Approaching Standards for Mathematics Assessment. ERIC/CSMEE Digest

ERIC Educational Reports by Patricia A. Brosnan, Martin D. Hartog

It is acknowledged that the typical mathematics curriculum of a generation ago emphasized teaching facts, standard procedures, and skills to groups of passive recipients. In the last decade, a more integrated, child-centered curriculum presented to more active, participating students has emerged in response to deteriorating public confidence in the quality of American education. However, curriculum, designed on the finest principles with the very best intentions, effects no change in classroom practice if assessment procedures remain the same [National Council of Teachers of Mathematics (NCTM), 1989; Mathematical Sciences Education Board & National Research Council (NRC), 1993]. Realizing this, the mathematical community is addressing multiple challenges to articulate and implement effective standards in the key areas of testing, assessment, and accountability. American students are subjected to a variety of tests, usually standardized, multiple-choice tests, from kindergarten to graduate school. Such tests are, according to widely held beliefs, inhibitors to change and improvement in education--especially in mathematics (MSEB & NRC, 1993). To make assessment instruments agents of change rather than preservers of the status quo, there are several major issues that must be addressed:

* Are current assessment practices and reporting methods problematic?

* What guiding principles should the mathematics community uphold when revamping assessment practices?

* Will alternative assessment methods really make a difference?

* Should use of alternative assessments be mandated?

* Should technology be available at all times? @With these issues emerge problems such as:

* How can assessment be designed equitably?

* Do all students have equal access to technology?

* How can standards be implemented nationally?

* Who will assess the assessment process? Who will enforce the standards?

* What needs to be done to convince teachers to change?WHAT MAKES CURRENT ASSESSMENT PRACTICES AND REPORTING METHODS

PROBLEMATIC?States and districts providing leadership in American education have identified the lack of shared standards for student achievement and good methods for assessment as the greatest obstacles to creating high performing schools. It is all too clear that current tests used for assessment of educational performance fail to measure adequately progress toward national standards (MSEB, 1993). This is especially true in mathematics, where curriculum and teaching standards recommended by the NCTM reflect broad nationwide consensus.

The new curriculum Standards call for an instructional setting that is very different from the classroom settings of the past. The curriculum combines new as well as traditional mathematical topics. Mathematics is presented to students in the form of rich situational problems that actively involve the students. Nonetheless, commonly used tests continue to stress routine, repetitive, rote tasks instead of offering children opportunities to demonstrate the full range of their mathematical power, including such important facets as communication, problem solving, inventiveness, persistence, and curiosity (MSEB, 1993).

Traditionally, instruction has been driven by the curriculum, but assessment has not been an effective part of a feedback loop linked to instruction. Assessment is most valuable when it is an integral part of teaching, not merely a tool for ranking students, but a mechanism for influencing instruction. To realize the full potential of the assessment process requires that the profession develop and implement assessment tasks to measure student productivity and performance on tests that require mathematical thinking (Pandey, 1990).

For too long teachers have been "teaching the test," students have been most interested in learning what will be on the test, and administrators have gauged progress from the results of these tests. If administrative personnel continue to demand and value static scores, teachers will continue to gather the type of data needed to make such a limited report. So, to change assessment practices, administrators must change what is required on reporting mechanisms.WHAT GUIDING ASSESSMENT PRINCIPLES SHOULD THE MATHEMATICS EDUCATION

COMMUNITY UPHOLD?A National Summit on Mathematical Assessment was held 23-24 April 1991 (MSEB, 1991). From the summit emerged a consensus that the evaluation standards of the NCTM Curriculum and Evaluation Standards for School Mathematics (1989) must be expanded. The following list of principles and goals for mathematical assessment was developed to guide the proposed expansion.

Principles

1. The primary purpose of assessment is to improve learning and teaching.

2. The primary use of results of assessment is to promote the development of the talents of all people.

3. The content of assessments is derived from the consensus of the discipline.

Goals

1. Assessments will be aligned with the mathematical knowledge, skills, and processes that the nation needs all of its students to know and be able to do.