COMET • Vol. 3, No. 6 – 15 February 2002


 (1) “Smithsonian Marks 200 Years of Teaching Math in America” (press release)

Source: Adrienne Durand ( – 24 January 2002


…An exhibition titled “Slates, Slide Rules, and Software: Teaching Math in America” [takes] museum visitors back to the classroom with a display of tools used to teach math across American history, from the 1800s to the present.  The Smithsonian’s National Museum of American History exhibition [opened] on Feb. 8.  An on-line exhibition can be viewed at

…”Almost all Americans have vivid recollections of time spent in math class,” said exhibition curator Peggy Kidwell.  “This showcase places objects they may have encountered there within the broader framework of American history.”

Visitors will be able to see a wide variety of teaching tools.  A wooden blackboard from the 1800s was used in a New Hampshire school, established when several states founded the first public schools to provide basic education for their citizens. Blackboards became popular after teachers with ties to England and France introduced the erasable surfaces.

… The [geoboard] was invented by Egyptian-born educator Caleb Gattengo, who together with Belgian school teacher Emile-Georges Cuisenaire argued that students should learn basic concepts about math with tangible objects.

Graph paper, a math class staple, was developed between 1890 and 1910, when the number of high school students in the U.S. quadrupled, and math professors took an active interest in improving high school education.

A late 1950s “On-Sets” game was used to teach “set theory” and other ideas associated with the New Math taught to high schoolers during the Cold War, in the hope of increasing national security.

Casio, a Japanese firm, introduced handheld electronic “graphing” calculators to U.S. schools in 1986.  The University of Hawaii developed computer programs such as muMath in 1979 and later DERIVE in 1988 that could perform such functions as calculating algebraic equations.  Computerized devices became commonplace in math teaching as they became accessible to public consumption, and 20th-century math courses were reshaped to take advantage of such tools.

The National Museum of American History, Behring Center traces American heritage through exhibitions of social, cultural, scientific and technological history.  Collections are displayed in exhibitions that interpret the American experience from Colonial times to the present.  The museum is located at 14th Street and Constitution Avenue N.W., and is open daily from 10 a.m. to 5:30 p.m.  For more information, visit the museum’s Web site at or call (202) 357-2700, 357-1729 (TTY), or 633-9126 (Spanish).

(2) “Making Mathematics Work for All Children: Issues of Standards, Testing, and Equity” by Alan H. Schoenfeld

Source:  Educational Researcher 31(1) – January/February 2002


Mathematical literacy should be a goal for all students–so what makes it a civil rights issue? The answer becomes clear when one looks at the numbers. Disproportionate numbers of poor, African-American, Latino, and Native American students drop out of mathematics and perform below standard on tests of mathematical competency, and are thus denied both important skills and a particularly important pathway to economic and other enfranchisement… Hence conversations about the mathematical needs of American students must focus not only on what mathematics the students should learn, but also on how we as a nation can insure that all students have the opportunity to learn it.

This article addresses those issues. To set the stage, it begins with a description of mathematics instruction over the second half of the 20th century, describing the nature of the mathematics studied and increasing perceptions through the 1980s of difficulties with the curriculum. There was unhappiness with the curriculum on a number of grounds: equity being first, a narrow content focus aimed at preparing students for college being second, and national security being third. Such discontent led to calls for reform, with the National Research Council (NRC) issuing Everybody Counts and the National Council of Teachers of Mathematics (NCTM) issuing Curriculum and Evaluation Standards for School Mathematics (the Standards) in 1989. On the basis of a decade’s experience and research, NCTM issued a new vision statement, Principles and Standards for School Mathematics (Principles and Standards) in 2000.

In the years since 1989 there have been significant changes in the curriculum. Many of these changes have been controversial: Opponents of reform feared that an emphasis on process over content would result in weakening the curriculum and decrease American children’s mathematical competencies. Until now, there has not been the opportunity to evaluate the potential effectiveness of reform efforts. Large-scale change is slow. It took some years after the 1989 Standards was issued before curricula aligned with its reform goals could be developed and implemented; it took more time still before data on their effectiveness would become available. Such data are now beginning to come in, allowing one to see if the new curricula provide a basis for achieving the content and equity goals of reform–enfranchising all students and having them learn more powerful and useful mathematics. This article presents some preliminary data indicating that there are grounds for optimism. In research on some of the first largescale implementations of reform curricula, data indicate that reform students do as well on skills as students who study the traditional curricula, and that they do better on an understanding of concepts and problem solving. Moreover, traditional performance gaps between majority students and poor or underrepresented minorities are diminished, though not eliminated.

