Issues for the Popularization of Mathematics
J O E L SCHNEIDER*
Children's Television Workshop, One Lincoln Plaza
New York, NY 10023, USA
The popularization of mathematics is a new topic for these congresses. Although it
has always been one of the main congress functions, popularization here is set at a
high level and for a very special audience, one for which mathematics is already a
congenial friend. But mathematics is not congenial to most people, even though it
may be important to them. This leads us to think of popularizing mathematics to
general audiences, young and old, learned or not, indeed any group we can reach.
The very etymology of the word "popular" impels us to adopt the widest possible
scope in our efforts.
My aim here is to popularize the popularization of mathematics. I will identify, discuss briefly, and illustrate some issues concerning its practice. Most of my
illustrations will come from Square One TV, & television series about mathematics
for children.
Background
The popularization of mathematics has a longer history than one might realize.
In Reid's biography we read that David Hilbert gave popular lectures in 1921
for students returning to the university after the war and continued the series
through the 1920s. [8, p. 154]. Lucas' "Towers of Hanoi" game is an example with
a much broader impact [cf. 4]. One of my favorite examples is The Ladies ' Diary,
published from 1704-1841 by the Company of Stationers (London). It advertised
itself as "Containing new improvements in arts and sciences and many entertaining particulars
" The "particulars" included mathematics problems and letters
about them [cf. 2, pp. 155 and 455].
Even though popularization has a long tradition, practitioners have only
begun to think about it systematically in the last few years. The stimulus for this
was an invitation by the International Commission on Mathematics Instruction
(ICMI) to participate in a study seminar at the University of Leeds (UK) in 1989.
In announcing the seminar, Howson, Kahane, and Pollak [5] described the need, a
framework, some principles, and methods of popularization.
Some ask, "Why do it at all?" For a long time, the mathematical community has maintained itself as a sort of priesthood. We've been rather passive with
regard to recruits, erected a difficult series of trials for anyone who would join
*)
[email protected]
Proceedings of the International Congress
of Mathematicians, Zürich, Switzerland 1994
© Birkhäuser Verlag, Basel, Switzerland 1995
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Joel Schneider
us, and even militated against participation by members of some groups. However, the world has changed so that more people need comfort and facility with
mathematics to get on with their lives. Local, regional, and global political and
economic realities generate increasingly complex demands, many involving some
mathematics. We might expect mathematicians, if only through self-interest, to
take some responsibility for the ways in which the general public sees and uses
mathematics. A society comfortable with mathematics is more likely to tolerate
and support those who want to work with it.
By its duration and intensity, school experience dominates all other influences
on people's attitudes toward mathematics. As most people have a bad experience
with mathematics in school, we need to improve the school situation in order to
hope for significant change in the popular view of mathematics. All mathematicians
should take note of the vigorous reform movement for mathematics education that
is at work in many places. Meanwhile, many people are beyond the reach of school.
For them and for the support of today's students, we must create opportunities to
learn about and to practice mathematics outside school. Programs to popularize
mathematics among a broad audience serve this purpose. Before proposing several
issues for our consideration, I will describe some exemplary programs.
Principles and Examples
In reviewing and comparing existing programs of popularization, several principles emerge that seem to guide them. We go to people where they are — watching
television, reading a newspaper or shopping for clothing — rather than expecting them to come to us. A program must be attractive to draw participants, as
participation is voluntary. The primary attraction may not be mathematics, but
rather something else such as music, humor, or physical activity. Without willing
participants, without an audience, there is no possibility of success, no matter
how worthwhile the mathematics. What we hope is that the satisfaction in the
experience will include pleasure in the mathematics and encourage a favorable
attitude and a readiness to consider more. The effects of any one experience are
often slight and diffuse, but popular activities are repeatable. One can revisit a
museum, watch a film again, follow a television series. The effects accumulate and
interact. A discussion of these principles appears in [5].
