ERIC Identifier: ED319628
Publication Date: 1988-00-00
Author: Howe, Robert W. - Warren, Charles R.
Clearinghouse for Science Mathematics and Environmental Education Columbus OH.
Accountability in Mathematics Education. ERIC/SMEAC Mathematics
Digest No. 3, 1988.
Participation and achievement in mathematics education in the United States
have not been satisfactory. Fewer than 50 percent of the students in high
schools take more than one mathematics course unless more courses are required.
There has been little improvement in the averages of total American samples on
the Scholastic Aptitude Test (SAT) and the National Assessment of Educational
Progress (NAEP) tests. American students scored substantially below students
from several other industrialized countries on the Second International
Mathematics Study (SIMS) tests.
Business and industry reports and remedial courses in mathematics at the
postsecondary levels of education provide further evidence that many students do
not develop satisfactory knowledge and skills for using mathematics.
As a result of these reports and other data, parents, school staff, local
school boards, state legislators, governors, and business and industry are
calling for higher student achievement and changes in school mathematics
programs. More assessment, different forms of assessment, and accountability
programs at local, state, and national levels are also recommended to guide
program improvement, lead to improved achievement, and identify variables that
relate to effective programs.
WHAT ARE THE PURPOSES AND CHARACTERISTICS OF A GOOD SCHOOL MATHEMATICS ACCOUNTABILITY AND IMPROVEMENT PROGRAM?
improvement programs are designed, developed and used for several purposes.
These include: (1) determining the planned curriculum; (2) determining what
curriculum is used; (3) determining how teachers teach; (4) determining the
impact of the curriculum and instruction on student achievement, attitudes, and
behavior for all students and samples of students; (5) determining school,
curriculum, teacher and student variables related to student achievement
attitudes and behavior; (6) communicating accountability results to school
personnel, parents, students, and others; (7) determining changes desired to
improve achievement, attitudes, and behaviors; and (8) changing policies,
resources, and practices to help effect change.
A good mathematics accountability and improvement program should (1) develop
a process that involves teachers, administrators, parents, students and other
citizens; (2) establish desirable goals and objectives for the mathematics
program; (3) select indicators to determine alignment of the curriculum,
curriculum and instructional resources, instruction and instructional climate,
program expectations and support, and student achievement and participation; (4)
provide a process for analyzing the data obtained to determine achievement and
participation levels and to identify variables related to program successes and
weaknesses; (5) communicate results to the school and public; (6) determine
changes desired; (7) establish policies, procedures, and practices to implement
the changes; (8) continuously monitor the program; and (9) provide mechanisms to
These procedures will provide information to help students, help improve the
program, and communicate program activity and effectiveness to the school and
WHAT MATERIALS ARE AVAILABLE TO ASSIST SCHOOLS IN DETERMINING DESIRED GOALS AND OBJECTIVES?
Several states have developed
state goals and objectives for mathematics to help schools determine their goals
and objectives. California, Hawaii, Michigan, and others have delineated their
goals and objectives and have produced documents that can provide guidance to
The National Council of Teachers of Mathematics (NCTM) has produced a series
of standards that identify student achievement, attitudes, and behaviors desired
and content and experiences to be included in a good mathematics program. The
NCTM Standards recommend stressing (1) mathematical power, (2) problem solving,
(3) communication, (4) reasoning, (5) mathematical concepts, (6) mathematical
procedures, and (7) mathematical disposition. The NCTM Standards provide a
detailed explanation of what is included in each of these categories.
The Council of Chief State School Officers convened a group to recommend what
abilities and content should be included in the fifth National Assessment of
Education Progress (NAEP) Assessment of Mathematics. The group considered the
NCTM Standards, previous NAEP tests, and state goals and objectives.
The group recommended that three mathematical abilities be assessed:
conceptual understanding, procedural knowledge, and problem solving. Content to
be assessed includes: number operations; measurement; geometry; data analysis,
statistics, and probability; and algebra and functions.
The group also recommended emphases for each of the abilities and for each of
the content categories for assessments at grades 4, 8, and 12.
WHAT DATA SHOULD BE COLLECTED RELATED TO CURRICULUM AND CURRICULUM RESOURCES?
Analyses of several accountability models and the
NCTM Standards suggest at least the following curricular items should be
analyzed: goals, objectives, and mathematical content; relative emphases of
various topics and processes and their relationships; assigned time;
articulation across grades; and availability of technological tools and support
materials. Data on these variables will provide an indication of the planned
curriculum and materials and resources provided to achieve its goals and
WHAT DATA SHOULD BE COLLECTED RELATED TO INSTRUCTION AND THE INSTRUCTIONAL ENVIRONMENT?
