Anchoring minneapolis problem-solving and computation instruction in context-rich learning environments

Exceptional Children

Volumn 76, Issue 4, 2010, Pages 417-437

  Bottge, Brian A ^a   Rueda, Enrique ^b   Grant, Timothy S ^c   Stephens, Ana C ^d   Laroque, Perry T ^e  

^a UNIVERSITY OF KENTUCKY   (United States)

^b Freelance Multimedia Research Artist   (United States)

^c UNIVERSITY COLLEGE DUBLIN   (Ireland)

^d UNIVERSITY OF WISCONSIN MADISON   (United States)

^e STATE UNIVERSITY OF NEW YORK AT POTSDAM   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84864932464     PISSN: 00144029     EISSN: None     Source Type: Journal    
DOI: 10.1177/001440291007600403     Document Type: Article

References (79)

1. Baroody, A., Feil, Y., & Johnson, A. (2007). An alternative reconceptualization of procedural and conceptual knowledge. Journal for Research in Mathematics Education, 38, 115-131.
2. Baroody, A. J., & Coslick, R. T. (1998). Fostering children's mathematical power. Mahwah, NJ: Lawrence Erlbaum.
3. Baroody, A. J., & Gannon, K. E. (1984). The development of the commutativity principle and economic addition strategies. Cognition and Instruction, 1, 321-339.
4. Behr, J. J., Wachsmuth, I., & Post, T. R. (1985). Construct a sum: A measure of children's understanding of fraction size. Journal for Research in Mathematics Education, 16, 120-131.
5. Behr, M., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio, and proportion. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 296-333). New York, NY: Macmillan.
6. Boaler, J. (2002). Experiencing school mathematics: Traditional and reform approaches to teaching and their impact on student learning. Mahwah, NJ: Lawrence Erlbaum.
7. Bottge, B., Rueda, E., & Skivington, M. (2006). Situating math instruction in rich problem-solving contexts: Effects on adolescents with challenging behaviors. Behavioral Disorders, 31, 394-407.
8. Bottge, B. A. (1999). Effects of contextualized math instruction on problem solving of average and below-Average achieving students. Journal of Special Education, 33, 81-92.
9. Bottge, B. A. (2001). Reconceptualizing math problem solving for low-Achieving students. Remedial and Special Education, 22, 102-112.
10. Bottge, B. A., Heinrichs, M., Mehta, Z., & Hung, Y. (2002). Weighing the benefits of anchored math instruction for students with disabilities in general education classes. The Journal of Special Education, 35, 186-200.
11. Bottge, B. A., Heinrichs, M., Mehta, Z. D., Rueda, E., Hung, Y., & Danneker, J. (2004). Teaching mathematical problem solving to middle school students in math, technology education, and special education classrooms. Research in Middle Level Education (on-line), 27. Retrieved from http://www.nmsa.org/Publications/RMLEOnline/Articles/Vol27No1Article1/tabid/529/ Default.aspx
12. Bottge, B. A., Rueda, E., LaRoque, P. T., Serlin, R. C., & Kwon, J. (2007). Integrating reform-oriented math instruction in special education settings. Learning Disabilities Research and Practice, 22, 96-109.
13. Bottge, B. A., Rueda, E., Serlin, R. C., Hung, Y., & Kwon, J. (2007). Shrinking achievement differences with anchored math problems: Challenges and possibilities. The Journal of Special Education, 41, 31-49.
14. Bottge, B. A., & Stephens, A. (2009). Advancing middle school students' understanding of fractions in technology education classrooms. Madison, WI: Wisconsin Center for Education Research.
15. Bricklin, P. M., & Gallico, R. (1984). Learning disabilities and emotional disturbance: Critical issues in definition, assessment, and service delivery. Learning Disabilities, 3, 141-156.
16. Butler, F. M., Miller, S. P., Crehan, K., Babbitt, B., & Pierce, T. (2003). Fraction instruction for students with mathematics disabilities: Comparing two teaching sequences. Learning Disabilities Research and Practice, 18, 99-111.
17. Calhoon, M. B., Emerson, R. W., Flores, M., & Houchins, D. E. (2007). Computational fluency performance profile of high school students with mathematics disabilities. Remedial and Special Education, 28, 292-303.
18. Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C., & Loef, M. (1989). Using knowledge of children's mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26, 499-531.
