OVERVIEW

This section presents fourteen evaluation standards, categorized by focus: General Assessment, Student Assessment, and Program Evaluation.

General Assessment

1. Alignment
2. Multiple Sources of Information
3. Appropriate Assessment Methods and Uses

   Student Assessment

4. Mathematical Power
5. Problem Solving
6. Communication
7. Reasoning
8. Mathematical Concepts
9. Mathematical Procedures
10. Mathematical Disposition

    Program Evaluation

11. Indicators for Program Evaluation
12. Curriculum and Instructional Resources
13. Instruction
14. Evaluation Team

Evaluation and Change

A common response to the challenge of the Standards is, "Yes, but who will change the tests?" Although pragmatic, this question shifts responsibility for change away from the individual to some unnamed higher authority. More productive--and more likely to make the vision embodied in the Standards a reality--are such responses as, "In what ways does the curriculum need to be changed?" "How best can these changes be made?" "How will we know when we have reached the Standards?" It is in the answers to these questions that the role of evaluation emerges as a critical component of reform. Evaluation is a tool for implementing the Standards and effecting change systematically. The main purpose of evaluation, as described in these standards, is to help teachers better understand what students know and make meaningful instructional decisions. The focus is on what happens in the classroom as students and teachers interact. Therefore, these evaluation standards call for changes beyond the mere modification of tests.

Yes, tests also need to change. They must change because a curriculum that fulfills the Standards will differ significantly, in both content and instruction, from most existing curricula. Many existing tests cannot measure the student outcomes identified in the Standards, for example, having K-4 students use many computation techniques and having 9-12 students make connections among mathematical topics. As the curriculum changes, so must the tests. Tests also must change because they are one way of communicating what is important for students to know. The tested curriculum can strongly influence what students are taught.

In this way tests can effect change. Finally, existing tests must change because they are based on different views of what knowing and learning mathematics means. Knowing mathematics by doing mathematics in a technological world differs from developing a sequence of skills or objectives when calculators and computers did not exist and when mathematical applications were primarily confined to the physical sciences and commerce.

Evaluation is fundamental to the process of making the Standards a reality. Just as the Curriculum Standards propose changes in K-12 content and instruction, the Evaluation Standards propose changes in the processes and methods by which information is collected. These changes, developed in light of current knowledge about evaluation, are intended to increase and improve the gathering of relevant, useful information. Assessment and program-evaluation practices must change along with the curriculum. The Evaluation Standards propose that--

• student assessment be integral to instruction;
• multiple means of assessment methods be used;
• all aspects of mathematical knowledge and its connections be assessed; and
• instruction and curriculum be considered equally in judging the quality of a program.

Other Issues

When programs are evaluated and students are assessed, the information collected must be aggregated to draw meaning from what was observed or measured. The aggregated information is reported, used to assign grades, or used as an indication of the quality of the program. Although the process of aggregating information, scoring, and reporting is not discussed in detail in these Evaluation Standards, these issues are important and should be addressed. Because the Evaluation Standards call for multiple means of assessment, they imply that a variety of scoring schemes are to be used. Such schemes can include ratings of students' work that are based on its overall quality or on the inclusion of specific features or parts. Record keeping can be writing notes on cards or on a computer or maintaining a portfolio of the students' work. Whatever the scheme, the results should constitute an accurate and thorough indication of the mathematics that students know. Merely adding scores on written tests will not give a full picture of what students know. The challenge for teachers is to try different ways of grading, scoring, and reporting to determine the best ways to describe students' knowledge of mathematics as indicated in these Standards.

Format of the Evaluation Standards

The Evaluation Standards are organized in three sections: General Assessment, Student Assessment, and Program Evaluation. The general-assessment standards discuss principles relevant to any form of assessment and program evaluation. The student-assessment standards consider aspects of mathematical knowledge that should be assessed, as derived from the Curriculum Standards. The program-evaluation standards examine the assessment of the extent to which a mathematics program is consistent with the Standards.

The format of the Evaluation Standards differs from that of the Curriculum Standards. Each evaluation standard begins with a statement about the topics or concepts that an assessment or program evaluation should address, followed by a list of indicators describing what can be observed. Indicators are used to identify outcomes because they denote a measure placed in some context. In this situation, the Curriculum Standards serve as the criteria against which to compare the evidence of what students can do.

Emphases of the Evaluation Standards

The fourteen Evaluation Standards emphasize aspects of assessment and program evaluation that depart from current practice. The following aspects are to receive increased and decreased attention:

     Increased Attention                 Decreased Attention







  * Assessing what students             * Assessing what students do



    know and how they think about         not know



    mathematics







  * Having assessment be an inte-       * Having assessment be simply



    gral part of teaching                 counting correct answers on



                                          tests for the sole purpose of



                                          assigning grades







  * Focusing on a broad range of        * Focusing on a large number of



    mathematical tasks and taking         specific and isolated skills or-



    a holistic view of mathematics        ganized by a content-behavior



                                          matrix







  * Developing problem situations       * Using exercises or word prob-



    that require the applications of      lems requiring only one or two



    a number of mathematical              skills



    ideas



    



    Using multiple assessment            * Using only written tests



    techniques, including written,



    oral, and demonstration for-



    mats







    Using calculators, computers,        * Excluding calculators, com-



    and manipulatives in assess-           puters, and manipulatives from



    ment                                   the assessment process







    Evaluating the program by sys-       * Evaluating the program only on



    tematically collecting informa-        the basis of test scores



    tion on outcomes, curriculum,



    and instruction







    Using standardized achieve-          * Using standardized achieve-



    ment tests as only one of              ment tests as the only indica-



    many indicators of program             tor of program outcomes



    outcomes                              

GENERAL ASSESSMENT

The general-assessment standards present principles for judging assessment instruments. These principles are relevant for assessment at all levels and provide a rationale for the student-assessment standards that follow. These principles also apply to program evaluation. Inherent in the general-assessment standards is an assumption that all evaluation processes should use multiple assessment techniques that are aligned with the curriculum and consider the purpose of an assessment.

The vision of mathematics education in the Standards places new demands on instruction and forces us to reassess the manner and methods by which we chart our students' progress. In an instructional environment that demands a deeper understanding of mathematics, testing instruments that call for only the identification of single correct responses no longer suffice. Instead, our instruments must reflect the scope and intent of our instructional program to have students solve problems, reason, and communicate. Furthermore, the instruments must enable the teacher to understand students' perceptions of mathematical ideas and processes and their ability to function in a mathematical context. At the same time, they must be sensitive enough to help teachers identify individual areas of difficulty in order to improve instruction.

Many assessment techniques are available, including multiple-choice, short-answer, discussion, or open-ended questions; structured or open-ended interviews; homework; projects; journals; essays; dramatizations; and class presentations. Among these techniques are those appropriate for students working in whole-class settings, in small groups, or individually. The mode of assessment can be written, oral, or computer-oriented.

These and other techniques reflect the diversity of instructional methods implied by the Curriculum Standards and the various ways in which students learn, allow for diversity in student responses and modes of processing information, and provide reliable and valid information. Instructional decisions should be based on the convergence of information from different sources that supports or corroborates the need for a given educational response. When available information is contradictory, as for example when a student achieves good test scores but is unable to communicate mathematical processes, an assessment must search for deeper explanation. Simply put, assessment should not rely on a single instrument or technique.