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Questions and Answers - The Standards and Maths. Educ.
Posted:
Sep 1, 1998 4:55 PM
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From the NCTM 1997-98 Handbook: NCTM Goals, Leaders, and Position
Statements, pp. 4-7
QUESTIONS AND ANSWERS
Answers to Questions about Mathematics Education
Improving the teaching and learning of mathematics has been a slow and
uneven process. But each year we see signs of progress in schools where
the National Council of Teachers of Mathematics (NCTM) Standards are used
as a guide. Students' scores are up. More students are taking--and
succeeding in--higher-level mathematics programs. More students are
mastering mathematical skills. And more students are gaining the
mathematical understanding they need to carry forth to the twenty-first
century.
But the road to change is rugged and full of twists and turns. The
questions that arise about where we are going and why we are going there
are good ones. Answering them helps us check our course and renew our
determination. You may have questions yourself, or you may like to have
better answers to questions from your students' parents, your colleagues
and administrators, and even business, political, and community leaders.
So below are some questions and answers--your road map--that might help
explain the journey we've undertaken to improve mathematics education.
Q: Why change mathematics education?
A: Because our mathematics needs have changed. Over the past decades, we
have seen changes in mathematics and its uses, changes in the roles of
technology, changes in the needs of society, changes in international
competitiveness, and changes in what we know about how students learn. In
this new world, we need to redefine the way we prepare our children to
understand and use the power of mathematics.
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Q: What are the NCTM Standards?
A: The NCTM's Curriculum and Evaluation Standards for School Mathematics
(1989), Professional Standards for Teaching Mathematics (1991), and
Assessment Standards for School Mathematics (1995) are guidelines for
excellence in mathematics education. They make recommendations about what
mathematics students should learn, what classroom practice should be, and
what guidelines can be used to judge student performance and evaluate the
effectiveness of mathematics programs. The NCTM Standards envision rich
mathematics opportunities and high achievement for all children in all
mathematics classrooms.
_________
Q: What changes do the NCTM Standards propose?
A: The NCTM Standards reflect the importance that society places on
reasoning and problem solving and research in how children learn. The
Standards recommend strengthening mathematics teaching and learning by
shifting practice in multiple areas:
- Curriculum--shifting toward a deeper study of mathematical concepts and a
broader study of mathematical content areas, along with their uses in
today's world
- Learning--shifting toward more active student involvement with
mathematics and the use of a variety of appropriate mathematical tools for
solving problems
- Teaching--shifting toward creating classrooms that are stimulating
learning environments in which all students have the opportunity to reach
their full mathematical potential
- Assessment--shifting toward assessment that is ongoing, continuous, and
multifaceted
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Q: On what foundation are the NCTM Standards based?
A: The NCTM Standards are based on research and our increased knowledge
about how children learn. For example:
- Mathematics content--the emerging views of the mathematics all students
should know is based on such reports as Renewing U.S. Mathematics,
Mathematics in American Schools, and New Goals for School Mathematics.
- Student learning--research on how students learn has been summarized in
the chapters in Handbook of Research on Mathematics Teaching and Learning
and the chapter on mathematics in Handbook of Educational Psychology.
- Teaching methods--research on the benefits derived when teachers
emphasize lessons designed to promote student understanding, conducted by
the Center for Research on Teaching, are discussed in the Handbook of
Research on Mathematics Teaching and Learning.
- Assessment--research that supports the shift in assessment--from a
measurement approach developed to compare students on the basis of their
answers to a set of brief questions toward a performance-criteria approach
designed to determine growth in each student's ability to solve nonroutine
problems--is summarized in Toward a New Science of Educational Testing and
Assessment, Mathematics Assessment and Evaluation: Imperatives for
Mathematics Education, and Reform in School Mathematics and Authentic
Assessment.
As projects based on the NCTM Standards evolve, data are being collected
showing the positive effects on students' achievement.
(A more complete description of this research may be obtained from the NCTM
Headquarters Office--NCTM, Infocentral, 1906 Association Drive, Reston, VA
20191-1593, or Fax on Demand, 800-220-8483, document #207.)
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Q: What should I see in a Standards-based mathematics classroom?
A: First and foremost, you'll see students doing mathematics. But you'll
see more than just students completing worksheets. You'll see students
interact with one another, use other resources along with textbooks, apply
mathematics to real-world problems, and develop strategies to solve complex
problems.
Teachers still teach. The teacher will pose problems, ask questions that
build on students' thinking, and encourage students to explore different
solutions. The classroom will have various mathematical and technological
tools (such as calculators, computers, and math manipulatives) available
for students to use when appropriate. The teacher may move among the
students to understand their thinking and how it is reflected in their
work, often challenging them to engage in deeper mathematical thinking.
The teacher will regularly encourage students to think carefully about the
mathematics in one situation and make connections to other ideas within
mathematics and other disciplines. The teacher will summarize the
mathematics that has been studied and clarify the students' understanding
of the mathematics in the lesson.
There are many models of Standards-based classrooms, but the focus will
always be on students' learning and doing high-quality mathematics.
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Q: Do the NCTM Standards support teaching the "basics"?
