Math movement robs generation of basic skills
SAN DIEGO UNION-TRIBUNE • SUNDAY, DECEMBER 22, 1996
Math movement robs generation of basic skills
By Steve Baldwin
One of public education’s biggest obstacles, I have often concluded, is its lack of an immune system to fend off foolish and untested ideas. As a result, bureaucrats and educational theorists waste not just the money spent on education, but our most precious resource: a generation of our children.
Take for example the recent results from the Third International Mathematics and Science Survey. Though low scores from U.S. students are old news, TIMSS is just another aftershock from the recent earthquakes that have rocked the educational establishment. For the uninitiated, TIMSS is the biggest and most thorough comparative math study ever produced. American math students ranked 21st out of 41 countries rated, well behind Japan, South Korea, France, Russia, and even Bulgaria.
Meanwhile defenders of Constructivist Math (or what its critics call the ‘New new math”), the movement that has swept math instruction in the last decade, are struggling to put the best face on this bad news.
For the record, the document that determines California’s math approach is the California Math Framework. The central features of the Math Framework are based on a teaching philosophy focusing specifically on child-centered “discovery learning,” group work, and an excessive focus on “real-world problems.” The current wave of popularity of these ideas dares from the early 1980s efforts of the National Council of Teachers of Mathematics to promote them. However, these proposals were crystallized and given official clout in the influential 1985 California Math Framework.
And we have paid the price. The most recent National Assessment of Educational Progress (NAEP) shows California near the bottom of the participating states.
When surveyed for TIMSS, 95 percent of American math teachers said that they were aware of the main tenets of Constructivist Math and almost 75 percent believe that they have implemented them in the classroom. Yet the Constructivist Math partisans at the U.S. National Research Center for TIMSS and at the U.S. Education Department’s National Center for Education Statistics seek to disassociate America’s continuing mediocre TIMSS scores from Constructivist Math itself. The principal excuse they offer is that it’s still too early to tell. But the reality is that the classroom mechanics of Contructivist Math have proved to be immensely popular with American math teachers.
In primary and secondary classrooms, math teachers have embraced:
Child-centered discovery learning, where the teacher asks unknowing students, “What do you think?” Critics contend that instead of explicitly teaching and directly answering questions, today’s math classes are nothing more than “math appreciation” that does not adequately prepare students for college or for the working world.
Students working on problems in classroom groups and having divergent levels of ability within those groups. What the theorists call “cooperative learning” contradicts real world experience. In actuality, adults who do math in organizations rarely do so in a group setting. However, with mixed abilities in an academic setting, the faster learners do most of the work. Regrettably, what we have is a group of students who only learn to split up the work and then copy the answers.
De-emphasis on learning essential and fundamental math skills (such as the multiplication tables) and standard solution-techniques (such as carrying and borrowing). Just as “whole language” skipped phonics and went straight to reading literature, today’s Constructivist Math has attempted to cast aside computational basics and go to the final productions that rely on math.
Student use of calculators at all times, sometimes beginning as early as kindergarten. The idea being that this will free the student from being bogged down from doing such mundane things as adding and subtracting. However, algebra students have been known to reach for a calculator in order to divide 300 by 3.
The T!MSS research of American classrooms shows, as the National Center for Education Statistics admits, “many examples of these techniques in the absence of high-quality mathematical content.” Sadly, by stressing exposure and not teaching fundamental skills, math instruction in American classrooms is a mile wide and an inch deep.
Thus, the results of TIMSS show that American math teachers and state and local education officials who have embraced Constructivist Math have failed. Specifically:
American teachers are not covering the important concepts of mathematics in systematic fashion and instead are teaching real-life and hands-on topics that are favorites of the constructivists. While many of these are cute, such as writing essays and doing math art, mathematically they are dead-ends and they waste precious time. Tragically, these topics do not lead to algebra and geometry, which are the gateways to further progress in math for the individual student.
American math classes are unfocused. This is a direct consequence of Constructivist Math, which often asks students to solve big, unwieldy, and fuzzy problems that at times do not have a clear answer. Quite often, unrelated topics tend to pop up sporadically in such problems. Hence they are not helpful in developing a thorough mastery of concepts.
American teachers are not covering math topics in depth. Teachers spend only a little time on most topics. Instead, American students shallowly repeat the same topics grade after grade. Students often encounter the same “fun” problem in several consecutive grades.
Some of this repetition can be traced to the lack of grade level standards. If we developed statewide standards and rigorously followed them, we would not be looking at a math disaster of gigantic proportions. The fact that a teacher cannot know whether an incoming third grader knows his times tables, coupled with the high mobility of today’s students, leads our schools to teach and re-teach topics such as multiplication, division and fractions in a cursory fashion year after year. Re-teaching some topics three to five times during grades two through eight leaves little time for algebra and geometry, which are taught in other nations by the eighth grade. Accordingly, foreign students have moved far ahead of American students.
Regrettably, American teachers have not taught students to understand and apply math concepts in novel (or even routine) situations. Proponents as well as critics of Constructivist Math want students to be able to do this. Teachers have adopted the gimmicks, processes and procedures of Constructivist Math, but without the advance in conceptual understanding that the best of the old math practitioners sought and that constructivists promised would come with conversion to their classroom techniques.
Bear in mind, however, that it is not the teachers who are responsible for pushing this technique, but rather it is the educational theorists at the state Department of Education, district administrators, and misguided and ill-informed school board members who must shoulder most of the responsibility.
Furthermore, as a member of the state Curriculum Commission, the agency entrusted with approving math textbooks, I was shocked to discover that the criteria used to determine which books are approved did not include field performance data. In fact, the most successful math book in the nation has been systematically excluded by the educational establishment.
The TIMSS test wake-up call may save California and the rest of the nation from a mistake that’s potentially as disastrous as whole language was to our reading scores. TIMSS shows that high-level mathematical reasoning is not going on in the classrooms.
As one parent told me, “When people are building bridges, we want them to have the right answers, and in math there is a right answer. What we want is a rigorous computation, not the touchy-feely stuff.”
With all the recent talk of building bridges to the 21st century, I just hope we will still have the ability to build them correctly.
Baldwin, R-La Mesa, is the outgoing chairman of the state Assembly Committee on Education