for teaching mathematics. Moreover, research indicates that higher proportions of classrooms in high-poverty areas, compared with classrooms in the nation as a whole, are staffed with poorly prepared teachers."

Concern about the quality of American math teachers was spurred by a 1999 book, "Knowing and Teaching Elementary Mathematics," by Liping Ma, whose early education was in her native China and who went on to study in American universities. For her doctoral dissertation - which grew into the book - she compared how teachers in China and in the U.S. handled routine topics in grade school math.

Her conclusion was that the Chinese teachers, who had much less advanced formal education, had much more profound knowledge of basic math and had worked much harder, individually and in groups, on developing effective ways to teach skills.

For example, she asked teachers from each country to divide 1 3/4 by 1/2 and explain how they would teach that to students.

Only nine out of 21 U.S. teachers even got the right answer, and just one suggested a method of teaching how to divide a fraction by a fraction that Ma listed as "conceptually correct."

All 72 Chinese teachers gave correct answers, and 65 created more than 80 story problems for illustrating the process that were creative, easy to understand and appropriate.

(The correct answer is not 7/8, a common mistake. That's what you get when you multiply 1 3/4 by 1/2. When you divide by 1/2, the answer is 3 1/2. You are, in effect, figuring out how many 1/2's there are in 1 3/4.)

Ma asks in her book, "What kind of 'teaching for understanding' can we expect" from teachers who do not have a profound understanding of math themselves and who are not given much opportunity to work on improving how they do their work, including time to work on developing their teaching skills? Teachers in China work extensively, individually and in small groups, on ways to make sure they are doing their jobs well. American teachers have larger amounts of actual classroom time and very little time to work on improving their effectiveness.

"What U.S. teachers are expected to accomplish then is impossible," she says. "It is clear that they do not have enough time and appropriate support to think through thoroughly what they are to teach. And without a clear idea of what to teach, how can one determine how to teach it thoroughly?"

Ma's book has become a must-read among math teaching activists, with points in it that appeal to advocates of differing views in the debate over math teaching.

What's being done?

For all of the concern, it is not easy to point nationally to what is being done about raising the quality of classroom work by math teachers.

A math "summit meeting" held by the U.S. Department of Education in February ended with agreement on a three-point agenda for improving math education: Get the public more involved, launch more research on what works, and spur improved teacher knowledge. Two follow-up sessions have been held, and department officials are looking to the federal education law, No Child Left Behind, as a way to push for more math teachers who have strong backgrounds in math.

The national math teachers council, which has pushed for less-traditional, constructivist math curricula, also strongly backs more professional development for teachers, and the National Science Foundation, which backs the reform curricula, has made numerous large grants aimed at improving math teaching, such as the Milwaukee grant.

Advocates across the spectrum of the curriculum debate say that some of the problems with the kind of curriculum they support have to do with weaknesses in teaching and not weaknesses in their program.

At the 1999 Harvard forum where Askey spoke, Michael Battista, a Kent State University professor, said that unsatisfactory results in many schools that say they are implementing reform curriculum have to do with flaws in the implementation, not flaws in the theories.

From the other side of the debate, Roger Shouse of Penn State told the same forum that "reformers' attacks on traditional practices appear to reflect a failure to distinguish between 'traditional math' and 'traditional math taught badly.' "

Liping Ma is associated now with the Carnegie Foundation in California and is beginning work on a project with a California school district on what is called "lesson study," an approach used in Japan and China in which teachers work together to improve their teaching methods.

Kasbaum, of the Wisconsin Department of Public Instruction, says that for a school to succeed in offering high-quality math education, it needs a good curriculum, connected from grade to grade to minimize repetition and maximize the amount of progress; good instructional leaders; teachers who have a passion for their subject and their students; and strong professional development that leaves teachers prepared to implement models of what should be going on in classrooms.

But within the realities of what is going on in Wisconsin and nationwide, it is not hard to envision that the complaints about teacher quality in 1923 will survive the continuing waves of change in math education and still remain 80 years from now.

From the Oct. 6, 2003 editions of the Milwaukee Journal Sentinel