**ERIC Identifier:** ED319630

**Publication Date:** 1990-00-00

**Author: **Suydam, Marilyn N.

**Source: **ERIC Clearinghouse for
Science Mathematics and Environmental Education Columbus OH.

## Curriculum and Evaluation Standards for Mathematics Education.
ERIC/SMEAC Mathematics Education Digest No. 1, 1990.

In 1989, the National Council of Teachers of Mathematics (NCTM) released a
document of major importance for improving the quality of mathematics education
in grades K-12. This document, "Curriculum and Evaluation Standards for School
Mathematics," contains a set of standards for judging mathematics curricula and
for evaluating the quality of the curriculum and student achievement. It
represents the consensus of NCTM's members about the fundamental content that
should be included in the school mathematics curriculum, establishing a
framework to guide reform in school mathematics. Inherent in the STANDARDS is
the belief that all students need to learn more, and often different,
mathematics.

### WHAT IS THE RATIONALE FOR THE STANDARDS?

Technology is
changing the workplace, the home, and daily life. Moreover, the mathematics a
person needs to know has shifted, and new mathematics is being created as
technological applications emerge. Yet the teaching of mathematics has remained
relatively unchanged. As it has for centuries, mathematics often relies on rote
memorization.

The objectives of mathematics education must be transformed to meet the
critical needs of our society: an informed electorate, mathematically literate
workers, opportunity for all students, and problem-solving skills that serve
lifelong learning. Both the content that is being taught and the way it is
taught need to be reconsidered and, in many cases, transformed. To ensure
quality, to indicate goals, and to promote change are the three reasons why NCTM
issued the STANDARDS.

### WHAT ARE THE UNDERLYING ASSUMPTIONS OF THE
STANDARDS?

Several assumptions shape the vision of mathematics set forth in
the STANDARDS: (1) Mathematical power can and must be at the command of all
students in a technological society. (2) Mathematics is something one
DOES--solve problems, communicate, reason; it is not a spectator sport. (3) The
learning of mathematics is an active process, with students constructing
knowledge derived from meaningful experiences and real problems. (4) A
curriculum for all includes a broad range of content, a variety of contexts, and
deliberate connections. (5) Evaluation is a means of improving instruction and
the whole mathematics program.

### WHAT GOALS ARE ESTABLISHED FOR STUDENTS?

All students
should have opportunities to learn a broad spectrum of mathematics. Toward that
end, the STANDARDS state five goals for students: to learn to value mathematics,
to learn to reason mathematically, to learn to communicate mathematically, to
become confident of their mathematical abilities, and to become mathematical
problem solvers.

### WHAT IS THE FRAMEWORK FOR SCHOOL MATHEMATICS?

The STANDARDS
offer a framework for curriculum development--a logical network of relationships
among identified topics of study. Although they specify the key elements of a
high-quality school mathematics program, they neither list topics for particular
grades nor show a "scope and sequence" chart. Instead, the 40 curriculum
standards discuss the content at three grade-level groups: K-4, 5-8, and 9-12.
The 14 evaluation standards provide strategies to assess the curriculum,
instruction, and program.

The first three curriculum standards for each grade level and three of the
evaluation standards deal with problem solving, communication, and reasoning. A
fourth curriculum standard, Mathematical Connections, is predicated on the
belief that mathematics must be approached as a unified whole. Consequently,
curricula should deliberately include instructional activities to reveal the
connections among ideas and procedures in mathematics and applications in other
subject matter areas.

For each grade-level group, nine or ten content standards supplement the
first four curriculum standards. While the titles are sometimes similar, the
concepts and processes vary by level. In a lengthy presentation for each
standard, the mathematical outcomes for students, the focus of the standard,
discussion of what the standard means, and examples of how the content might be
taught are provided.

### WHAT STANDARDS ARE INCLUDED FOR EACH GRADE CLUSTER?

The 13
standards for K-4 are: Mathematics as Problem Solving, as Communication, and as
Reasoning, and Mathematical Connections; Estimation; Number Sense and
Numeration; Concepts of Whole Number Operations; Whole Number Computation;
Geometry and Spatial Sense; Measurement; Statistics and Probability; Fractions
and Decimals; and Patterns and Relationships.

There are 13 standards for grades 5-8: Mathematics as Problem Solving, as
Communication, and as Reasoning, and Mathematical Connections; Number and Number
Relationships; Number Systems and Number Theory; Computation and Estimation;
Patterns and Functions; Algebra; Statistics; Probability; Geometry; and
Measurement.

Fourteen standards pertain to grades 9-12: Mathematics as Problem Solving, as
Communication, and as Reasoning, and Mathematical Connections; Algebra;
Functions; Geometry from a Synthetic Perspective; Geometry from an Algebraic
Perspective; Trigonometry; Statistics; Probability; Discrete Mathematics;
Conceptual Underpinnings of Calculus; and Mathematical Structure.