All of this is very much in the spirit of the Leeds conference. The conference
proceedings [6] are worth reviewing because they describe a variety of projects in
several formats and venues: lectures, competitions, games, exhibitions, magazines
and newspapers, and broadcast media — radio and television. Another source
of examples is the ICMI report in the proceedings of the Seventh International
Congress on Mathematics Education [7]. Following are a few examples from the
Leeds' papers by way of illustration.
Shannon describes his experience in talking to a Rotary Club unit in Sydney
(Australia). He alerts us to an important audience, available to each of us, namely
the local business and professional groups in our home communities. It's worth
noting that they often represent the local political and economic power. This is a
project that can be taken up by any mathematician.
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1553
Competitions can be great fun and rewarding for those who enjoy them.
Burjan and Vrba describe an extensive national system of competitions. We usually
think of the International Mathematics Olympiads and the national competitions
that produce the teams, but for our goal of affecting a broad audience, general
competitions are more important. The programs of Gilles Cohen (La Federation
Française des Jeux Mathématiques et Logiques) [cf. 7] in France and of George
Lenchner (Mathematics Olympiads for Elementary Schools) in the USA both show
that there is a large general audience for competitions even at the elementary level.
Games give many people their earliest experiences with probability, strategy,
and patterns. They are an especially effective format for popularization in that
they readily involve parents and children. DeGuzman discusses games in terms of
popularization.
Exhibitions are increasingly successful means for attracting attention and
interest. Brown and Porter describe the problems that arise in constructing an
effective exhibition and their experience in creating "Mathematics and Knots".
This interesting exhibit was also included in the PopMaths Roadshow at the Leeds
conference [cf. 6, Foreword].
Mathematics and newspapers and other varieties of print are natural vehicles
for popularization. Many popular science magazines feature problems or a column
on a mathematical topic. Barbeau, Emmer, and Larsen all discuss writing about
mathematics. Of course, each of them is a mathematician writing about mathematics. Steen addresses the difficulties in promoting articles on mathematics in
the newspapers, where writers and editors will usually not be friendly to mathematics. It is worth noting that the Zürich newspapers ran at least five articles [3]
on mathematics during the congress. Of course, one would rather not have to go
to the trouble of convening an international conference to read about mathematics
in the newspapers.
The broadcast media, both radio and television, are powerful tools for delivering information and for shaping public opinion. They are prominent elements of
popular culture. Power and prominence make them attractive to us, too. Four of
the Leeds papers deal with these media. Barbeau writes about discussing mathematics on a radio interview program; Emmer about making films relating art and
mathematics; and Hoyles about Fun and Games, a televised mathematical game
show. Fun and Games is an important project because of its success as a program for an adult audience broadcast in a prime viewing time. Esty and Schneider
describe Square One TV, a television series for children, broadcast in the USA.
Square One TV is a daily series broadcast in the USA from 1987-1994 late
in the afternoon. The primary audience is 8-to- 12-year-old children viewing at
home, not in school. Each of the 230 half-hour shows comprises 6-12 independent
segments drawn from a pool of 1100. The segments are humorous parodies of
television broadcasting conventions: dramas, musicals, game shows, commercials,
and so on. In keeping with the principles of popularization mentioned above, we
tried to produce a series that would compete for viewers among the great variety of
entertaining alternatives available at the same time on commercial television. The
primary audience varies greatly in age, taste, and social as well as mathematical
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Joel Schneider
sophistication. In response, we also varied the shows in style and format and in
level and type of mathematics. Our Leeds paper describes the project in detail.
Issues
In the course of producing Square One TV, we learned a lot about dealing with
mathematics in a popular medium, as have all of the other practitioners. In reviewing a large number of programs, one notices, in addition to guiding principles,
at least nine issues that should concern us:
1.
2.
3.
4.
5.
6.
7.
8.
9.
What is the relation to school mathematics?
What is the influence of the setting or venue?
