Mathematics assessments play a valuable role in identifying students' strengths and weaknesses and in developing and monitoring instructional practice. Over the last century, mathematics assessment has been refined as math content has changed as a result of curriculum reform. Today, researchers and practitioners use various assessment techniques to (a) identify students who have mathematics learning disabilities (LD), (b) target individual strengths and weaknesses across mathematics areas, (c) document the effects of mathematics instruction in a remedial or special program, (d) identify strategies that students employ during math activities, (e) conduct research about the characteristics of students with math LD, and (f) examine the technical characteristics of mathematics tests. This article provides an historical overview of the development of mathematics assessment and a description of specific strategies for conducting math evaluations.
Get full access to this article
View all access options for this article.
References
1.
American Educational Research Association & National Council on Measurement in Education (1955). Technical recommendations for achievement tests.Washington, DC: National Education Association.
2.
American Psychological Association. (1954). Technical recommendations for psychological tests and diagnostic techniques.Washington, DC: Author.
3.
American Psychological Association. (1966). Standards for educational and psychological tests and manuals.Washington, DC: Author.
4.
Baroody, A., & Ginsburg, H. (1991). Mathematics assessment. In H. L. Swanson (Ed.), Handbook on the assessment of learning disabilities (pp. 177–227). Austin, TX: PRO-ED.
5.
Binet, A., & Simon, T. (1905). Methods nouvelles pour le diagnostic de niveau intellectuel des anormaux. Annec Psychologique, 11, 191–244.
6.
Bryant, B. R., & Maddox, T. (in press). Using alternative assessment techniques to plan for and evaluate mathematics instruction. LD Forum.
7.
Bryant, B. R., Patton, J., & Dunn, C. (1991). Scholastic abilities test for adults.Austin, TX: PRO-ED.
8.
Bryant, B. R., Taylor, R., & Rivera, D. P. (1994, October). Mathematics assessment and the NCTM standards: Implications for students with learning disabilities. Paper presented at the International Conference on Learning Disabilities, San Diego.
9.
Buros, O. K. (Ed.). (1975). Mathematics tests and reviews.Highland Park, NJ: Gryphon Press.
10.
Burt, C. (1922). Mental and scholastic tests.London: P.S. King and Son.
11.
Buswell, G. T., & John, L. (1926). Diagnostic studies in arithmetic. (Supplementary Educational Monograph No. 30). Chicago: The University of Chicago.
12.
Case, L. P., Harris, K. R., & Graham, S. (1992). Improving the mathematical skills of students with learning disabilities: Self-regulated strategy development. The Journal of Special Education, 26, 1–19.
13.
Connolly, A. J. (1988). KeyMath-Revised.Circle Pines, MN: American Guidance Service.
14.
Connolly, A., Nactman, W., & Prichett, E.M. (1971). KeyMath diagnostic arithmetic test.Circle Pines, MN: American Guidance Service.
15.
Cooper, B. (1985). Renegotiating secondary school mathematics: A study of curriculum change and stability.London: Falmer Press.
16.
Coutinho, M., & Malouf, D. (1993). Performance assessment and children with disabilities: Issues and possibilities. Teaching Exceptional Children, 25, (4), 62–67.
17.
Cronin, M. E. (1985). Assessment techniques and practices for classroom behaviors, social/emotional factors, and attitudes. In J.F. Cawley (Ed.), Practical mathematics: Appraisal of the learning disabled (pp. 215–247). Rockville, MD: Aspen.
18.
Deno, S. L. (1985). Curriculum-based measurement: The emerging alternative. Exceptional Children, 52, 219–232.
19.
DeRuiter, J. A., & Wansart, W. L. (1982). Psychology of learning disabilities.Rockville, MD: Aspen.
20.
Fuchs, L., & Fuchs, D. (1988). Curriculum-based measurement: A methodology for evaluating and improving student programs. Diagnostique, 14, 3–13.
21.
Fuchs, L., Fuchs, D., Hamlett, C., & Allinder, R. (1989). The reliability and validity of skills analysis within curriculum-based measurement. Diagnostique, 14, 203–221.
22.
Fuchs, L., Fuchs, D., Hamlett, C., & Allinder, R. (1991). The contribution of skills analysis to curriculum-based measurement in spelling. Exceptional Children, 57, 441–452.
23.
Fuchs, L., Fuchs, D., Hamlett, C. L., Thompson, A., Roberts, P. H., Kubek, P., & Stecker, P. (1994). Technical features of a mathematics concepts and applications curriculum-based measurement system. Diagnostique, 19, (4), 23–50.
24.
Fuchs, L. S., Hamlett, C., & Fuchs, D. (1990). Monitoring basic skills progress: Basic math.Austin, TX: PRO-ED.
25.
Gilliland, A. R., & Jordan, R. H. (1924). Educational measurements and the classroom teacher.New York: Century.
26.