### WHAT STANDARDS ARE INCLUDED FOR EVALUATION?

Three standards
pertain to general assessment: Alignment, Multiple Sources of Information, and
Appropriate Assessment Methods and Uses. Seven standards concern student
assessment: Mathematical Power, Problem Solving, Communication, Reasoning,
Mathematical Concepts, Mathematical Procedures, and Mathematical Disposition.
Finally, four standards are on program evaluation; Indicators for Program
Evaluation, Curriculum and Instructional Resources, Instruction, and Evaluation
Team.

### WHAT ARE SOME SUGGESTED CHANGES THAT SHOULD BE INCLUDED IN MATHEMATICS INSTRUCTION?

Some aspects of doing mathematics have changed
in the last decade, in large part because of technology. Changes in technology
and the broadening of the areas in which mathematics is applied have resulted in
growth and changes in mathematics itself. Technology makes it imperative that:
(1) appropriate calculators should be available to all students at all times;
(2) a computer should be available in every classroom for demonstration
purposes; (3) every student should have access to a computer for individual and
group work; and (4) all students should learn to use the computer as a tool for
processing information and performing calculations to investigate and solve
problems.

The availability of calculators does not eliminate the need for students to
learn algorithms; some proficiency with paper-and-pencil computational
algorithms is important. Contrary to the fears of many, there is no evidence to
suggest that the availability of calculators makes students dependent on them
for simple calculations. Students should be able to decide when they need to
calculate and whether they require an exact or approximate answer. They should
be able to select and use the most appropriate tool.

A constructive, active view of the learning process must be reflected in the
way much of mathematics is taught. Thus, instruction should vary and include
opportunities for: appropriate project work; both group and individual
assignments; discussion between teacher and students and among students;
practice on mathematical methods; and exposition by the teacher.

The STANDARDS were developed with consideration to the content appropriate
for all students. This does not suggest that all students are alike; it does
suggest that all students should have an opportunity to learn the important
ideas of mathematics.

### WHAT ARE SOME NEXT STEPS FOR TEACHERS AND
ADMINISTRATORS?

The NCTM challenges all to work toward the goal of improving
the school mathematics program as identified by the STANDARDS.

Teachers and administrators should obtain the materials listed in the
reference section to learn more about the STANDARDS. The school staff should
review the current program and instruction to identify changes that are
desirable and begin to modify the experiences provided for pupils.

Several states and many school districts have started to modify programs.
Materials describing these activities will be published in journals of the NCTM
(The Arithmetic Teacher and The Mathematics Teacher) on a regular basis. Schools
desiring more information or assistance should contact their state department of
education mathematics education coordinator/ specialist, and periodically check
Resources in Education and the Current Index to Journals in Education for
information and materials.

### SELECTED REFERENCES

"Curriculum and Evaluation Standards
for School Mathematics." Reston, VA: National Council of Teachers of
Mathematics, 1989. (Address: 1906 Association Drive, Reston, VA 20091; $25.00,
with reduced prices for multiple copies).

Heid, M. Kathleen. "Uses of Technology in Prealgebra and Beginning Algebra."
MATHEMATICS TEACHER 83: 194-198; March 1990.

Hirsch, Christian R. and Harold L. Schoen. "A Core Curriculum for Grades
9-12." MATHEMATICS TEACHER 83: 696-701; December 1989.

Mumme, Judith and Julian Weissglass. "The Role of the Teacher in Implementing
the Standards." MATHEMATICS TEACHER 82: 522-526; October 1989.

Payne, Joseph N. and Ann E. Towsley. "Implications of NCTM's Standards for
Teaching Fractions and Decimals." ARITHMETIC TEACHER 37: 23-26; April 1990.

"Reshaping School Mathematics: A Philosophy and Framework for Curriculum."
MATHEMATICS SCIENCES EDUCATION BOARD, NATIONAL RESEARCH COUNCIL, National
Academy Press, Washington, D.C., 1990. SE 051 291.

Rowan, Thomas E. "The Geometry Standards in K-8 Mathematics." ARITHMETIC
TEACHER 37: 24-28; February 1990.

Schoen, Harold L. "Beginning to Implement the Standards in Grades 7-12."
MATHEMATICS TEACHER 82: 427-430; September 1989.

Thompson, Alba G. and Diane J. Briars. "Assessing Students Learning to Inform
Teaching: The Message in NCTM's Evaluation Standards." ARITHMETIC TEACHER 37:
22-26; December 1989.

Thompson, Charles S. "Number Sense and Numeration in Grades K-8." ARITHMETIC
TEACHER 37: 22-24; September 1989.