Committees and Reports that Have Influenced the Changing Mathematics Curriculum

1. This resource was developed by CSMC faculty and doctoral students with support from the National Science Foundation under Grant No. ESI-0333879. The opinions and information provided do not necessarily reflect the views of the National Science Foundation. 11-26-04

2. Committees and Reports that Have Influenced the Changing Mathematics Curriculum This set of PowerPoint slides is one of a series of resources produced by the Center for the Study of Mathematics Curriculum. These materials are provided to facilitate greater understanding of mathematics curriculum change and permission is granted for their educational use. Everybody Counts A Report to the Nation on the Future of Mathematics Education National Research Council • 1989 http://www.mathcurriculumcenter.org

3. Background A Nation at Risk, published in 1983, brought to the public’s attention the failure of U.S. schools to provide all students the intellectual tools needed for the 21st century. In response, the National Research Council (NRC) undertook a study of U.S. mathematics education from kindergarten through graduate school. A number of challenges were identified: • Too many students were leaving school before they acquired the mathematical preparation necessary for productive lives; • There was a shortage of qualified mathematics teachers ; • U.S. students, on the average, were not mastering mathematics sufficiently to sustain the needs of a technological society; • Curricula and instruction in American schools and colleges were years behind the times; • Calculators and computers had virtually no impact on mathematics instruction; • Public attitudes encouraged low expectations in mathematics; • The U.S. had neither a national curriculum nor nationwide curriculum guidelines.

4. Shirley A. Hill, Curators’ Professor of Mathematics and Education, University of Missouri, Kansas City, Chairman 33 other members: 16 college and university professors of mathematics, science, and education 5 school administrators 4 teachers 4 representatives from state departments of education 2 representatives from business and industry, 1 National Congress of Parents and Teachers, 1 National School Board Association Report Based on Studies by Three NRC Units Mathematical Sciences Education Board Board on Mathematical Sciences • Phillip A. Griffiths, Provost and James B. Duke Professor of Mathematics, Duke University, Chairman • 14 other members: • 9 university professors of mathematics, statistics, and science • 3 university administrators • 1 institute director • Executive director of AMS Committee on Mathematical Sciences in the Year 2000 • J. Fred Bucy, Chief Executive Officer, Texas Instruments Inc. (retired), Chairman • 20 other members: • 7 college and university administrators • 7 college and university professors of mathematics, statistics, and science • 1 high school teacher/administrator • 4 representatives from business and industry • 1 institute director

5. Contents of the Report • Opportunity … tapping the power of mathematics • Human Resources … investing in intellectual capital • Mathematics … searching for patterns • Curriculum … developing mathematical power • Teaching … learning through involvement • Change … mobilizing for curricular reform • Action … moving into the 21st century

6. Opportunity … tapping the power of mathematics • The scope and the application of mathematics have changed significantly in the past 25 years. • The level of education formerly required of the few who enrolled in college must now be a goal for all. • Mathematics filters students out of programs leading to professional careers. “The half-life of students in the mathematics pipeline is about one year.” (NRC, 1989, p. 7) • Research shows that most students cannot learn mathematics by only listening and imitating, yet this is how most teachers teach mathematics. • Poor performance in mathematics has become socially acceptable. • Children can succeed in mathematics, as evidenced by the achievements of many students in other countries and some U.S. students.

7. Human Resources … investing in intellectual capital • American education must provide for equity of opportunity and excellence in results. • More young people must be attracted to the mathematics teaching profession. From 1990-2010, the number of 20-30 year olds in the U.S. will decline by 25%, while the number of school age children will increase by about 25%. • Teachers of mathematics must have appropriate mathematical and pedagogical training. Over half of the secondary school mathematics teachers in the U.S. and as many as 90% of elementary teachers do not meet current standards for teaching mathematics.

8. Human Resources … investing in intellectual capital • More minorities must be attracted to the field of mathematics. In the 1990s, 30 percent of public school children will be minorities, but only 5 percent of mathematics teachers will be minorities, eliminating classroom role models and perpetuating a cycle of mathematical poverty among minority groups. • More women must be encouraged to study advanced mathematics. There is no difference in performance between male and female students who have taken advantage of similar opportunities to study mathematics, yet only 35% of master’s degrees and 17% of Ph.D. degrees in mathematics are earned by women. • U.S. students must be encouraged to take advantage of the educational opportunities available to them. Fewer than half of the mathematics doctorates awarded by U.S. universities go to U.S. citizens.

9. Mathematics … searching for patterns • Mathematics can be viewed as a “science of patterns” that deals with: – Data – Measurements – Observations from science – Inference, deduction, and proof – Mathematical models of natural phenomena, of human behavior, and of social sciences • The process of “doing” mathematics is more than just calculation and deduction; it involves observing patterns, testing conjectures and estimating results.

