Mathematics Curriculum:

Essential Knowledge for Mathematicians

Working to Improve K–12 Education

Given the central role of mathematics in the K–12 education

of all students, mathematicians should understand the 

focus of school mathematics and the influences that shape that

focus. Every higher education institution that is engaged in

teacher education expects departments of mathematics to

offer mathematics courses aimed at the education of future

teachers. In order to prepare future mathematicians to edu-

cate preservice K–12 teachers and to contribute to the articulation of ongoing iterations of mathematics curriculum ex-

pectations and textbook development, studying mathematics

curricula should be a part of all Ph.D. programs in mathematics.

We raise questions and provide examples to make our case

for the systematic education of doctoral students in mathe-

matics about the history and development of K–12 mathematics

expectations and text materials.

Mathematicians should be knowledgeable about the history

and evolution of mathematics curricula. For example, consider

the sequence of algebra, geometry, advanced algebra, and pre-

calculus used in secondary schools in the United States. One

hundred years ago compulsory ages for school attendance were

still being established, and few students graduated from high

school. In order to meet the needs of those students attending

only two years of high school, it was felt that students should

study some algebra and geometry. Thus a yearlong algebra

course followed by a yearlong geometry course was organized

and offered. For those students who remained in high school for

a third year, a more advanced treatment of algebra was offered.

What are the ramifications of there being no national mathe-

matics curriculum in the United States?The tradition is that each

state or locality is responsible for establishing mathematics 

expectations for its school population. What mathematics is

learned, when it is learned, and to what extent specific mathe-

matical topics are emphasized varies from school to school 

and state to state. This patchwork quilt approach impacts what

mathematics knowledge students bring to higher-education 

institutions. Learning how mathematics curricula have been 

established and are set by states and other entities can help 

mathematicians better understand some of the strengths and

weaknesses inherent in our educational system and enable them

to become more effective in helping to improve the system.

What are the many diverse and powerful forces that influ-

ence the K–12 mathematics curriculum? While societal needs

and the discipline of mathematics are two forces influencing

the mathematics curriculum, there are many other forces

that shape the topics and the emphasis given to these topics

in mathematics textbooks. Currently accountability systems,

including high-stakes assessment prompted by the No Child

Left Behind federal legislation, are major forces influencing

many K–12 mathematics curriculum decisions. Other forces

impacting mathematics curricula include research about 

how students learn; evolving technology, such as graphing

calculators, symbolic manipulation tools, dynamical geome-

try exploration tools; and recommendations from learned so-

cieties.

What is the process underlying the development of mathe-

matics text materials? Historically most mathematics textbooks

are not researched and piloted before being sold commercially.

The notable exceptions are federally supported mathematics

curriculum, most of which are funded by the National Science

Foundation. It should also be noted that during the last two

decades the elementary-secondary publishing industry for 

mathematics has gone from having considerable competition

among independent publishing houses to a quartet of mega-

publishers. These publishers are businesses and as such are 

primarily concerned with sales and profit. As with any business,

they are customer driven and not necessarily driven by the 

content concerns of academic communities.

What previous eras of change or tugs of war has the curricu-

lum experienced and what prompted them?History does repeat

itself. Current “math debates” about the lack of involvement of

mathematicians in K–12 curriculum development were preceded

more than forty years by criticism of the domination of the “new

math” era by mathematicians. Knowledge of these tugs of war

provides a valuable context within which to interpret current de-

bate and perhaps make more reasoned and informed judgments

that will raise the intellectual level of the ensuing debates.

What visions for the mathematics curriculum have been 

offered by mathematicians that are yet to be realized? In 1902 

E. H. Moore in his AMS Presidential Address called for a 

revamping of the K–12 mathematics curriculum, with more 

attention given to how mathematics was taught. Hyman Bass

echoed a similar message in discussing the need to teach math-

ematics better in 2001. Knowledge of such visions provides a

context to better understand areas of the mathematics curricu-

lum where progress has been made and where work remains.

How have major committee reports impacted mathematics 

curriculum? Major CBMS and NCTM documents have provided

additional visions for the K–12 school mathematics curricu-

lum. Understanding both the rationale for and substance of the

recommended changes is essential for promoting constructive

discussion and criticism.

What role can and should mathematicians play in the

process? Mathematicians have assumed many leadership roles

in promoting change in mathematics curriculum. By learning

about the contributions of previous mathematicians to math-

ematics curriculum, future mathematicians can become more

active and informed contributors to mathematics curriculum

change in the future. Knowledge of the history of mathe-

matics curriculum development will help them better under-

stand the challenges of curriculum change and provide insight

into effective ways mathematicians can contribute to the 

development of mathematics curriculum in an ever-changing

educational system.

—Glenda Lappan (glappan@math.msu.edu),

Michigan State University, East Lansing,

—Barbara Reys (reysb@missouri.edu), and Robert Reys

(reysr@missouri.edu), University of Missouri, Columbia

This Opinion piece is based on the work of the Center for

the Study of Mathematics Curriculum, supported by the Na-

tional Science Foundation under Grant No. ESI-0333879.

Letters to the Editor

End Torture and Detention

As expressed in the UN charter, torturing and detaining people indefinitely without due process is a serious crime against humanity (http://www. hrweb.org/legal/undocs.html). We call on all governments (especially our own): to stop these ugly practices; to prosecute individuals who are involved in such practices; and to ask courts to bring these individuals to justice, whether they are involved directly or by giving orders and setting policies. By now an overwhelming amount of evidence (news, pictures, testimonials, admissions, Amnesty International and UN reports, and even FBI reports) makes it clear that these kinds of shameful inhuman practices have been taking place. This distresses us greatly and

moves us to speak out. 

—Selman Akbulut, Paul Gauthier,

Mary Gray

(the chair and two members of the

AMS Human Rights Committee*)

akbulut@math.msu.edu

*This is not an official position of

the AMS HRC. In fact, some of the

other members of the HRC feel that

this issue is not within our mandate.

(Received July 1, 2005)

The Message of “Who Wants to

Be a Mathematician”

When attending the Joint Mathematics Meetings in Atlanta, I watched the contest “Who Wants to Be a Mathematician”. I acknowledge that it is a big event for the participants, but un-fortunately it sends a completely wrong message to the high school students. The students are required

to solve problems in extremely limited time, usually 60 or 90 seconds. Thus, the message is: if you want to be a mathematician, you have to be able to answer math questions very quickly. This is wrong, wrong, wrong!!! In fact, one of the main reasons why it is so

difficult to teach math to students at the universities is that most of them were not taught in school how to think, and they were not even taught that one should think about math problems. Tests of the type “answer

60 questions in 60 minutes” are quite popular. They should be banned. Many times I heard from frustrated parents who tried to explain math to their kids that the kids told them they cannot do this in school: “I cannot think, I have no time for that, I have to know when I am asked.” And then

those kids get to universities and we try to teach them to think, but it is too late for this.

Instead of the “Who Wants to Be a Mathematician” contest, which only makes the situation worse, the AMS should organize more contests of the Mathematical Olympiad type, where problems are more difficult but the participants have enough time to think.

—Michal Misiurewicz

Indiana University Purdue University

Indianapolis

mmisiure@math.iupui.edu

(Received July 2, 2005)

Ad Reinhardt Martin Gardner mentions the “black paintings” of “Ed Rinehart” in your recent interview. The painter he referred

to was of course the pioneer conceptual artist Adolph “Ad” Reinhardt.

—Jeffrey Olson

University of Illinois at Chicago

jsolson@math.uic.edu

(Received July 2, 2005).