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Topic: Essay: The Future of High School Math
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Jerry P. Becker

Posts: 16,576
Registered: 12/3/04
Essay: The Future of High School Math
Posted: Dec 10, 2013 5:40 PM
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Sent at the request of Jim Fey.
In an introductory note to the essay below, Jim Fey writes as follows:

In September of 2008, the Center for Mathematics Education at the
University of Maryland organized a conference in Washington, DC to
examine core questions about the future of high school mathematics
and to showcase promising innovative projects. The conference theme
attracted over 300 leaders in school and college mathematics
education with shared concerns about the need for fundamental reform
in the content and teaching of mathematics in grades 9 - 12.

Just three weeks ago a much smaller group of senior mathematicians,
teachers, statisticians, and curriculum developers met in Boston to
revisit issues addressed by the 2008 conference-this time in the
context of Common Core State Standards implementation. Participants
in that meeting, sponsored by the Consortium for Mathematics and Its
Applications, formulated a set of recommendations for progressive
action in the field and drafted an essay to explain their ideas.

Since results of the most recent PISA assessment were scheduled for
release on December 3 and PISA focuses on high school mathematics,
science, and literacy, we linked our essay about needed reforms to
what would almost certainly be the principal findings of PISA. That
essay is now posted on the blog of Valerie Strauss at the Washington
Post. In what appears to be the common pattern of reactions to blog
postings, the first responses have largely ignored our plea for a
dialing down of acrimony in discussion of the issues. We all know
that your various lists reach thoughtful and influential audiences in
mathematics education, and we would be pleased if you would help us
circulate the recommendations of the Boston meeting.

The essay drafted by the Boston group follows (and is also attached).

The Future of High School Math

Let's Try Something Different

Results from the most recent Program for International Student
Assessment (PISA), released on December 3, showed once again that U.
S. high school students are in the middle of the pack when it comes
to science, mathematics, and literacy achievement. The findings
quickly elicited an outburst of public hand wringing, criticism of U.
S. schools and their teachers, and calls to emulate the curriculum
and teaching practices of high achieving countries. Then, just as
predictably, there were a variety of explanations why we cannot
import the policies and practices of other quite different countries
(e.g. , South Korea, Taiwan, Finland, and Singapore). Instead,
schools were urged to redouble efforts along lines that have been
largely ineffective for the past decade and are not common in any
high performing country-a regimen of extensive standardized testing
with mostly punitive consequences for schools and teachers that fail
to make adequate yearly progress. Public attention to the challenge
of international competition has already begun to fade and we will
hear little about the meaning of the PISA results until the next
'wakeup call' arrives.

What might happen if we tried something different this time around?
Countries that have made real progress in their performance on
international assessments share several characteristics. First and
foremost is broad agreement on the goals of education and sustained
commitment to change over time. In the U. S. there has been steady,
if modest, improvement in student mathematics performance at the
elementary and middle school levels on the National Assessment of
Educational Progress (NAEP) and some improvement in results on
college entrance examination tests (SAT and ACT) over the past two
decades-a period when efforts have been guided by the National
Council of Teachers of Mathematics (NCTM) standards for curriculum,
evaluation, teaching, and assessment.

Over the past three years, 46 of the 50 U. S. states have been
engaged in an effort to implement Common Core State Standards (CCSS)
for mathematics and literacy. With respect to mathematics, those
standards, prepared under the aegis of the National Governors'
Association with generous private financial support, are in many ways
an extension of key ideas in the earlier NCTM standards. Despite
understandable controversy about particulars of the CCSS and the
processes by which they were developed and states were induced to
adopt them, the Common Core standards provide a useful framework for
further efforts. Partisan political pressures (from both left and
right) are already leading some state governors to reconsider their
participation in this national compact to improve education-before
even the first assessments of progress are reported. But we believe
that education policy makers and mathematics educators should resist
the common wish for a quick fix and stay the course, modifying goals
and efforts as results suggest such actions.

What should students, teachers, parents, and policy-makers look for
in the emerging reform of high school mathematics? From our
perspective-as mathematicians, teachers, statisticians, teacher
educators, and curriculum developers with extensive experience in
school mathematics innovation-there are at least four key elements of
the Common Core program that provide a basis for productive change in
U. S. high school mathematics:

o Comprehensive and Integrated Curriculum. The traditional
American high school mathematics curriculum consists of two year-long
courses in algebra and a one-year course in geometry. The CCSS for
mathematics retain essential elements of those topics, but they also
prescribe significant attention to important concepts and skills in
statistics, probability, and discrete mathematics that are now
fundamental in computer, management, and social sciences. The Common
Core guidelines describe an attractive integrated curriculum
option-suggested by the common practice in other countries of
addressing each mathematical content strand in each school year.
That international curriculum design helps students learn and use the
productive connections between algebra, geometry, probability,
and discrete mathematics.