Ginsburg, H. P. (1987). The development of arithmetic thinking. In D. D. Hammill (Ed.), Assessing the abilities and instructional needs of students (pp. 423–440). Austin, TX: PRO-ED.
27.
Ginsburg, H. P., & Baroody, A. (1990). Test of early mathematics abilities (2nd ed.). Austin, TX: PRO-ED.
28.
Ginsburg, H., & Mathews, S. C. (1984). Diagnostic test of arithmetic strategies.Austin, TX: PRO-ED.
29.
Goodlad, J. I., Stoephasius, R. V., & Klein, M. F. (1966). The changing school curriculum.New York: Fund for the Advancement of Education.
30.
Greene, H. A., Jorgensen, A. L., & Gerberich, J. R. (1953). Measurement and evaluation in the elementary school.New York: Longsman, Green.
31.
Hammill, D., Ammer, J., Cronin, M., Mandlebaum, L., & Quinby, S. (1987). Quick-score achievement test.Austin, TX: PRO-ED.
32.
Hammill, D. D., Brown, L., & Bryant, B. R. (1992). A consumer's guide to tests in print (2nd ed.). Austin, TX: PRO-ED.
33.
Hammill, D. D., & Bryant, B. R. (1991). Standardized assessment and academic intervention. In H. L. Swanson (Ed.), Handbook on the assessment of learning disabilities: Theory, research, and practice (pp. 373–406). Austin, TX: PRO-ED.
34.
Hammill, D. D., & Larsen, S. (1974). The effectiveness of psycholinguistic training. Exceptional Children, 41, 5–15.
35.
Hasselbring, T. S., Goin, L. I., & Bransford, J. D. (1987). Effective mathematics instruction: Developing automaticity. Teaching Exceptional Children, 19, (3), 30–33.
36.
Hofmeister, A. M. (1993). Elitism and reform in school mathematics. Remedial and Special Education, 14, (6), 8–13.
37.
Hutchinson, N. L. (1993). Second invited response: Students with disabilities and mathematics education reform—Let the dialogue begin. Remedial and Special Education, 14, (6), 20–23.
38.
Jenkins, J. R., & Jewell, M. (1992). An examination of the concurrent validity of the Basic Academic Skills Samples (BASS). Diagnostique, 17, (4), 273–288.
39.
Johnson, D. J., & Mykelbust, H. R. (1967). Learning disabilities: Educational principles and practices.New York: Grune & Stratton.
40.
Kaufman, A. S., & Kaufman, N. L. (1985). Kaufman test of educational achievement-Comprehensive form.Circle Pines, MN: American Guidance Service.
41.
Kennedy, L. M., & Tipps, S. (1994). Guiding children's learning of mathematics (7th ed.). Belmont, CA: Wadsworth.
42.
Kirk, S. A., McCarthy, J. J., & Kirk, W. D. (1968). Illinois test of psycholinguistic abilities.Champaign: University of Illinois Press.
43.
Kliebard, H. M. (1995). The struggle for the American curriculum: 1893–1958 (2nd ed.). New York: Herbert M. Kliebard.
44.
Lopez-Reyna, N. A., Bay, M., & Patrikakou, E. N. (1996). Use of assessment procedures: Learning disabilities teachers' perspectives. Diagnostique, 21, (2), 35–49.
45.
Markwardt, F. C. (1989). Peabody individual achievement test-Revised.Circle Pines, MN: American Guidance Service.
46.
McKinney, J. D., Osbourne, S. S., & Schulte, A. C. (1993). Academic consequences of learning disability: Longitudinal prediction of outcomes at 11 years of age. Learning Disability Research & Practice, 8, (1), 19–27.
47.
McNeil, J. D. (1977). Curriculum: A comprehensive introduction.Boston: Little, Brown.
48.
Mercer, C. D., Harris, C. A., & Miller, S. P. (1993). First invited response: Reforming reforms in mathematics. Remedial and Special Education, 14, (6), 14–19.
49.
Mercer, C. D., & Mercer, A. R. (1993). Teaching students with learning problems (4th ed.). New York: Merrill-Macmillan.
50.
Miller, S. P., & Mercer, C. D. (1993). Using data to learn about concrete-semiconcrete-abstract instructions for students with math disabilities. Learning Disability Research & Practice, 8, (2), 89–96.
51.
Montague, M., & Applegate, B. (1993). Mathematical problem solving characteristics of middle school students with learning disabilities. The Journal of Special Education, 27, 175–201.
52.
Montague, M., Applegate, B., & Marquard, K. (1993). Cognitive strategy instruction and mathematical problem-solving performance of students with learning disabilities. Learning Disability Research & Practice, 8, (4), 223–232.
53.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics.Reston, VA: Author.
54.
Newcomer, P. (1990) Diagnostic achievement battery.Austin, TX: PRO-ED.
55.
Newcomer, P., & Bryant, B. R. (1992). Diagnostic achievement test for adolescents (2nd ed.). Austin, TX: PRO-ED.