10. Mathematics … searching for patterns • There is a dialectic relationship between computers and mathematics: computers afford new opportunities for mathematics, and mathematics makes computers more effective. • Mathematical power develops a capacity of mind that enables one to read critically, to identify fallacies, to detect bias, to assess risk and to suggest alternatives. • Mathematics empowers us to better understand the information world in which we live. • The ideas of mathematics infiltrate our lives in many ways, including in practical, civic, professional, leisure and cultural activities.

11. Curriculum … developing mathematical power • All students should study mathematics every year they are in school. • The major objective of elementary school mathematics should be to develop number sense, including: – common sense about how to find an answer – knowledge of when a calculation is necessary, and when estimation is sufficient – the ability to choose from a range of choices of methods – the ability to use calculators intelligently • Elementary mathematics should reinforce a child’s natural curiosity about patterns. • Secondary school mathematics should focus on the transition from concrete to conceptual mathematics and the development of symbol sense. • All high school students should study a common core of broadly useful mathematics. Different groups of students should not be separated by curricular goals, but only by speed, depth and approach.

12. Curriculum … developing mathematical power • Skills prerequisite for college mathematics include: – background in mathematical methods required for calculus, statistics, and computer science. – versatility, confidence, experience, reasoning, and communication about mathematics. • Mathematics instruction must not reinforce the idea that all problems have just one correct answer or leave the impression that mathematical ideas are the product of authority. • A primary objective of undergraduate mathematics should be to develop function sense, a familiarity with expressing relations among variables.

13. Teaching …learning through involvement • Effective teachers help students to learn mathematics through the construction of understanding. • Teaching must take into account students’ prior ideas. • The teacher should be a consultant and moderator, not just a presenter and authority. • Less teacher-centered strategies require greater effort and more time, but less teaching will yield more learning. • Learning mathematics should not focus on memorization, but on developing the confidence to find and use mathematical tools. This confidence is built through the process of creating, constructing and discovering mathematics. • Text-based learning in mathematics needs to be reduced. • Assessment should be an integral part of teaching.

14. Teaching … learning through involvement • Calculators and computers require educators to rethink the priorities for mathematics education. • School mathematics should become more like the mathematics people really use. • Weakness in algebraic skills should not prevent students from understanding more advanced mathematics. • Mathematics learning should become more active and dynamic. • Students should use technology to explore mathematics and ask “what if” questions.

15. Change … mobilizing for curricular reform Lessons learned from past reform efforts: • Full-service curriculum development projects adopted intact by school districts do not work; • A district-by-district approach to curriculum change will not work given the demands placed on educators; • An extensive public information campaign will be necessary if any effort to change mathematics education is to be successful.

16. Change … mobilizing for curricular reform Transitions that must dominate the process of change: • A shift in curricular focus from mathematics for some to a significant common core of mathematics for all students; • A shift from a teacher-centered instructional model to a student-centered model; • A shift from an almost exclusive focus on teaching routine procedures to developing broad-based mathematical power; • A shift to greater emphasis on contemporary mathematics: data analysis and statistics, probability, mathematical modeling, operations research, and discrete mathematics. • A shift from an emphasis on paper-and-pencil calculations to the use of calculators and computers; • A shift to improved public perception of what mathematics is and recognition of its importance in society.

17. Action … moving into the 21st century • The key to making significant improvements in mathematics education on a national scale will be national standards with local implementation. • The Curriculum and Evaluations Standards for School Mathematics, to be published in 1989 by the National Council of Teachers of Mathematics (NCTM), will provide parents and teachers a vision of what a school mathematics program might look like if it is to serve our national objectives. • For change to occur, one must influence teachers, state and local agencies, administrators, local and state school boards, colleges and universities, textbook publishers, software developers, professional societies, test-makers, state legislators, employers, parents and the general public.

18. Significance of Report • Report established a need for change and provided a vision of what mathematics education should look like in the U.S. in order for our students to reach the achievement levels of students in other countries. • Report helped to pave the way for the launching of NCTM’s Curriculum and Evaluation Standards for School Mathematics (McLeod, 2003).

19. References McLeod, D. B. (2003). From consensus to controversy: The story of the NCTM Standards. In G. Stanic & J. Kilpatrick (Eds.), A history of school mathematics (Vol. 1, pp. 753-818). Reston, VA: National Council of Teachers of Mathematics. National Commission on Excellence in Education. (1983). A nation at risk: The imperative for educational reform. Washington, DC: U.S. Government Printing Office. National Council of Teachers of Mathematics Commission on Standards for School Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: The Council. National Research Council. (1989). Everybody counts: A report to the nation on the future of mathematics education. Washington, DC: National Academy Press.