THE PRACTICE: Assessment That Informs Practice in Middle School Mathematics
Content Presented By:
Eisenhower National Clearinghouse
Overview of Assessment in Middle School Math
This overview was originally published in ENC Focus: A Magazine for Classroom Innovators, vol. 7 no. 2, "Assessment That Informs Practice," and can be found online at:
Standardized Test Scores and Alternative Assessments:
Different Pieces of the Same Puzzle
by William E. Loadman and Anne Marie Thomas, The Ohio State University
Far-reaching policies are often based on the results of state-imposed standardized testing programs. Concerned individuals, both in the educational community and beyond, have questioned this. The usefulness of these tests in terms of actual student assessment has been debated. The testing programs and their scores have been blamed for disrupting normal classroom learning and assessment. Often the tests are viewed as being one dimensional, biased, and simply not useful for classroom teachers (Haney & Madeus, 1989; Mehrens and Kaminski, 1989; Cattrel , 1991; Cooley, 1991; Darling-Hammond, 1991; Jaeger, 1991; Smith & Rottenberg, 1991; Stake, 1991; Lanese,1992; Mehrens, 1992; Popham, 1992; Herman & Golan, 1993).
Alternative assessment strategies, such as teacher observation, personal communication, and student performances, demonstrations, and portfolios, have been offered by experts as having greater usefulness for evaluating students and informing classroom instruction (Dorr-Bremme & Herman, 1986; Stiggins, 1994; Brookhart, 1999). In addition, the contentious atmosphere surrounding standardized testing has resulted in a backlash against that format and in favor of alternative or "authentic" strategies (Stiggins, 1994).
We would like to suggest to classroom teachers that standardized test scores and alternative student assessments both have an important place in our classrooms. Both offer different pieces of information about a given student. Teachers who are comfortable with both types of assessment have the ability to assess student knowledge, skills, and abilities more comprehensively.
Understanding Different Types of Assessment
Both standardized testing and alternative assessment strategies are designed to assess student learning, but the purposes behind these two types of assessment frequently differ. Large-scale, high-stakes standardized tests do gather information about individual student performance, but most of these assessments are primarily designed to inform decision makers about performance on the school, district, and/or state level. On the other hand, alternative assessment strategies are more frequently used to provide information about individual students.
Beyond understanding the basic purposes of each type of assessment, teachers need to take into account two other important considerations.
The first consideration is a question of values. Assessment, whether reflected in a standardized test score or in a teacher-written description of a student performance, is based in subjective human value. People have different values. These differing values often lead to different evaluation criteria, which ultimately result in different final assessments.
The second consideration is the underlying reference model. There are three prominent models used in education:
- The norm-referenced model, in which individual student performance is compared with a norm group;
- The criterion-referenced model, in which individual student performance is compared to a standard or criterion; and
- The growth model, in which individual student performance is assessed by examining student growth on a concept, knowledge base, or skill between two points in time.
Lack of understanding of which model is being used in interpreting student achievement often confuses the debate over the merits of various assessment strategies.
Each of these considerations is pertinent for both standardized test scores and the interpretation of alternative assessments.
What Standardized Test Scores Can Tell Us
Standardized test scores properly obtained through a valid and reliable instrument and used appropriately can offer a wealth of information. For example, to evaluate mathematics achievement in algebra, students could be asked to solve 15 different algebra problems. The criterion might be set that seventh graders should be able to solve 12 out of the 15 correctly to meet the standard for achievement in algebra. The same test might also be referenced normatively. Perhaps the school district average for algebra achievement among seventh graders was solving eight problems. Finally, if these standardized test measures on algebra were gathered over time or across grade levels, the assessment of growth is possible.
We illustrate the possibilities by looking at one student, Ashley, who solved nine out of the 15 problems correctly. In a similar assessment taken when she was in sixth grade, Ashley solved five out of ten algebra problems. Given the reference points, the teacher has valuable information about Ashley. She did not meet the criterion, but she did perform better than the district average, and it appears that she has grown from the previous academic year. All three pieces of information should be shared with Ashley and her parents so that the fact that she did not meet the criterion is not interpreted as academic failure.
The reference points also provide information on the level of achievement in the district. The fact that the norm for the district was below the criterion achievement level certainly is a cause for concern. Perhaps there is some curricular misalignment. The match between the district algebra curriculum and the algebra items on the exam should be examined before teachers make any drastic changes in classroom instruction. If there is a match, delivery of the material could be modified for the next year. A mismatch would suggest that district leadership should review both the curriculum and the test.
What Alternative Assessments Can Tell Us
Alternative assessment formats, such as teacher observation, personal communication, and student performances, demonstrations, and portfolios, offer students and teachers a forum where the knowledge or skill to be assessed is grounded in the kind of work people actually do in the real world (Wiggins, 1989). Moreover, the varied formats offer additional and, in many instances, more comfortable ways for students to demonstrate what they know and are able to do.
