by Dr. Mark H. Shapiro
"The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry."... ...Bertrand Russell.
Commentary of the Day - March 12, 2008: Singapore Math and a Possible Truce in the "Math Wars."Mathematics education in the United States has been in somewhat of a crisis for nearly two decades owing to ongoing battles between vocal factions that disagree about how math should be taught in elementary and secondary schools. One side, represented mainly by math educators and the National Council of Teachers of Mathematics (NCTM), has pushed for an approach to math education that places far less emphasis on rote memorization and drill, and much more emphasis on "constructivist" techniques that encourage students to learn basic mathematical principals through a process of "guided discovery". This approach often is accompanied by the early introduction of calculators for the solution of numerical problems.
The other side, represented by parent groups and many university mathematicians, favors a return to more traditional methods (direct instruction) that include greater emphasis on such things as learning the multiplication tables, repeated drills on the basic algorithms of arithmetic, and traditional word problems. Paper and pencil calculations often are favored over the use of calculators in the early grades.
The rhetoric in the "math wars" frequently has been heated. Traditionalists have called the constructivist methods "fuzzy math", and the constructivists have called the traditional approach "drill and kill." The situation has been complicated by the fact that the each state has its own standards for public school math education, and these standards vary widely. This, combined with the fact that most math curricula are taught in a "spiral" fashion where individual math concepts are revisited many times as students progress through the grades, has presented problems for the textbook publishers. It's not unusual for math textbooks to run well over 500 pages in length, regardless of approach, in order to meet the various state requirements.
Recently, the National Mathematics Advisory Panel (appointed by President Bush in 2006) has tried to broker a truce by noting that there is little scientific research that definitively shows one method of math instruction to be better than the other. Instead, the panel has called for a strong focus on essential math concepts, and has provided a series of benchmarks that should be achieved regardless of the method used and location within the United States. For example, under the "Fluency with whole numbers" benchmark "By the end of grade three, students should proficient with the addition and subtraction of whole numbers"; and, under the "Fluency with fractions" benchmark "By the end of grade four, students should be able to identify and represent fractions and decimals ..." et cetera.
The panel also expressed concern about the continuing mediocre performance of American students on international tests of mathematics proficiency. Although the averages for American students on most of these tests are modestly above the overall international averages in almost all cases, a number of Asian countries including Singapore, the Republic of Korea, Hong Kong, Taiwan, and Japan significantly outscore American students. While some part of the difference in performance can be attributed to the highly heterogeneous nature of the American student body, it often has been suggested that much of the difference can be traced to less effective teaching techniques.
Because Singapore students almost always end up in first place in the international comparisons, the methods used to teach mathematics there have received some attention here. In particular, English versions of the textbooks used to teach mathematics in Singapore have become available in the United States; and, they have been used in test programs in a few school districts in different parts of the country. Mitchell Landsberg, writing in The Los Angeles Times reported on the experience with "Singapore math" at Ramona Elementary School in Hollywood (Los Angeles). He found that in 2005 only 45% of Ramona Elementary fifth-graders scored at grade level on a standardized state test. In 2006, after Singapore math had been introduced, 76% of fifth-graders were scoring at grade level. That was considered significant because most of the students at Ramona Elementary are from low-income, immigrant families (mostly from Central America and Armenia), and nearly 60% of them speak English as a second language.
As Landsberg's article notes, the unique feature of the Singapore approach to math education is that it emphasizes the basics while at the same time instilling a deep understanding of key mathematical ideas. The pedagogy has been structured to use drill to reinforce patterns of mathematical thinking that appear again and again throughout the curriculum. Singapore math thus bridges the concerns of both traditionalists and constructivists, and develops mathematical intuition in "gentle, clever ways" according to University of Illinois at Chicago mathematics professor Yoram Sagher, who trains teachers to use the Singapore math materials. In addition, the Singapore math texts avoid the repetition common in most American math texts. Only a limited number of concepts are introduced in each year of the program. Each new concept builds on previously learned ones, and students must master each concept before progressing to the next one. Clearly, not every student will proceed at the same rate, but this approach helps teachers to identify students who need more help.
The experience at Ramona Elementary and at a few other schools elsewhere in the country shows that the approach works provided that teachers are carefully trained to use it correctly. Unfortunately, when the Singapore math materials were first introduced in the United States they included little support material for teachers. That has changed to some extent. But, more importantly, California has placed the Singapore math books on its list of approved elementary math texts, which means that school districts in California that want to use the books will receive a subsidy to purchase them, and this may lead to wider adoption. Wider adoption should determine if this approach can provide the boost that American mathematics education needs.