Who Owns School Mathematics?
Different Visions, Different Expectations
No one ever seems satisfied with school mathematics. Test scores are always
too low, students are often bored, and adults feel students don't learn
what they need to know.
"Schools need to provide students with the tools of productivity,"
says Linda McIsaac, CEO of EXPCT, Inc. in Middleton, Wisconsin. "For
mathematics, that means spreadsheets, computer graphics, and other software
that is of vital importance in today's workplace. These things can be taught,
and should be taught."
"But mathematics is a language," says Tom Kurtz, Professor of
Mathematics at the University of Wisconsin, "and without mastery of
skills in basic algebra and geometry students will never understand how
mathematics is used. Students without skills are students without language."
On October 19, 1995, twenty individuals from the Madison area gathered at
the University of Wisconsin to discuss the issue of "Who Owns School
Mathematics?" The session was sponsored by the National Institute for
Science Education (NISE) and chaired by Denice Denton, Professor of Engineering
and Co-Director of the Institute. The discussion ranged fluidly over a diverse
set of issues, mostly centered on the different expectations of business
and higher education, and on the dichotomy of skills and understanding.
Individuals who participated in this discussion--business leaders, educators,
mathematicians, and policy leaders--expressed sharply different visions
of what mathematics students should know and be able to do when they finish
high school. Through this Web report, we open the dialogue to others, and
invite submissions of commentary and electronic letters for subsequent posting
in this space. Just send e-mail to email@example.com or click
Different Visions, Different Expectations
Professional Standards and Public Expectations
The National Council of Teachers of Mathematics ([NCTM]) offers one vision
of school mathematics in their 1989 report Curriculum and Evaluation
Standards for School Mathematics. This vision is rooted in the lessons
of educational research (that students learn better when they construct
their own insights) and in the implications of the global shift from an
industrial to an information economy (which suggests the need for greater
emphasis on data, on computers, and on communication skills).
More recently, the American Mathematical Association of Two-Year Colleges
([AMATYC]) issued its own standards called Crossroads in Mathematics:
Standards for Introductory College Mathematics Before Calculus. This
report calls for a broad foundation in core mathematics as preparation for
technical mathematics, liberal arts mathematics, or transfer programs.
Both the NCTM and AMATYC standards are "constructivist" documents,
emphasizing the need for students to actively participate in mathematical
discourse by working in groups, using technology, and communicating mathematically.
Yet polls consistently show that parents believe that mastery of basic skills--not
calculators and computers--are the foundation of excellence in mathematics
education. Parents want the primary emphasis in mathematics class to be
on developing mathematics skills, not on other goals such as communication
or teamwork. Especially in a supposedly absolute subject like mathematics,
parents expect teachers to teach and children to learn. Many parents are
uneasy at the thought of children discovering or constructing mathematics
for themselves. Most parents want their children to be grouped according
to their mathematical abilities and interests. They want their children
to learn mathematics for practical reasons--primarily to earn a good wage.
Thus parents' goals often appear to be very different from the published
standards of the mathematics profession.
Mathematics for Work and for University
"In today's world, the application of knowledge is as essential as
the attainment of it." This observation, cited in the recent [MSEB]
report [Mathematical Preparation of the Technical Work Force], signals
a significant reorientation in the nature and purpose of school mathematics.
Even as leaders of NCTM and AMATYC have expressed educators' goals for mathematics
education, so also technical industries are now developing sets of [occupational
skills standards] to provide transportable, national expectations for well-prepared
workers. These skills are often quite specific (e.g., calculate percentages
and ratios, solve algebraic equations) and frequently include topics (e.g.,
control charts) that are rarely taught in school. Business leaders often
stress specific skills important for the world of work.
Although both government and employers frequently express the need for graduates
who are better prepared for the world of work, the dominant influence on
school mathematics remains the siren call of universities. "Our curriculum
is driven by the university," reports John Janty, Mathematics Coordinator
of Waunakee High School in Waunakee, Wisconsin. "Despite the obvious
benefits of graphing calculators, we had to wait for the blessing of the
University before we were able to fully utilize them in our classrooms."
University faculty, especially mathematicians, often decry the open-ended
problems that dominate emerging curricula, believing that this approach
undermines the technical fluency crucial to success in later courses. Mathematicians
worry that by stressing exploration and multiple approaches to solving problems,
the new curricula undermine important characteristics that give mathematics
its distinctive power: accurate answers and definitive proof. Indeed, many
colleges and universities continue to expect proficiency in traditional
skills that are no longer emphasized in some school curricula.
Divergent views about the nature of mathematics put teachers in the awkward
position of choosing among differing expectations-- of NCTM, of parents,
of higher education, and of the technical work force. Who really should
determine what is taught in school mathematics? Teachers or parents? Employers
or universities? Scientists or mathematicians?
Conflicting expectations are themselves an impediment to change. "We
have teachers who are afraid to change," says Mazie Jenkins of Abraham
Lincoln Elementary School in Madison "because they have to face parents
who come in and say 'Why aren't you teaching this and that...That's the
way I learned it.' We have others who say that we need to teach kids to
be thinkers and problems solvers, to be motivated about mathematics. We
can't expect teachers to sort all this out. Until we bring our different
communities together, classroom teachers will not be able to meet the needs
of kids in the classroom. If we don't all start speaking the same language,
we're not going to get teachers to change-- because teachers have to face
Questions for Discussion
To begin the process of "speaking the same language," we invite
commentary on key questions concerning expectations of school mathematics:
In short, is school mathematics really one subject? Is mathematics for work
the same as mathematics for education? Or are there perhaps "multiple
mathematics," as some argue that there are "multiple literacies?"
Questions such as these are at the heart of many of the public debates about
standards in mathematics education.
- What are the real mathematical skills needed for today's workplace?
How are they likely to change in coming years?
- What mathematical skills are especially suited to supporting students'
learning in science and technology?
- Are the mathematical skills required for work significantly different
from those required for post-secondary education?
- How should college expectations change in response to changes in the
K-12 mathematical preparation of students or expectations of employers?
- Can a curriculum built on needs of the workplace successfully address
the broad expectations for school mathematics?
Excerpts from the Roundtable
Voices at the Madison Roundtable reflect views of many citizens about mathematics
education--conflicted, concerned, and anxious. Samples of these views are
on key issues can be found by clicking on the following:
What Society Expects of School Mathematics
Teaching for Skills vs.Understanding
Views on Effective Pedagogy
To add you voice to this discussion, e-mail comments, letters, and op-ed
articles to: firstname.lastname@example.org or click here
if your Web browser is set up for e-mail.
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Last Update:> 12/21/95