A broad and integrated vision of high school mathematics would serve
our students better than the narrow and compartmentalized structure
of traditional programs.

o Mathematical Habits of Mind-For most people the phrase 'do the
math' means following standard algorithms for calculation with whole
numbers, fractions, decimals, and the symbolic expressions of
algebra. But productive quantitative thinking also requires
understanding and skill in use of what the Common Core Standards call
mathematical practices. To apply mathematical concepts and methods
effectively to the kind of realistic problem solving and decision
making tasks that PISA assessments highlight, students need to
develop the habits of: (1) analyzing complex problems and persevering
to solve them; (2) constructing arguments and critiquing the
reasoning of others; (3) using mathematical models to represent and
reason about the structure in problem situations; and (4)
communicating results of their
thinking in clear and precise language.

Developing important mathematical habits of mind should become a
central goal of high school instruction, especially the process of
mathematical modeling that is required to solve significant
real-world problems.

o Balanced Attention to Technique, Understanding, and
Applications-One of the most common student views about mathematics
is the belief that what they are asked to learn is not supposed to
make sense and that it bears little relationship to the reasoning
required by everyday life. Those views are expressed well in the
whimsical rhyme about division of common fractions, "Yours is not to
reason why, just invert and multiply," and the common student
question, "When will I ever use this stuff?" Unfortunately, many
teachers encourage those beliefs about mathematics learning by
suggesting that understanding and application of mathematical ideas
and methods can only occur after rote mastery of technical skills.

Findings of cognitive and curriculum design research over the past
two decades challenge such conventional beliefs and common practices.
Curricula and teaching that engage students in collaborative
exploration of realistic problems have been shown to be effective in
developing student mathematical understanding, skills, and problem
solving simultaneously. These problem-based approaches in the
classroom also develop the essential disposition to use mathematics
as a reasoning tool outside of school.

Improved performance on international assessments like PISA are
likely to result from moves toward curricula and teaching methods
that balance and integrate mathematical techniques, understanding,
and applications.

o Information Technologies-Powerful tools that allow users to find
and process information with mathematical methods are now ubiquitous
in American life. But schools are only beginning to respond to the
profound implications of this information technology for teaching and
learning. If it is possible to simply ask your cell phone to perform
any of the routine calculations taught in traditional school
arithmetic, algebra, and calculus courses, what kind of mathematical
learning remains essential? If those same tools can be applied to
support student-centered exploration of mathematical ideas, how will
the new learning options change traditional roles of teachers and
students in the mathematics classroom and raise expectations for the
mathematical challenges that students can tackle?

Personal computers, tablets, smartphones, and other computing devices
will almost certainly transform school mathematics in fundamental
ways. Intelligent response to that challenge will require creative
research and development efforts and the courage to make significant
changes in traditional practices.

If the content and teaching of high school mathematics are
transformed in the directions we recommend, schools and teachers will
also need new tools for assessing student learning. One of the
clearest findings of educational research is the truism that what
gets tested gets taught. PISA is not a perfect or complete measure
of high school student achievement. Neither are the TIMMS
international assessments, the NAEP tests, the SAT and ACT college
entrance exams, college placement exams, or, quite likely, the coming
assessments attached to the Common Core State Standards.

Some would respond to the inadequacy of current assessment tools by
sharply curtailing high stakes standardized testing; others would
actually increase the testing and raise the consequences for students
and schools. It is almost certainly true that the best course lies
somewhere between those extremes. We need new and better tools for
assessing student learning, and we need to employ those assessments
in constructive ways to help teachers improve instruction and to
inform educational policy decisions.

Finally, we need to change the tenor of public discourse about
mathematics education. If we are to reach the shared goal of
preparing young people for productive and satisfying lives, we need
to work together to develop progressive goals for school mathematics
and high quality instructional resources. Most important of all, we
need to dial down the acrimonious policy arguments and relentless
criticism of schools and teachers. Teaching is one of the most
important and demanding tasks for adults in our society, and teachers
deserve our encouragement and support as they work to provide the
best possible life preparation for their students.

Jim Fey
Sol Garfunkel
University of Maryland Consortium for
Mathematics and Its Applications

Diane Briars
Intensified Algebra Project, University of Illinois at Chicago

Andy Isaacs
University of Chicago

Henry Pollak
Teachers College, Columbia University

Eric Robinson
Ithaca College

Richard Scheaffer
University of Florida

Alan Schoenfeld
University of California, Berkeley

Cathy Seeley
Dana Center, University of Texas

Dan Teague
North Carolina School of Science and Mathematics

Zalman Usiskin
University of Chicago

Jerry P. Becker
Dept. of Curriculum & Instruction
Southern Illinois University
625 Wham Drive
Mail Code 4610
Carbondale, IL 62901-4610
Phone: (618) 453-4241 [O]
(618) 457-8903 [H]
Fax: (618) 453-4244

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