Diagnosing students' misconceptions in algebra: Results from an experimental pilot study

Behavior Research Methods

Volumn 41, Issue 2, 2009, Pages 414-424

  Russell, Michael ^a   O'Dwyer, Laura M ^a   Miranda, Helena ^b  

^a BOSTON COLLEGE   (United States)

^b FLORIDA GULF COAST UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CLINICAL TRIAL; COMPARATIVE STUDY; COMPUTER ASSISTED DIAGNOSIS; CONTROLLED CLINICAL TRIAL; CONTROLLED STUDY; ETHNIC GROUP; HUMAN; LEARNING; MATHEMATICS; METHODOLOGY; PHYSIOLOGY; PILOT STUDY; PSYCHOMOTOR PERFORMANCE; RANDOMIZED CONTROLLED TRIAL;

DIAGNOSIS, COMPUTER-ASSISTED; ETHNIC GROUPS; HUMANS; LEARNING; MATHEMATICS; PILOT PROJECTS; PSYCHOMOTOR PERFORMANCE;

EID: 66149145319     PISSN: 1554351X     EISSN: None     Source Type: Journal    
DOI: 10.3758/BRM.41.2.414     Document Type: Article

References (37)

1. Airasian, P. W. (1991). Classroom assessment. New York: McGraw-Hill.
2. Anderson, L. (2003). Classroom assessment: Enhancing the quality of teacher decision making. Mahwah, NJ: Erlbaum.
3. Birenbaum, M., Kelly, A. E., & Tatsuoka, K. K. (1992). Towards a stable diagnostic representation of students' errors in algebra. Princeton, NJ: Educational Testing Service (ERIC Document Reproduction Service No. ED 356973).
4. Booth, L. R. (1984). Algebra: Children's strategies and errors. Windsor, U.K.: NFER-Nelson.
5. Clement, J. (1982). Algebra word problem solutions: Thought processes underlying a common misconception. Journal for Research in Mathematics Education, 13, 16-30.
6. Clement, J. (1989). The concept of variation and misconceptions in Cartesian graphing. Focus on Learning Problems in Mathematics, 11, 77-87.
7. Council of Chief State School Officers (2008). Formative assessment for students and teachers. Retrieved May 3, 2008, from www.ccsso.org/projects/scass/Projects/Formative%5FAssessment%5Ffor%5FStudents%5Fand%5FTeachers/.
8. Cullen, J., & Shaw, S. (2000). The accuracy of teacher prediction of student test performance for students referred to special education. Danbury, CT: Western Connecticut State University, Department of Education and Educational Psychology.
9. Davis, R. B. (1971). Cognitive processes involved in solving simple algebraic equations. Journal of Children's Mathematical Behavior, 1, 7-35.
10. Demaray, M. K., & Elliot, S. N. (1998). Teachers' judgments of students' academic functioning: A comparison of actual and predicted performances. School Psychology Quarterly, 13, 8-24.
11. Falkner, K. P., Levi, L., & Carpenter, T. P. (1999). Children's understanding of equality: A foundation for algebra. Teaching Children Mathematics, 6, 232.
12. Fuller, M. L. (2000, April). Teacher judgment as formative and predictive assessment of student performance on Ohio's fourth and sixth grade proficiency tests. Paper presented at the Annual Meeting of the American Educational Research Association, New Orleans.
13. Herscovics, N. (1989). Cognitive obstacles encountered in the learning of algebra. In S. Wagner & C. Kieran (Eds.), Research issues in the learning and teaching of algebra (pp. 60-86). Reston, VA: National Council of Teachers of Mathematics.
14. Hestenes, D., Wells, M., & Swackhamer, G. (1992). Force concept inventory. Physics Teacher, 30, 141-158.
15. Hiebert, J., & Carpenter, T. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65-100). New York: Macmillan.
16. Hoge, R. D., & Coladarci, T. (1989). Teacher-based judgments of academic achievement: A review of the literature. Review of Educational Research, 59, 297-313.
17. Kieran, C. (1992). The learning and teaching of school algebra. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390-419). New York: Macmillan.
18. Küchemann, D. E. (1978). Children's understanding of numerical variables. Mathematics in School. 7, 23-26.
19. Küchemann, D. E. (1981). Algebra. In K. Hart (Ed.), Children's understanding of mathematics. London: Murray.
20. Matz, M. (1980). Towards a computational theory of algebraic competence. Journal of Mathematical Behavior, 3, 93-166.
21. Mestre, J. (1987). Why should mathematics and science teachers be interested in cognitive research findings? Academic Connections (pp. 3-5, 8-11). New York: The College Board.
22. Mulholland, L. A., & Berliner, D. C. (1992, April). Teacher experience and estimation of student achievement. Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco.
23. No Child Left Behind Act of 2001, Pub. L. 107-110, §1606, 115 Stat. 1425 (2002).
24. Pellegrino, J. W., Chudowsky, N., & Glaser, R. (Eds.) (2001).Knowing what students know: The science and design of educational assessment. Washington, DC: National Academy Press.
25. Popham, W. J. (1995). Classroom assessment: What teachers need to know. Needham Heights, MA: Allyn and Bacon.
26. Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods. Newbury Park, CA: Sage.
27. Rosnick, P. (1981). Some misconceptions concerning the concept of variable: Are you careful about defining your variables? Mathematics Teacher, 74, 418-420.
28. Rosnick, P., & Clement, J. (1997). Learning without understanding: The effect of tutoring strategies on algebra misconceptions. Journal of Mathematical Behavior, 3, 3-27.
29. Russell, M. (2002). How computer-based technologies can disrupt the technology of testing. In Technology and assessment: Thinking ahead-Proceedings from a workshop (pp. 63-78). Washington, DC:National Research Council.
30. Russell, M., Kay, R., & Miranda, H. (2008). Diagnostic algebra assessment study technical report. Chestnut Hill, MA: Technology and Assessment Study Collaborative.
31. Sáenz-Ludlow, A., & Walgamuth, C. (1998), Educational Studies in Mathematics, 35, 153-187.
32. Schwartzman, S. (1996). Some common algebraic misconceptions. Mathematics & Computer Education, 30, 164-173.
33. Shepard, L. (1990). Inflating test score gains: Is the problem old norms or teaching the test? Educational Measurement: Issues & Practice,9, 15-22.
34. Snow, R. E., & Lohman, D. F. (1989). Implications of cognitive psychology for educational measurement. In R. L. Linn (Ed.), Educational measurement (pp. 263-331). New York: Macmillan.
35. Spybrook, J., Raudenbush, S. W., Liu, X., & Condon, R. (2006). Optimal design for longitudinal and multilevel research: Documentation for the Optimal Design software. V. 1.76.
36. Stacey, K., & McGregor, M. (1997). Ideas about symbolism that students bring to algebra. Mathematics Teacher, 90, 110-113.
37. U.S. Department of Education (2008). Federal Register, Vol. 73, No.23, p. 6487-6491. Retrieved May 5, 2008, from www.ed.gov/legislation/FedRegister/announcements/2008-1/020408d.pdf.