Critical Issue: Implementing Curriculum, Instruction, and Assessment Standards in Mathematics


ISSUE: National educational standards are being developed in nearly all subject areas. The National Council of Teachers of Mathematics has recently developed standards for mathematics. Their Curriculum and Evaluation Standards for School Mathematics reflect a concern that students in the U.S. are not mathematically literate and often fail to see the relationship between mathematics learned in school and real-life situations.

The NCTM Standards are primarily expressed as goals for students. It is up to schools and communities to determine how to make sure all students reach these goals. Schools are faced with a huge challenge: to offer curriculum content, instructional methods, and forms of assessment that are aligned with the goals described in the Curriculum and Evaluation Standards.


OVERVIEW: Most U.S. students learn basic mathematical facts and formulas but many of them are unable to use this knowledge to solve everyday problems! Results of the National Assessment of Educational Progress (NAEP) help us understand the extent to which students in our country can solve problems with their mathematical knowledge. Employers tell us about the skills they wish public school graduates would bring to the workforce.

One way that the United States has addressed this situation in math as well as other subject areas is to develop a nationwide system of standards and assessments. The Goals 2000 legislation and the reauthorized Elementary and Secondary Education Act, known as Improving America's Schools Act of 1994, have formalized this system. Both laws indicate that compliance to these standards is voluntary, although states applying for Goals 2000 funds from the Department of Education must agree to develop and implement higher standards. Furthermore, many states are developing curriculum frameworks based on national standards.

Teachers participated in the creation and review of the standards for math through their professional organization, NCTM. Many teachers and many schools communities--both prior to and subsequent to the release of the standards in 1989--have tried to provide the meaningful learning experiences implicit in the standards. Other teachers and school communities find it a challenge to design curriculum, instruction, and assessment that reflect national standards as well as curriculum frameworks developed by their state. Teachers, whether they specialize in teaching mathematics or teach it along with other subjects, may lack confidence in the progress of their own mathematical knowledge. The challenge to apply the standards may be greatest for school personnel who see the standards movement as just another wave of school reform such as the New Math movement of the 1960s.

Although the Standards have been described as the largest mathematics reform effort in the United States since 1900, many of us vividly remember a reform effort that dates from the 1960s, popularly referred to as New Math. The modern math or New Math movement was the outgrowth of the Cold War and a pervasive perception that the United States was not training enough mathematicians and scientists. There was significant pressure to increase the capability of our institutions of higher education and to redefine the secondary school curriculum as well as altering the way in which mathematics was taught. New Math created temporary changes in the secondary school curricula, but the process of teaching mathematics courses has changed very little over the last few decades. The New Math movement was not successful at bringing about overall improvement in mathematics teaching and learning.

The New Math movement and today's challenge as articulated in the Standards, although both focused on improving students' understanding of mathematics, are significantly different. New Math was aimed at developing student understanding through mathematical structure and a focus on abstractions, appealing to students' intellect. Meaning was imposed out of the structure of mathematics. The Standards recommend developing understanding by using realistic contexts and applications as well as concrete pictorial models, appealing more to students' intuitive sense. Therefore, meaning is constructed out of prior knowledge and experiences.

Image of Susan GehnSusan Gehn, a first-grade teacher in Cottage Grove, Wisconsin, talks about why she uses modeling and problem-solving activities in her mathematics curriculum rather than the memorization of facts. [252k audio file] Excerpted from the video series Schools That Work: The Research Advantage, videoconference #2, Children as Problem Solvers (NCREL, 1991). A text transcript is available.

Despite the difference, we can learn several lessons about implementation of large-scale reform by revisiting New Math. Rather than blaming the mathematics content of the New Math movement, many critics believe that the real problem with its lack of success lay in the implementation process. As efforts to produce large-scale curriculum dissemination began, instructional issues were addressed tangentially, if at all. Only small-scale, short-term training was made available to teachers, and no real implementation plans were designed. For a reform effort to be successful, all classroom teachers affected by it need to be involved in all implementation stages:

The key question to be addressed in this issue is: What actions must be taken to integrate the spirit of the Standards into classroom practice?


GOALS:

ACTION OPTIONS:

The goals above present a challenge to students, teachers, administrators, parents, and community members to create and implement a comprehensive and long-term plan for the improvement of mathematics curriculum, instruction and assessment in the education system. The goals were developed to ensure that all student become mathematically literate. The following action options are divided into implications for each of the significant stakeholders within the educational system as they move toward ensuring mathematical literacy for all students.

In order to become mathematically literate, students must:

In order to facilitate students becoming mathematically literate, teachers must:

To support all students becoming mathematically literate, administrators must:

To enhance the learning of students, parents and community leaders must:


IMPLEMENTATION PITFALLS:



DIFFERENT POINTS OF VIEW:



ILLUSTRATIVE CASES:

The Illustrative cases listed as samples below have been described as such by many teachers and curriculum developers because of their usefulness as models and frameworks for developmentally sequenced curriculum units.

Problem Solving and Critical Thinking in Mathematics: K-8 Professional Development and Interdisplinary Curriculum Development

The Algebra Project

Resources:

Math by All Means

Middle Grades Mathematics Project

The NCTM Addenda Series

The Quantitative Literacy Series

Used Numbers: Real Data in the Classroom


CONTACTS

Midwest Consortium for Mathematics and Science Education
North Central Regional Educational Laboratory
1120 Diehl Road, Suite 200
Naperville, IL 60563-1486
(630) 649-6500, fax (630) 649-7600
E-mail: mailto:info@ncrel.org
WWW: http://www.ncrel.org/msc/msc.htm

Eisenhower National Clearinghouse for Mathematics and Science Education
The Ohio State University
1929 Kenny Road
Columbus OH 43210-1079
614-292-7784, fax 614-292-2066
E-mail: info@ENC.org

The EQUALS Project
Lawrence Hall of Science
University of California
Berkeley, CA 94720
510-652-1823; fax 510-643-5757
e-mail: equals@maillink.berkeley.edu
WWW: http://equals./lhs.berkeley.edu

Mathematical Sciences Education Board, National Academy of Science, and National Research Council
2101 Consitution Avenue, N.W.,
Washington, DC 20418
202-334-2000

National Council of Teachers of Mathematics
1906 Association Drive
Reston, VA 22091-1593
703-620-9840
Fax: 703-476-2970
e-mail: InfoCentral@nctm.org
WWW: http://www.nctm.org


References


This Critical Issue Summary was researched and written by Cathy J. Cook, mathematics education and professional development specialist, Midwest Consortium for Mathematics and Science Education, North Central Regional Educational Laboratory.

Date posted: 1995

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