Analyses of several accountability models and
the NCTM Standards suggest at least the following items related to instruction
and the instructional environment should be analyzed: mathematical content and
its treatment; relative emphases assigned to various topics and processes and
the relationship among them; opportunity to learn; instructional resources;
classroom climate; assessment methods and instruments used; and articulation of
instruction across grades.
WHAT DATA ON STUDENT LEARNING AND PARTICIPATION SHOULD BE COLLECTED?
Data collected related to student learning and participation
should be aligned with the curriculum and instruction in terms of (1) goals,
objectives, and content, and (2) relative emphasis on topics and processes and
Data on student learning should be collected from a variety of sources. The
NCTM Standards recommend including data from tasks that are aligned to the
curriculum, demand different kinds of mathematical thinking and present the same
mathematical concept or procedure in different contexts, formats, and problem
situations. The assessment methods and instruments selected should consider the
type of information sought, the probable use of the information, and the
development and maturity of the student.
This evaluation will require different forms of assessment instruments and
procedures than those normally used. Schools should use instruments that assess
their goals and objectives, as well as state or national goals and objectives,
or they will not know how well their programs are functioning. Assessment
procedures also need to emphasize performance and higher order objectives of the
Data should also be collected to measure courses students take,
extra-curricular activities and mathematical experiences.
WHAT PROCESSES AND PROCEDURES SHOULD BE ESTABLISHED FOR USING THE DATA?
The goal of a mathematics accountability and improvement
program is to provide a more effective mathematics program to improve student
achievement, attitudes, and behaviors.
In most schools a climate needs to be established that supports planning,
data use, and program modification (developing policies, practices, and resource
allocations) based on data. This requires administrative support and commitment,
involvement of important constituent groups, an action system and resources for
change, and technical expertise and support. Research on change indicates that
change occurs most frequently and with more effectiveness when there is regular
participation of the principal and the teaching staff in reviewing and using the
data, meetings focused on practices to be maintained or modified, regular
communication of activities and progress, development of local materials to use
in the program, assistance for teachers when needed, opportunity to observe
effective programs/teachers, and credit or visibility for progress.
If schools are to have community support, there also needs to be community
involvement and regular communication with the community. The community needs to
understand and share the vision of the mathematics program. Representatives of
the community should be involved in recommending goals and objectives, analyzing
data, and recommending changes in policies and practice.
Assessing Mathematics in 1990 by the
National Assessment of Educational Progress, Recommendations. Council of Chief
State School Officers, Washington, DC, March 1988.
Blank, R. and P. Espenshade. State Education Indicators of Science and
Mathematics. Council of Chief State School Officers State Education Assessment
Center, Washington, DC, 1988.
David, Jane L. Improving Education with Locally Developed Indicators. Center
for Policy Research in Education, Rutgers University, October, 1987. ED 293 847.
Dossey, John A. and Others. Mathematics: Are We Measuring Up? The Mathematics
Report Card. Executive Summary. NAEP, Princeton, NJ, June 1988. ED 300 207.
Murnane, R. J. and S. A. Raizen. Improving Indicators of the Quality of
Science and Mathematics Education in Grades K-12. National Academy Press,
Washington, DC, 1988. ED 294 717.
OERI State Accountability Study Group. Creating Responsible and Responsive
Accountability Systems. United States Government Printing Office, Washington,
DC, 1988. ED 299 706.
On Reporting Student Achievement at the State Level by the National
Assessment of Educational Progress, Recommendations. Council of Chief State
School Officers, Washington, DC, March 1988.
Overview of the Curriculum and Evaluation Standards for School Mathematics
(An Abridgement and Excerpts). National Council of Teachers of Mathematics,
Reston, VA, October 1988.
Romberg, T. A., Ed. The Monitoring of School Mathematics: Background Papers.
Volume 1: The Monitoring Project and Mathematics Curriculum. Progam Report 87-1.
Wisconsin Center for Education Research, Madison, WI, 1987. ED 289 708.
Shavelson, R., L. McDonnell, J. Oakes, and N. Carey. Indicator Systems for
Monitoring Mathematics and Science Education. The Rand Corporation, Santa
Monica, CA, 1987. ED 294 738.
Suydam, Marilyn. Evaluation in the Mathematics Classroom: From What and Why
To How and Where (Revised Edition). ERIC/SMEAC, Columbus, OH, December 1986. ED
Wayson, William W., Charles Achilles, Gay Su Pinnell, M. Nan Lintz, Lila N.
Carol, and Lavern Cunningham. Handbook for Developing Public Confidence in
Schools. Phi Delta Kappa Educational Foundation, Bloomington, IN, 1988. ED 299
Weiss, Iris. Indicators of Science and Mathematics Education. Providing Tools
for State Policymakers. Council of Chief State School Officers, Washington, DC,
April 1988. ED 295 844.