Those data indicate that the first few steps of reform seem to be going in the right directions. Given that, what kind of infrastructure is required to stabilize and build on this progress? Sustained, incremental progress calls for the availability of high quality curricula; for a stable, knowledgeable, and professional teaching community; for high quality assessment that is aligned with curricular goals; and for stability and mechanisms for the evolution of curricula, assessment, and professional development. This article briefly assesses the current state of each of these and the possibilities for improvement…

(3) Quantitative Literacy: Why Numeracy Matters for Schools and Colleges by Lynn Arthur Steen

Source:  MAA Online – February 2002


“As our society is driven increasingly by science and technology,” observed NSF Director Rita Colwell at recent Washington forum, “the need to establish levels of quantitative literacy becomes ever more important”…

Colwell’s remarks were made to an audience of over 100 scientists, mathematicians, educators, and policy leaders at a forum on quantitative literacy (QL) held at the National Research Council last December. Supported by the Pew Charitable Trusts, the forum was sponsored by the National Council on Education and the Disciplines (NCED) and hosted by the Mathematical Sciences Education Board (MSEB) in cooperation with the MAA. A report on the forum, including background papers distributed to participants and a white paper on quantitative literacy will be published later this spring. (The current version of the white paper is available online at

For purposes of discussion, the forum’s white paper defines quantitative literacy (also called “numeracy”) as the “quantitative reasoning capabilities required of citizens in today’s information age.” Speakers elaborated on this broad definition in various ways. Harvard mathematician Daniel Goroff illustrated QL with applications of Bayes’ theorem to health policy; Yale mathematician Roger Howe emphasized the policy implications of understanding orders of magnitude and significant digits…”The most important constraint on public policy,” argued Johns Hopkins economist Arnold Packer, “is public ignorance.”

…Most of the discussion focused on implications for educational policy of a commitment to achieve the appropriate levels of quantitative literacy that Rita Colwell emphasized in her remarks.

One challenge was conveyed by Anthony Carnevale, Vice President for Public Leadership of the Educational Testing Service (ETS). He asserted, with uncommon eloquence, that quantitative literacy is not so much about mathematics and democracy as about the “democratization of mathematics.” Citing data from many sources, he argued that mathematics education has always been about separation–of rich from poor, of boys from girls, of elites from plebeians. Mathematics, reported Carnevale, is the “biggest barrier to upward mobility in educational attainment.”

Because of the strong association of mathematics with economic success, mathematics education has had the effect–if not the aim–of affirming existing social structures. Carnevale argued that the QL movement is really part of a much larger societal effort towards increased democratization. While conceding that a segregated economy headed by mathematically trained elites is efficient from a strictly economic perspective, he urged the QL movement to focus on egalitarian rather than economic goals.

A different challenge came from Janis Somerville, Senior Associate with the National Association of (College and University) System Heads. Somerville described the incoherence of messages about mathematics conveyed in the transition from high school to college, where different tests (high school exit, college admissions, college placement) administered at different times for different purposes stress very different aspects of mathematics. For many reasons, these inconsistencies have disparate impact on students from different socio-economic groups so that by age 24, the proportion of youth from high-income families who have graduated from college is seven times that of those from low-income families. And, as Carnevale’s data shows, mathematics is the biggest contributor to this differential.

Somerville cautioned participants not to make a bad situation worse by adding quantitative literacy to this mix without first resolving the dilemma that might be created if schools adopted two different tracks–algebra, trig, calculus for elites, quantitative literacy for others, most of whom will be either poor or minority. NCTM president-elect Johnny Lott observed that in such a system the calculus-bound students might be the most ill-served since they receive a much narrower foundation in mathematics.

Several papers and participants added an international perspective to the forum’s QL discussions. MSEB member Jan de Lange of the Freudenthal Institute in Utrecht argued in a background paper that “mathematical literacy” is a broader and better term than QL. Moreover, he asserts, if mathematics were taught as it should be taught–for reasoning rather than for mastery of algorithms–there would be little need for a distinction between mathematics and mathematical literacy. Michel Merle of the University of Nice described plans of a commission in France to refocus school mathematics on four areas of contemporary importance: geometry, numeracy, statistics, and computer science. Mogens Niss of Roskilde University in Denmark, former secretary of the International Commission on Mathematical Instruction (ICMI), described similar changes under way in Denmark in which the school mathematics curriculum will be defined not by a list of topics but by the characteristics of different levels of proficiency in relation to a core set of mathematical competencies (e.g., reasoning, argumentation, communication, modeling, representation).