What is the nature of cooperation with partners?
What is the interplay with the wider culture?
What is the relation to the problem of women's participation in mathematics
at all levels?
What is the relation to the problem of cultural minorities' participation in
mathematics at all levels?
What is the relationship with popularization of science?
How do we define and assess the impact of projects?
How do we promote a healthy flow of information and encourage collaboration
among practitioners?
I propose that we begin to look at these issues to improve our practice and
to increase our effectiveness. I will draw on my experience with Square One to
illustrate some of them.
School. Surely any effort to popularize mathematics should support school reform.
Successful programs might and, often, do migrate into the schools in some form.
Popular lectures may be repeated to new audiences, especially by using film or
video recording. Schools are a natural place to prepare for competitions, which in
turn have the potential to influence curricula. Many teachers use games in their
teaching. School trips to visit exhibitions are common. Magazines and newspapers
are a standard feature of many classrooms. We can also have a migration from the
medium of open-circuit broadcast television, such as in the case of Square One TV.
Even though we were producing Square One TV for an audience at home,
we were alert to the possibility that the shows might be useful in school. In fact,
some teachers used the shows at the very beginning. With this encouragement, we
are producing a version of the series specifically designed for classroom use. The
derivative series, Square One TV Math Talk, comprises twenty new 15 minute
shows. Each of the new shows will deal with a single topic (e.g., bilateral symmetry). We will provide a book that describes ways for teachers to use the shows
in classrooms. An instructional television network will broadcast the shows for
teachers to videotape, and we will also offer them on video cassette for purchase.
Each Math Talk show features two animated cartoon characters as hosts,
Maria Lopez and her partner, Buster, who is a parrot. They respond to telephone
calls from people asking questions about mathematics and they illustrate their
responses with video from the Square One TV library. For example, in the show
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1555
dealing with bilateral symmetry, Maria and Buster illustrate the concept with a
segment of "Mathman" (a parody of the once-popular video game "Pacman"). In
this segment, the character must identify geometric shapes with a line of symmetry. Maria and Buster continue with a segment of "General Mathpital" (a parody
of "General Hospital", a popular soap opera). In it, surgeons must operate on an
asymmetric shape so as to reassemble the pieces into one that is bilaterally symmetric. In doing so, the surgeons discuss the concept and explore several solutions
to the problem. The show concludes with a portion of one of the nine Square One
TV game shows. Of course, it features a task for the contestants that involves
symmetry.
Context. In producing Square One TV, we placed our material deeply in the context of our medium. Soap operas and game shows are perennial favorites among
radio and television audiences. Video games are more recent innovations, but just
as popular. The conventions and constraints of the medium governed many of our
decisions and certainly impinged on the mathematics. For example, in producing
Square One TV, we had a persistent conflict between our wanting to give a viewer
time to think about a problem and the producers' sense that the best show is a
fast-paced show.
Partners. In using a popular medium, we have not been able to act alone or to act
solely from the standpoint of mathematics. Television production involves a large
number of people — producers, directors, writers, carpenters, and many more.
The goal for each of these talented people was to produce an attractive piece of
television that would be a good addition to the Square One TV library — lively
and repeatable. They were not also expected to attend to the additional goal that
it convey some worthwhile information about mathematics. That is, mathematics
was not the concern for most of the group. In fact, they typified our audience in
terms of attitudes toward mathematics. This was a useful check on those of us
who were responsible for the mathematics.
Because the primary goal was to attract an audience, our partners controlled
the overall content, style, and tone of the product as well as the packaging. This
is a valid model, whether the medium is a magazine or a newspaper, radio or
television. Of course, we expect that all sides engage in friendly and respectful
negotiation. Related questions for us include how to find and encourage partners,
how to turn their attention in our direction, and how to create opportunities for
them and for us. It is important to realize that they are entrepreneurs. They have
a business to run, even if they run it in the public interest. They naturally want
to continue their work and to do so they must not only generate and satisfy an
audience, but also justify their decisions to the sources of their money. A decision
to carry out a project on mathematics, instead of some other worthwhile subject,
may have more to do with the availability of money than with their interest in one
subject or another.
