Contribution of Equal-Sign Instruction Beyond Word-Problem Tutoring for Third-Grade Students with Mathematics Difficulty

Journal of Educational Psychology

Volumn 102, Issue 2, 2010, Pages 381-394

  Powell, Sarah R ^a   Fuchs, Lynn S ^a  

^a VANDERBILT UNIVERSITY   (United States)

Author keywords

Equality; Mathematics difficulty; Word problems

Indexed keywords

EID: 77955028890     PISSN: 00220663     EISSN: None     Source Type: Journal    
DOI: 10.1037/a0018447     Document Type: Article

References (49)

1. Diagnostic and statistical manual of mental disorders 1994, American Psychiatric Association, Author, Washington, DC. 4th ed.
2. Baron R.M., Kenny D.A. The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology 1986, 51:1173-1182.
3. Baroody A.J., Ginsburg H.P. The effects of instruction on children's understanding of the " equals" sign. Elementary School Journal 1983, 84:199-212.
4. Behr M., Erlwanger S., Nichols E. How children view the equals sign. Mathematics Teaching 1980, 92:13-15.
5. Blanton M.L., Kaput J.J. Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education 2005, 36:412-446.
6. Capraro M.M., Ding M., Matteson S., Capraro R.M., Li X. Representational implications for understanding equivalence. School Science and Mathematics 2007, 107:86-88.
7. Carpenter T.P., Franke M.L., Levi L. Thinking mathematically: Integrating arithmetic and algebra in elementary school 2003, Heinemann, Portsmouth, NH.
8. Carpenter T.P., Levi L. Developing conceptions of algebraic reasoning in the primary grades. (Report No. 00-2) 2000, University of Wisconsin-Madison, National Center for Improving Student Learning and Achievement in Mathematics and Science, Madison, WI.
9. Carpenter T.P., Moser J.M., Bebout H.C. Representation of addition and subtraction word problems. Journal for Research in Mathematics Education 1988, 19:345-357.
10. Cooper G., Sweller J. Effects of schema acquisition and rule automation on mathematical problem-solving transfer. Journal of Educational Psychology 1987, 79:347-362.
11. Falkner K.P., Levi L., Carpenter T.P. Children's understanding of equality: A foundation for algebra. Teaching Children Mathematics 1999, 6:232-236.
12. Fuchs L.S., Fuchs D. Mathematical problem-solving profiles of students with mathematics disabilities with and without comorbid reading disabilities. Journal of Learning Disabilities 2002, 35:563-573.
13. Fuchs L.S., Compton D.L., Fuchs D., Paulsen K., Bryant J.D., Hamlett C.L. The prevention, identification, and cognitive determinants of math difficulty. Journal of Educational Psychology 2005, 97:493-515.
14. Fuchs L.S., Fuchs D., Finelli R., Courey S.J., Hamlett C.L. Expanding schema-based transfer instruction to help third graders solve real-life mathematical problems. American Educational Research Journal 2004, 41:419-445.
15. Fuchs L.S., Fuchs D., Stuebing K., Fletcher J., Hamlett C.L., Lambert W. Problem-solving and computational skill: Are they shared or distinct aspects of mathematical cognition?. Journal of Educational Psychology 2008, 100:30-47.
16. Fuchs L.S., Powell S.R., Seethaler P.M., Cirino P.T., Fletcher J.M., Fuchs D., Zumeta R.O. Remediating number combination and word problem deficits among students with mathematics difficulties: A randomized control trial. Journal of Educational Psychology 2009, 101:561-576.
17. Fuchs L.S., Seethaler P.S., Powell S.R., Fuchs D., Hamlett C.L., Fletcher J.M. Effects of preventative tutoring on the mathematical problem solving of third-grade students with math and reading difficulties. Exceptional Children 2008, 74:155-173.
18. Geary D.C., Hamson C.O., Hoard M.K. Numerical and arithmetical cognition: A longitudinal study of process and concept deficits in children with learning disability. Journal of Experimental Child Psychology 2000, 77:236-263.
19. Ginsburg H. Children's arithmetic 1977, Van Nostrand, New York, NY.
20. Greenes C., Larson M., Leiva M.A., Shaw J.M., Stiff L., Vogeli B.R., Yeatts K. Houghton Mifflin math 2005, Houghton Mifflin, Boston, MA.
21. Hanich L.B., Jordan N.C., Kaplan D., Dick J. Performance across different areas of mathematical cognition in children with learning difficulties. Journal of Educational Psychology 2001, 93:615-626.
22. Hedges L.V., Olkin I. Statistical methods for meta-analysis 1985, Academic Press, Orlando, FL.
23. Herscovics N., Kieran C. Constructing meaning for the concept of equation. The Mathematics Teachers 1980, 73:572-580.
24. Hinton P.R., Brownlow C., McMurray I., Cozens B. SPSS Explained 2004, Routledge, New York, NY.