In a robust discussion, participants reacted to what they had heard in the context of what they know from their own experiences. Linda Kime (University of Massachusetts) and Don Small (US Military Academy) suggested focusing QL efforts on college algebra because “that is what everybody takes.” Linda Rosen, Vice President for Education of the National Alliance of Business, reminded participants of the “accountability juggernaut” that is bearing down on education, and urged advocates of QL to think more carefully about how to “scale up” to levels that can have a measurable impact. Charlotte Frank, vice president of McGraw Hill and a member of the New York State Board of Regents, pointed out that QL will not happen unless it is measured in assessments. Gene Bottoms of the Southern Regional Education Board (SREB) urged greater flexibility in mathematics instruction: “It shouldn’t take 36 weeks to fail Algebra I.” Arizona mathematician William McCallum said that other disciplines need to take ownership of QL, since QL cannot succeed if it remains only an initiative within mathematics departments.

Indeed, Jeanne Narum opened the forum by suggesting how QL can support the “what works” philosophy of the science-oriented Project Kaleidoscope which she directs. George (Pinky) Nelson, director of AAAS Project 2061–a major national K-12 program designed to bring science to all Americans–saw in QL an opportunity for much-needed increased cooperation between science education and mathematics education. He suggested that the social sciences may be best suited to take the lead in supporting QL across the curriculum.

In summarizing major themes of the forum, AMS President and former MSEB chair Hyman Bass noted the nearly unanimous view that quantitative literacy must be taught across the curriculum (or perhaps “in the disciplines,” which is not quite the same thing). While mathematics and statistics contribute central knowledge and skills, other disciplines provide the contexts which are so important for quantitative literacy. A second observation, echoed by many participants, is that quantitative literacy is not a curriculum (and certainly not a single course), but an approach to pedagogy. Russell Edgerton, former president of the American Association of Higher Education (AAHE) linked these observations together: “The more that QL education is about pedagogical practices (for example, the kinds of assignments students are given), the wider the possibilities are that many courses across the curriculum can contribute to students’ quantitative literacy.”

One outgrowth of the forum is a National Numeracy Network (NNN) that is being created to help support schools and colleges that are exploring ways to infuse QL into their curricula. The NNN will provide support in five areas: policy, practice, professional development, dissemination, and assessment. Several centers will serve as the core of NNN…Susan Ganter ( of Clemson University is director of National Numeracy Network. Further information about NNN can be obtained from Ganter or from one of the NNN Centers; further information about the NCED initiative in quantitative literacy can be found on the web at

Advanced Study Math, Science Programs in U.S. High Schools

Should Offer Greater Depth and Be Available to More Students” (Press release)

Source: Vanee Vines, Media Relations Officer; Andrea Durham, Media Relations Assistant  (202) 334-2138; e-mail – 14 February 2002


High school courses for advanced study in mathematics and science should focus on helping students acquire in-depth understanding rather than the more superficial knowledge that comes from covering too much material too quickly, says a new report from the National Academies’ National Research Council. Educators also should work to make such courses available to more students who could benefit, especially minorities and those attending rural and inner-city schools.

“The primary aim of programs such as Advanced Placement and International Baccalaureate should be to help students achieve deep understanding of the content and unifying ideas of a science or math discipline,” said Jerry P. Gollub, co-chair of the committee that wrote the report, and professor of physics, Haverford College, Haverford, Pa… On the whole, well-designed advanced programs must provide opportunities to experiment, critically analyze information, argue about ideas, and solve problems. Simply exposing students to advanced material or duplicating college courses is not by itself a satisfactory goal.”

Accelerated classes that cover a smorgasbord of topics and final examinations that devote insufficient attention to the integration of important ideas cannot produce superior learners, says the report, which concentrates on biology, chemistry, physics, and mathematics in Advanced Placement (AP) and International Baccalaureate (IB) programs in U.S. secondary schools…

Today advanced study is practically the norm for secondary students seeking admission to the most competitive colleges, which view enrollment in demanding courses as an indication of a student’s willingness to work hard. But access to such programs is limited for many students who are poor or minorities, the report says. For example, the number of AP programs in a school tends to decrease as the percentage of minority or low-income students increases. Even when college-level courses are available, studies show that such students may not be sufficiently encouraged to take them, or nurtured to succeed after enrollment.