56.
Parmar, R. (1992). Protocol analysis of strategies used by students with mild disabilities when solving arithmetic word problems. Diagnostique, 17, (4), 227–243.
57.
Parmar, R. S., Frazita, R., & Cawley, J. F. (1996). Mathematics assessment for students with mild disabilities: An exploration of content validity. Learning Disability Quarterly, 19, (2), 127–136.
58.
Paulson, F. L., Paulson, P. R., & Meyer, C. A. (1991). What makes a portfolio a portfolio?. Educational Leadership, 48, (5), 60–63.
Ragan, W. B., & Shepherd, G. D. (1971). Modern elementary curriculum (4th ed.). New York: Holt, Rinehart and Winston.
61.
Resnick, L. B., & Ford, W. W. (1981). The psychology of mathematics for instruction.Hillsdale, NJ: Erlbaum.
62.
Rivera, D. (1993). Third invited response: Examining mathematics reform and the implications for students with mathematics disabilities. Remedial and Special Education, 14, (6), 24–27.
63.
Rivera, D. (1994). Portfolio assessment. LD Forum, 19, (4), 14–17.
64.
Rivera, D. P., & Bryant, B. R. (1992). Mathematics instruction for students with special needs. Intervention in School and Clinic, 28, 71–86.
65.
Rivera, D. P., & Smith, D. D. (1996). Teaching students with learning and behavior problems (3rd ed.). Boston: Allyn & Bacon.
66.
Rivera, D. P., Taylor, R. L., & Bryant, B. R. (1994–1995). Review of current trends in mathematics assessment for students with mild disabilities. Diagnostique, 20, (1–4), 143–174.
67.
Ruch, G. M., Knight, F. B., Greene, H. A., & Studebaker, J. W. (1925). Compass diagnostic tests in arithmetic.Chicago: Scott, Foresman.
68.
Salvia, J., & Ysseldyke, J. E. (1995). Assessment (6th ed.). Boston: Houghton Mifflin.
69.
Sandler, A. D., Hooper, S. R., Scarborough, A. A., Watson, T. E., & Levine, M. D. (1993). Adolescents talking about thinking: Preliminary findings of a self-report instrument for the assessment of cognition and learning. Diagnostique, 19, (1), 361–376.
70.
Shinn, M. R., & Hubbard, D. D. (1993). Curriculum-based measurement and problem-solving assessment: Basic procedures and outcomes. In E. L. Meyen, G. A. Vergason, & R. J. Whelan (Eds.), Challenges facing special education (pp. 193–226). Denver: Love.
71.
Slate, J. R., Jones, C. H., Graham, L. P., & Bower, J. (1994). Correlations of WISC-III, WRAT, KM-R, PPVT-R scores in students with specific learning disabilities. Learning Disability Research & Practice, 9, (2), 104–107.
72.
Swicegood, P. (1994). Portfolio-based assessment practices. Intervention in School and Clinic, 30, (1), 6–15.
73.
Taylor, R. L. (1993). Assessment of exceptional children (3rd ed.). Needham Heights, MA: Allyn & Bacon.
74.
Taylor, R. L., Tindal, G., Fuchs, L., & Bryant, B. R. (1993). Assessment in the nineties: A possible glance into the future. Diagnostique, 18, (2), 113–122.
75.
Thorndike, E. L. (1912). Education: A first book.New York: Macmillan.
76.
Thorndike, E. L. (1929). Elementary principles of education.New York: Macmillan.
77.
Thorndike, R. L., & Hagen, E. (1955). Measurement and evaluation in psychology and education.New York: Wiley.
78.
Tiegs, E. W. (1931). Tests and measurement for teachers.Cambridge, MA: Riverside.
79.
Tucker, J. (1985). Curriculum-based assessment: An introduction. Exceptional Children, 52, 199–204.
80.
Valencia, S. (1990). A portfolio approach to classroom reading assessment: The whys, whats, and hows. The Reading Teacher, 43, 338–340.
81.
Vogel, S., Hruby, P. J., & Adelman, P. B. (1993). Educational and psychological factors in successful and unsuccessful college students with learning disabilities. Learning Disability Research & Practice, 8, (1), 35–43.
82.
Wesson, C. L., & King. R. P. (1992). The role of curriculum-based measurement in portfolio assessment. Diagnostique, 18, (1), 27–37.
83.
Whinnery, K. W., & Fuchs, L. S. (1993). Effects of goal and test-taking strategies on the computation performance of students with learning disabilities. Learning Disability Research & Practice, 8, (4), 204–214.
84.
Whinnery, K. W., & Stecker, P. M. (1992). Individual progress monitoring to enhance instructional programs in mathematics. Preventing School Failure, 36, (2), 26–29.
85.
Wolf, K. (1991). The school teacher's portfolio: Issues in design, implementation, and evaluation. Phi Delta Kappan, 73, (2), 130–136.
