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. ---------- 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 ---------- 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.) ---------- 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. ---------- 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. ---------- 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. ---------- 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. ---------- 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. __________
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 email@example.com ********************************************************************* 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