From Matthew Larson's Blog, NCTM
President, Wednesday,
February 21, 2018. SEE
https://my.nctm.org/blogs/matthew-larson
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Why Teach Mathematics?
By Matthew Larson
As a teacher of mathematics, you have no doubt had multiple
students ask what
is actually a very complicated question: "Why do I have to learn
this?" At one time or another, perhaps while grinding through a
series of
context-free symbolic manipulation exercises, nearly every one
of us has
struggled to provide our students with an answer they, and/or
we, find
satisfactory. But the student "why?" question raises an equally
important, but less often-asked question: "Why do we teach
math?"
Francis Su, past president of the Mathematical Association of
America, has
argued that this is a very important question because how we
answer it strongly
influences who we think should do mathematics and how we will
teach it.
So why do we teach mathematics?
Paul Ernest (2010), emeritus
professor of philosophy of mathematics education at the
University of Exeter,
UK, offered three major reasons (and additional sub-reasons) why
we teach
mathematics:
Necessary Mathematics - mathematics for
employment and the
economy. Ernest included functional numeracy; practical and
work-related
knowledge; and advanced specialist knowledge under this reason.
Social and Personal Mathematics - mathematics
for personal
and social relevance. Here Ernest included mathematical problem
posing and
solving; the development of mathematical confidence, including
mathematical
persistence; and social empowerment through mathematics.
Appreciation of
Mathematics as an Element
of Culture -- the importance not only of appreciating
mathematics itself, but
also its role in history, culture and society in general.
Mathematics education has
traditionally emphasized what
Ernest labeled "Necessary Mathematics" over other reasons for
teaching and learning mathematics. This bias has long historical
roots
stretching back to the fourteenth century when European
mercantile schools
first began teaching arithmetic out of an economic need for
efficient
calculation.
Similarly, arithmetic was added to
the curriculum in the
American colonies largely in response to the needs of business.
And the current
standards-based mathematics education reform effort, which
continues to be
driven by discussion of national economic interests and the
associated emphasis
on college and career readiness, has its roots in national
defense and economic
concerns stretching back to WWII and the Soviet launching of
Sputnik. (For
those interested in the history of school mathematics education
in the United
States, I highly recommend NCTM's two-volume set, A History
of School
Mathematics.)
As early as An Agenda for Action
(1980) NCTM argued
that students should learn mathematics for more than economic
reasons stating
that "all reasonable means should be employed to assure that
everyone will
have the foundation of mathematical learning essential to
fulfilling his or her
potential as a productive citizen" (p. 16).
In Principles and Standards for
School Mathematics
(2000) the Council strongly stated that students need to learn
mathematics, and
by extension we teach mathematics, for reasons beyond, but
including,
"necessary mathematics."
Mathematics for Life - knowing mathematics
can be personally
satisfying and empowering.
Mathematics as Part of Cultural Heritage
Mathematics for the Workplace
Mathematics for the Scientific and Technical
Community (p.
4)
The recent emphasis on college and career readiness standards
has certainly
emphasized the latter two reasons over the first two as the
primary reasons for
teaching and learning mathematics. I admit I have more than once
told a student
that the reason they have to learn something is because "they
will need it
for college" or "the next course." Today I appreciate that this
response was lazy on my part, and from my perspective, while
critically
important, not even the primary reason why we should teach
mathematics.
I believe the answer as to why we teach mathematics is in part
answered in the
NCTM Vision statement. The NCTM vision statement in part states
that "We
envision a world where everyone is enthused about mathematics,
sees the value
and beauty of mathematics, and is empowered by the opportunities
mathematics
affords." In this statement we find an emphasis on the first two
reasons
for teaching and learning mathematics first offered in
Principles and
Standards.
What does it mean to be empowered by mathematics? In addition to
preparing
students for careers and post-secondary education, I believe it
means we also
teach mathematics in order to equip students for active
participation in our
democratic society. We accomplish this goal by emphasizing
analysis and critical
thinking with mathematics so that individuals can identify and
interpret claims
made by those in power as truthful or false and misleading.
We live in a world where mathematics is increasingly used to
characterize
societal problems and formulate proposed solutions. Without
mathematics
literacy, and a strong mathematics identity and sense of agency,
members of our
society will increasingly find it difficult to comprehend and
critique, let
alone challenge, many of the decisions and actions of those in
power in
political, social, scientific, and economic institutions.
Ultimately, I believe we should teach mathematics (and students
should learn
mathematics) for multiple reasons - a theme that NCTM will
expand upon in the
forthcoming publication Catalyzing Change in High School
Mathematics:
Initiating Critical Conversations, which will be released at the
Annual Meeting
in Washington. In most cases this means we need to increase our
emphasis on
teaching "Mathematics for Life" and "Mathematics as Part of Our
Cultural Heritage." Teaching mathematics as part of cultural
heritage
means that we do not just emphasize the dominant culture and
heritage. By
valuing and developing a better understanding of each other and
other cultures,
including the multiple contributions various cultures have made
to mathematics,
we cultivate and nurture student identities. If we teach
mathematics so
that students are empowered by it, preparation for college and
careers will
largely take care of itself.
We should never forget, or fail to appreciate, that as teachers
of mathematics,
each and every one of us is engaged in something much more
important that our
daily tasks of instruction, curriculum, and assessment. We are
engaged in
empowering our students so that they can improve not only their
own lives, but
can also better understand and critique the world around them.
I challenge you and your colleagues
to discuss the
following:
. Why do you teach
mathematics?
. What are your school or
math department's learning
goals for students? Do those goals need to
be broadened?
. Are your school or math
department's learning goals
clear to students and parents?
. Are your school or math
department's learning goals
reflected in your curriculum?
If we start by engaging in critical conversations around these
questions, many
of the debates in mathematics education and how we resolve them
concerning our
instructional tasks, our curriculum, and our assessments, will
suddenly have
more clear direction.
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