A lack of well-prepared teachers and the inadequacy of students’ prior schooling are two factors that shrink the number of prospective participants. “Improvements on these fronts could significantly enlarge the population that the programs could serve well,” said committee co-chair Philip C. Curtis Jr., professor emeritus of mathematics, University of California, Los Angeles.

In addition to recommending that courses be designed for in-depth learning, the report calls for several other changes to boost quality and expand access. At the outset, advanced courses in mathematics and science should not be designed primarily to replicate typical introductory college classes, which may not take into account the best current practices in education. The way many advanced courses are taught also does not reflect the recent explosion in scientific understanding about how people learn. Research indicates, for instance, that encouraging students to learn by engaging in active problem solving and discussion, as scientists do, is an effective teaching tool. Yet rote memorization of facts, one of the least effective approaches, seems to be stressed in many advanced classes. Furthermore, teachers should work harder to build on students’ prior knowledge and address misconceptions.

Students learn more from teachers who know their subjects well and can convey that knowledge clearly, the committee noted. However, the New York City-based College Board and the International Baccalaureate Organization, located in Geneva, Switzerland – which oversee the AP and IB programs, respectively – support professional development of teachers only to a limited extent. Schools and school districts offering advanced study should provide frequent opportunities for teachers’ professional development. The AP and IB organizations should clarify the knowledge and skills that are needed by beginning teachers of advanced courses, and provide models of professional development likely to foster high-quality instruction. This is an admittedly major task.

The College Board also should exercise greater quality control by spelling out standards for what constitutes an AP course, the kind of student preparation expected, and strategies for ensuring equity and access, the report says. As AP has taken on more weight as a perceived measure of excellence and school quality, some schools have sponsored AP classes without providing proper laboratories or other teaching and learning resources.

The committee pointed out that academic preparation for advanced study actually begins in middle school. At that level, however, mathematics and science courses often lack focus, may be repetitious across grades, and are taught inconsistently. To address the problem, education officials should weave advanced study into a coherent plan that integrates coursework from middle school through the last year of high school. Furthermore, classes with reduced academic expectations should not be options for most students. Too many youngsters are steered toward such offerings, leaving them unprepared for advanced study in high school or later in college. School administrators also should make additional efforts to persuade parents of the long-term benefits of having their children participate in rigorous academic programs, and to increase students’ access to skilled guidance counselors and mentors.

Developed by the College Board in 1955, AP is now the country’s predominant program for accelerated high school courses. It offers 11 separate classes in eight areas of mathematics and science alone, and is built around voluntary, end-of-course exams. Many colleges and universities use qualifying scores from these national exams as a basis for awarding academic credit to incoming students or making course-assignment decisions after admission has been granted. AP originally served only the very top students from select schools, but is now offered in approximately 62 percent of high schools.

IB was developed in the late 1960s to provide an international standard of secondary education for the children of diplomats and others stationed outside their home countries. The International Baccalaureate Organization must endorse participating schools. It also administers final exams, which students must pass to receive a full-fledged IB diploma. Some colleges grant academic credit based on IB participation in high school. IB currently is offered in 1,270 schools in 110 countries.

A major problem with both programs is the lack of detailed research about what their examinations actually measure, the committee found. In particular, not enough is known about what kind of thinking the exams elicit. Given this data gap, colleges and universities should view AP and IB test scores as only one of many sources of information needed to accurately assess each student’s capabilities and level of understanding. The governing bodies for both programs should provide better guidance to educators, policy-makers, and the general public concerning proper uses of their exam scores for college admission, placement decisions in college, and evaluation of those who teach AP and IB courses.

At the same time, educators and researchers should explore the development of alternative programs for advanced study in the nation’s high schools, and evaluate new and promising approaches. The availability of more alternatives could increase students’ access to advanced study and lead to innovative and effective teaching strategies.

The study was sponsored by the U.S. Department of Education and the National Science Foundation. The National Research Council is a private, nonprofit institution that provides science policy advice under a congressional charter granted to the National Academy of Sciences…

[* The full text of this report is available online at]