Culture. Although the culture in which we work is always important, music videos
raise the issue most directly. The music video is a very popular television format.
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Joel Schneider
We produced more than fifty of them and often had the cooperation of wellknown popular singers. Associating celebrities with a product is a long-standing
commercial practice and is useful even if the product is mathematics. We produced
music in several genres: blues, heavy metal, rock and roll, country and western,
rap, and others. No one style appeals to everyone. We broadcast in the USA, which
has a complex web of subcultures. What does a black, urban rap lyric mean to
viewers in rural Iowa or suburban Phoenix? Square One TV was also licensed for
broadcast in more than twenty other countries. What does Square One TV mean
to a viewer in Bermuda, Indonesia, or Zimbabwe? It is obvious that culture plays
a role in any of the means of popularization that we have discussed. This is a
complex issue and worthy of careful thought. Bishop's book [1] is a good starting
point in addition to the growing literature of the field of cthnomathematics [cf. 7].
A new project based on Square One TV speaks to this issue. Risky Numbers
is the working title of a half-hour game show based on the mathematical game
shows that are a part of Square One TV. We are negotiating with producers in
several countries for them to produce their versions of this show. Although the new
format stems from Square One TV, these new productions will be rooted in their
local cultures. The prospect is that we will have several variants of Risky Numbers
for comparison and contrast within a few years. Szalone Liczby, the Polish version
of Risky Numbers, premiered in January 1995. An Indonesian version will appear
in January 1996.
Other Issues. The related issues of women and mathematics and of cultural minorities and mathematics are very much part of the politics of the mathematics
community. Should programs to popularize mathematics promote the interests of
special groups? Can they do so? In the case of Square One TV, wc deliberately
cast our actors with these issues in mind. Popularization of science is better established than popularization of mathematics in popular culture. Science centers
and science museums exist in many places, but mathematics centers and museums
are rare. How can popularization of mathematics cooperate with popularization
of science? How do we avoid losing the mathematics in the science? In the case of
Square One TV, our nonrealistic, comedy-variety format allowed us to effectively
highlight the mathematics and we made no particular attempt to expose aspects
of science. We need to develop techniques to assess programs for their impact.
We need to understand what we mean by impact or value. The Square One TV
project had a large research and evaluation component, which generated a mass
of reports [cf. our Leeds paper in 6]. The ninth issue transcends the others. We
need to develop convenient means for effective communication among practitioners. Given the increasing availability of electronic tools, we do not need to wait
for international conferences and publication of their proceedings to learn from
others' experiences. I call on the community to invest some of their energies in
this direction.
Conclusion
The popularization of mathematics has a long tradition, but relatively recent impetus for systematic scrutiny. There are several issues to consider as we develop
Issues for the Popularization of Mathematics
1557
and improve our practice. Although it is often incorrectly identified with "informal
mathematics education", popularization also has a valid function for professional
mathematicians and for formal mathematics education. Even so, we need to concentrate on developing effective programs t o help a broad, general population to
develop a fruitful appreciation and facility for mathematics.
Note on Video
T h e audience for this lecture from which this paper stems viewed three selections from Square One TV. First was a portion of the Square One TV Math Talk
show on symmetry, described above. Second was "Rule of T h u m b " , a music video
featuring Kid 'N Play. It deals with measurement by estimation. Third was a
mock commercial for geometry with the t a g line: "Geometry — another division
of mathematics. It's more t h a n just arithmetic."
References
[1] A. Bishop, Mathematical Enculturation, Kluwer, Dordrecht, 1991.
[2] L. E. Dickson, History of the Theory of Numbers, Chelsea Publishing Co., New
York, 1966.