25. Hoover H.D., Dunbar S.B., Frisbie D.A. Iowa Tests of Basic Skills-Form A 2001, Riverside, Rolling Meadows, IL.
26. Hudson P., Miller S.P. Designing and implementing mathematics instruction for students with diverse learning needs 2006, Pearson Education, Boston, MA.
27. Jacobs V.R., Franke M.L., Carpenter T.P., Levi L., Battey D. Professional development focused on children's algebraic reasoning in elementary school. Journal for Research in Mathematics Education 2007, 38:258-288.
28. Jitendra A.K., Griffin C.C., Deatline-Buchman A., Sczesniak E. Mathematical problem solving in third-grade classrooms. Journal of Educational Research 2007, 100:283-302.
29. Jordan N.C., Hanich L.B., Kaplan D. A longitudinal study of mathematical competencies in children with specific mathematics difficulties versus children with comorbid mathematics and reading difficulties. Child Development 2003, 74:834-850.
30. Kieran C. Concepts associated with the equality symbol. Educational Studies in Mathematics 1981, 12:317-326.
31. Knuth E.J., Stephens A.C., McNeil N.M., Alibali M.W. Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education 2006, 37:297-312.
32. Kroesbergen E.H., Van Luit J.E.H., Maas C.T.M. Effectiveness of explicit and constructivist mathematics instruction for low-achieving students in the Netherlands. The Elementary School Journal 2004, 104:233-251.
33. Lindvall C.M., Ibarra C.G. Incorrect procedures used by primary grade pupils in solving open addition and subtraction sentences. Journal for Research in Mathematics Education 1980, 11:50-62.
34. Matthews P.G., Rittle-Johnson B. In pursuit of knowledge: Comparing self-explanations, concepts, and procedures as pedagogical tools. Journal of Experimental Child Psychology 2009, 104:1-21.
35. Mazzocco M.M.M. Challenges in identifying target skills for math disability screening and intervention. Journal of Learning Disabilities 2005, 38:318-332.
36. McNeil N.M., Alibali M.W. Why won't you change your mind? Knowledge of operational patterns hinders learning and performance on equations. Child Development 2005, 76:883-899.
37. McNeil N.M., Grandau L., Knuth E.J., Alibali M.W., Stephens A.C., Hattikudur S., Krill D.E. Middle-school students' understanding of the equal sign: The books they read can't help. Cognition and Instruction 2006, 24:367-385.
38. Parmar R.S., Cawley J.F., Frazita R.R. Word problem-solving by students with and without mild disabilities. Exceptional Children 1996, 62:415-429.
39. Powell S.R. Open equations 2007, Available from S. R. Powell, Box 228 Peabody, Nashville, TN 37203.
40. Powell S.R. Story problems 2007, Available from S. R. Powell, Box 228 Peabody, Nashville, TN 37203.
41. Powell S.R., Fuchs L.S., Fuchs D., Cirino P.T., Fletcher J.M. Effects of fact retrieval tutoring on third-grade students with math difficulties with and without reading difficulties. Learning Disabilities Research and Practice 2009, 24:1-11.
42. Wechsler Abbreviated Scale of Intelligence 1999, Psychological Corporation, Harcourt Brace, San Antonio, TX.
43. Rittle-Johnson B., Alibali M.W. Conceptual and procedural knowledge of mathematics: Does one lead to the other?. Journal of Educational Psychology 1999, 91:175-189.
44. Saenz-Ludlow A., Walgamuth C. Third graders' interpretations of equality and the equal symbol. Educational Studies in Mathematics 1998, 35:153-187.
45. Seo K., Ginsburg H.P. " You've got to carefully read the math sentence...": Classroom context and children's interpretations of the equals sign. The development of arithmetic concepts and skills: Constructing adaptive expertise 2003, 161-187. Erlbaum, Mahwah, NJ. A.J. Baroody, A. Dowker (Eds.).
46. Swanson H.L., Beebe-Frankenberger M. The relationship between working memory and mathematical problem solving in children at risk and not at risk for serious math difficulties. Journal of Educational Psychology 2004, 96:471-491.
47. Swanson, J., Schuck, S., Mann, M., Carlson, C., Hartman, M., Sergeant, J., McCleary, R. (n.d.). Categorical and dimensional definitions and evaluations of symptoms of ADHD: The SNAP and SWAN Ratings Scales. Retrieved August 19, 2007, from http://www.adhd.net.
48. Weaver J.F. The symmetric property of the equality relation and young children's ability to solve open addition and subtraction sentences. Journal for Research in Mathematics Education 1973, 4:45-56.
49. Wilkinson G.S. Wide Range Achievement Test 1993, Wide Range, Wilmington, DE. Rev. 3.