A: Absolutely. The NCTM Curriculum and Evaluation Standards for School
Mathematics clearly and unequivocally states that students should "model,
explain, and develop reasonable proficiency with basic facts and
algorithms" (p. 44). Computational proficiency has always been, and will
continue to be, an integral part of mathematics education. Yet
computational proficiency alone is not enough. To be successful in today's
world, students need proficiency with basic facts, and they must be adept
in reasoning, in problem solving, and in communicating mathematics. They
must also have the ability to make mathematical connections, and they must
be able to use their computational skills to apply mathematics to problems
in other disciplines.
----------
Q: What is the role of technology in a Standards-based classroom?
A: A comprehensive mathematics curriculum should help students learn to
use calculators, computers, and other technological tools. These tools are
used in many aspects of their education and influence how they study
mathematics, science, or engineering in college or how they will do
mathematics in the workplace. It would be remiss not to make their use a
part of contemporary mathematics education.
The Curriculum and Evaluation Standards for School Mathematics makes it
clear, however, that such tools "do not replace the need to learn basic
facts, to compute mentally, or to do reasonable paper-and-pencil
computation" (p. 19). The Standards also suggest that when used
appropriately, calculators and computers enable students to explore new
areas of mathematics and to tackle many challenging mathematical problems
that are impractical to attempt without the aid of such tools. Indeed,
calculators and computers with appropriate software can transform the
classroom into a laboratory where students can investigate and experiment
with mathematical ideas.
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Q: What is the role of textbooks in mathematics education?
A: This is one issue on which many people have misunderstood the position
of the NCTM Standards. Every school should have a coherent, coordinated
curriculum. A good mathematics textbook is almost always an essential
element in implementing that curriculum.
The NCTM Curriculum and Evaluation Standards for School Mathematics
stresses that the textbook should not be the exclusive source of knowledge
(p. 129); rather, a textbook should be one of many resource available to
students. A good textbook, in conjunction with other rich curriculum
materials, will help the teacher emphasize important mathematical ideas and
move beyond routine instruction on procedures and vocabulary to having
students apply these mathematical ideas and use them to solve challenging
problems.
----------
Q: What are the changes in assessment?
A: Teachers should not rely on paper-and-pencil tests and time drills as
their only means to judge students' performance because doing so will not
provide a complete picture of most students' mathematical knowledge and
ability. Students should be given ample opportunity to demonstrate their
mathematical understanding through a variety of methods, including
portfolios, discussions, presentations, and projects in addition to the
traditional approach of written tests. This variety enables teachers to
review, assess, and gauge students' progress.
----------
Q: How can we engage all students in mathematics?
A: The NCTM Standards issue a call for all students to engage in higher
levels of mathematics. All students should have the same opportunities to
learn the same mathematics. All students should have equal opportunities
to use the same resources, including appropriate technology, to engage in
mathematical thinking and reasoning and to become involved with tasks that
are challenging and focused on good mathematics and that encourage further
learning.
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Q: Why should parents become involved in improving mathematics education,
and what role can they play?
A: A survey by Money magazine found that the amount of support received
from parents and the community was the most important factor in academic
excellence in the best school districts in the country. The importance of
parent and community support should not be underestimated.
Parents should work with teachers to understand the mathematical goals for
the classroom, how these goals will be measured, and the ways in which
parents can further mathematical understanding at home. Parents can
support their children's mathematics education by looking for ways to link
mathematics to daily activities. By becoming active partners in the
homework process, parents can increase students' confidence in their
mathematics abilities and encourage students to value mathematics and to
continue their learning.
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Q: What do U.S. business leaders have to say about the future of
mathematics education?
A: U.S. business leaders recognize that what was traditionally known as
shopkeeper's arithmetic is insufficient in the Information Age. They have
repeatedly reported the need for employees who can think and communicate
mathematically, who can solve problems, and who can work in teams as well
as alone. Strengthening Your Child's Academic Future, published by the
Education Excellence Partnership (a consortium of business and education
organizations), states, "Unlike ten or fifteen years ago, we now live in a
world of computers, Web sites, and international competition. In a number
of other countries and American communities, academics are more rigorous
and challenging, and their students graduate better prepared to compete in
our increasingly complex world. In order for your child to succeed in
school, at work and in the community, he or she will need more skills and
knowledge than ever before." According to the Partnership, "raising
academic standards will help your child succeed in today's increasingly
competitive world." The NCTM Standards establish those high, rigorous
standards for mathematics excellence.
----------
Q: Do the NCTM Standards represent a national curriculum?
A: No. The NCTM Standards are not a national curriculum; rather they
provide a framework for teaching, learning, and assessing mathematics that
can be used by states and local school districts to shape their own
mathematics curriculum.
__________
Conclusion
There have never been "good old days" for mathematics education. Today,
many more students can and must attain a level of mathematics understanding
traditionally reserved for only a few. That is why we must move forward in
our efforts to ensure that all students receive a rigorous, high-quality
education in mathematics.
For information about NCTM's Mathematics: Making a Living, Making a Life,
contact the NCTM Headquarters Office at (703) 620-9840, ext. 113, or send a
note by e-mail to infocentral@nctm.org
*********************************************************************
Jerry P. Becker
Dept. of Curriculum & Instruction
Southern Illinois University
Carbondale, IL 62901-4610 USA
Fax: (618)453-4244
Phone: (618)453-4241 (office)
E-mail: JBECKER@SIU.EDU
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