ERIC Identifier: ED319628
Publication Date: 1988-00-00
Author: Howe, Robert W. - Warren, Charles R.
Source: ERIC 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?
Accountability and 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 reward success.
These procedures will provide information to help students, help improve the program, and communicate program activity and effectiveness to the school and public.
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 others.
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 objectives.
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 their relationships.
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 mathematics curricula.
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 284 717.
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 299 700.
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.
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