[3] Five newspaper articles covering the congress:
-Die Mathematiker kommen, p. 45 in Neue Zürcher Zeitung, 28. Juli 1994.
-Mathematiker geehrt, p. 1 in Tagesanzeiger, 4. August 1994.
- T . Müller, Die Mathematiker sind in der Stadt, p. 17 in Tagesanzeiger, 4. August
1994.
- B . Eckmann, Mathematik: Fragen und Antworten, p. 49 in Neue Zürcher Zeitung,
3. August 1994.
- Bundesrätin Dreifuss mahnt zur Verantwortung, p. 41 in Neue Zürcher Zeitung,
3. August 1994.
[4]
[5]
[6]
A. M. Hinz, The Tower of Hanoi, L'Enseignement Mathématique 35 (1989), 289321.
A. G. Howson, J.-P. Kahane, and H. Pollak, The popularization of mathematics,
L'Enseig. Math. 34 (1988). [This is the discussion paper for the Leeds Conference.]
A. G. Howson and J.-P. Kahane (eds.), The Popularization of Mathematics, ICMI
Study Series, Cambridge University Press, Cambridge (UK), 1990.
- G . Howson and J.-P. Kahane, A study overview;
-Mathematics in different cultures (report of the working group);
- E . J. Barbeau, Mathematics for the public,
- V . Burjan and A. Vrba, The role of mathematical competitions in the popularization of mathematics in Czechoslovakia;
- M . de Guzman, Games and mathematics;
- M . Emmer, Mathematics and the media;
- E . Esty and J. Schneider, Square One TV: A venture in the popularization of
mathematics;
- G . Hatch and C. Shiu, Frogs and candles — Tales from a mathematics workshop;
- C . Hoyles, Mathematics in prime-time television: The story of fun and games;
- G . Knight, Cultural alienation and mathematics;
- M . Larsen, Solving the problem of popularizing mathematics through problems;
- B . Mortimer and J. Poland, Popularizing mathematics at the undergraduate level;
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Joel Schneider
- T . Nemetz, The Popularization of mathematics in Hungary;
- T . Shannon, Sowing mathematical seeds in the local community,
- L . Steen, Mathematical news that's fit to print;
- C . Zeeman, Christmas lectures and mathematics masterclasses;
- D . Z . Zhang, H.K. Kiu and S. Yu, Some aspects of the popularization of mathematics in China.
[7]
[8]
H. Pollak, ICMI Study 2, The popularization of mathematics, in Proceedings of the
7th International Congress on Mathematical Education (C. Gaulin et al., eds.), Les
Presses de L'Université Laval, Sainte-Foy, 1994.
C. Reid, Hilbert, Springer-Ver lag, New York, 1970.
Some other items of interest:
[9]
[10]
[11]
[12]
[13]
B. Cipra, What's Happening in the Mathematical Sciences, v. 1-2 (P. Zorn, ed.),
AMS, Providence (RI), 1993, 1994. (Recent advances in mathematics for a sophisticated audience.)
V. Crane et al., Informal Science Learning, Research Communications Ltd., Dedham (MA), 1994. (Papers on a research basis for informal science and mathematics
education.)
A. Joseph, F. Mignot, F. Murat, B. Prüm, and R. Rentschler (eds.), First European
Congress of Mathematics, Round Tables, Birkhäuser, Basel, Boston, and Berlin,
1994. (Includes papers on Mathematics and Society with a section on Mathematics
and the General Public.)
J.-P. Kahane, The Popularization of Mathematics, in Proceedings of the UCSMP International Conference on Mathematics Education, Developments in School Mathematics Education Around the World, v. 3 (I. Wirzup and R. Streip, eds.), National
Council of Teachers of Mathematics, Reston (VA), 1992.
The Popularization of Mathematics, ICMI Secretariat, Southampton, 1989. (The
working papers for the Leeds conference.)