For example, if we turn to Ashley again, it could be that she has algebra knowledge and skills that were untapped by the paper-and-pencil format of the standardized test. Alternative algebra assessments could allow for that discovery. Perhaps an algebra game would show that Ashley can solve 14 out of the 15 problems correctly. Or direct communication with the teacher might result in Ashley getting all 15 correct.
Formats such as personal communication or teacher observation also offer teachers information on their curricula and their instruction. A teacher might believe she has covered all the terminology necessary for the students to demonstrate algebra skills. However, during a student demonstration, she realizes that the term "variable" had not been clear during the instruction.
Given the opportunity, students can become actively involved in assessment of their own performance and of the curriculum and instruction. For example, students might communicate that the instruction contradicted items on the test.
Pieces of information such as these would not have been available through a paper-and-pencil standardized test. Alternative assessments have been criticized as not being objective enough and not being generalizable, but they offer a new dimension as well as the opportunity for successful performance by students who may be disadvantaged by standardized tests.
What Does This Mean for Teachers?
Multiple methods and perspectives must go into the assessment of students by classroom teachers. Use of all assessment tools available, including standardized test scores, is imperative. We as educators have the responsibility to build reliable portraits of individual student achievement and to use that information to shape both curriculum and instruction.
(Note: Use "back" button and click on "References" to access the reference list for this article.)
Brookhart, S.M. (1999). The art and science of classroom assessment: The missing part of pedagogy. ASHE-ERIC Higher Education Report, 27 (1).
Catteral, J. (1991). A reform cooled out: Competency testing required for high school graduation. The High School Journal, 75 (1), 7-16.
Cooley, J.P. (1991). State-wide student assessment. Educational Measurement: Issues and Practice, 10 (4), 3-6, 15.
Darling-Hammond, L. (1991). The implications of testing policy for quality and equality. Phi Delta Kappan, 73 (3), 220-225.
Dorr-Bremme, D. & Herman, J. (1986). Assessing student achievement: A profile of classroom practices. A Center for the Study of Evaluation Document. Los Angeles, CA.
Haney, W. & Madaus, G. (1989). Searching for alternatives to standardized tests: Whys, whats and whithers. Phi Delta Kappan, 70 (9), 683-687.
Herman, J.L. & Golan, S. (1993). The effects of standardized testing on teaching and schools. Educational Measurement: Issues and Practice, 12 (2), 20-26.
Jaeger, R.M. (1991). Legislative perspectives on statewide testing: Goals, hopes and desires. Phi Delta Kappan, 73 (3), 239-242.
Lanese, J.F. (1992). Statewide proficiency testing: Establishing standards or barriers. (ERIC Document 347 196.)
Mehrens, W.A. (1992). Using performance assessment for accountability purposes. Educational Measurement: Issues and Practice, 11 (1), 3-9.
Mehrens, W.A. & Kaminski, J. (1989). Methods for improving standardized test scores: Fruitful, fruitless or fraudulent? Educational Measurement: Issues and Practice, 8 (1), 14-22.
Popham, W.J. (1992). The perils of responsibility sharing. Educational Measurement: Issues and Practice, 11 (4), 16-17.
Smith, M.L. & Rottenberg, C. (1991). Unintended consequences of external testing in elementary schools. Educational Measurement: Issues and Practice, 10 (4), 7-11.
Stake, R. (1991). The teacher, the standardized test and prospects of a revolution. Phi Delta Kappan, 72 (11), 243-247.
Stiggins, R. (1994). Student-centered classroom assessment. Ontario: Macmillan College Publishing Co.
Wiggins, G. (1989). A true test: Toward more authentic and equitable assessment. Phi Delta Kappan, 70 (10), 703-713.
Web Sites of Interest:
- Principles and Standards for School Mathematics can be accessed online at http://standards.nctm.org/
- Illuminations - http://Illuminations.nctm.org/index2.html
- ENC Online - http://enc.org - Eisenhower National Clearinghouse offers excellent resources including:
- Middle school mathematics teachers will find a wide variety of professional development resources, curriculum materials, Internet sites, and other tools to enhance their teaching and learning. ENC's Digital Dozen, (http://enc.org/weblinks/dd/) a monthly selection of 13 math and science related web sites, is one place teachers will find an assortment of Internet resources to use in their classroom or for their own professional growth.
- Educators can also search for resources on assessment through ENC's collection of more than 17,000 math and science educational materials (to browse the collection, go to http://enc.org/resources/browse/ for subject categories).
- A section of ENC Online specifically devoted to the topic of assessment can be found at http://www.enc.org/topics/assessment/. By clicking on "Selected Resources," teachers can find a selection of professional development resources, curriculum materials, and Internet sites on assessment.
- Dr. Helen Barrett's Favorite Links and Alternative Assessment & Electronic Portfolios: http://electronicportfolios.org/portfolios/bookmarks.html