19. Cawley, J., Parmar, R., Foley, T. E., Salmon, S., & Roy, S. (2001). Arithmetic performance of students: Impli-cations for standards and programming. Exceptional Children, 67, 311-328.
20. Cawley, J. F., & Miller, J. H. (1989). Cross-sectional comparisons of the mathematical performance of learning disabled children: Are we on the right track toward comprehensive programming? Journal of Learning Disabilities, 22, 250-255.
21. Cawley, J. F., Parmar, R. S., Yan, W., & Miller, J. H. (1998). Arithmetic computation performance of students with learning disabilities: Implications for curriculum. Learning Disabilities Research and Practice, 13(2), 68-74.
22. Charalambous, C. Y., & Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study students' understandings of fractions. Educational Studies in Mathematics, 64, 293-316.
23. Chval, K. B., Reys, R., Reys, B. J., Tarr, J. E., & Chavez, O. (2006). Pressures to improve student performance: A context that both urges and impedes school-based research. Journal for Research in Mathematics Education, 37, 158-166.
24. Cognition and Technology Group at Vanderbilt University. (1990). Anchored instruction and its relationship to situated cognition. Educational Researcher, 19(3), 2-10.
25. Educational Testing Service (ETS). (2007). America's perfect storm: Three forces changing our nation's future. Princeton, NJ: Author.
26. Fuchs, L. S., & Fuchs, D. (2002). Mathematical problem-solving profiles of students with mathematics disabilities with and without comorbid reading difficulties. Journal of Learning Disabilities, 35, 563-573.
27. Fuson, K. (1990). Conceptual structures or multiunit numbers: Implications for learning and teaching multidigit addition, subtraction, and place value. Cognition and Instruction, 7, 343-403.
28. Gallico, R., Burns, T. J., & Grob, C. S. (1991). Emotional and behavioral problems in children with learning disabilities. San Diego, CA: Singular.
29. Geary, D. (1993). Mathematical disabilities: Cognitive, neuropsychological, and genetic components. Psychological Bulletin, 114, 345-362.
30. Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37, 4-15.
31. Geary, D. C., Hamson, C. O., & Hoard, M. K. (2000). Numerical and arithmetical cognition: A longitudinal study of process and concept deficits in children with learning disability. Journal of Experimental Psychology, 77, 236-263.
32. Ginsburg, H. P. (1998). Mathematics learning disabilities: A view from developmental psychology. In D. P. Rivera (Ed.), Mathematics education for students with learning disabilities: Theory to practice (pp. 33-58). Austin, TX: Pro-Ed.
33. Goldman, S. R., Hasselbring, T. S., & Cognition and Technology Group at Vanderbilt. (1998). Achieving meaningful mathematics literacy for students with learning disabilities. In D. P. Rivera (Ed.), Mathematics education for students with learning disabilities: Theory to practice (pp. 237-254). Austin, TX: Pro-Ed.
34. Hickey, D. T., Moore, A. L., & Pellegrino, J. W. (2001). The motivational and academic consequences of elementary mathematics environments: Do constructivist innovations and reforms make a difference? American Educational Research Journal, 38, 611-652.
35. Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65-97). New York, NY: Macmillan.
36. Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., ⋯Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational Researcher, 25(4), 12-21.
37. Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students' learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371-404). Greenwich, CT: Information Age.
38. Holm, S. (1979). A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics, 6, 65-70.
39. Hutchinson, N. L. (1993). Students with disabilities and mathematics education reform-Let the dialogue begin. Remedial and Special Education, 14(6), 20-23.
40. Jitendra, A., DiPipi, C. M., & Perron-Jones, N. (2002). An exploratory study of schema-based wordproblem-solving instruction for middle school students with learning disabilities: An emphasis on conceptual and procedural understanding. The Journal of Special Education, 36, 23-38.
41. Jitendra, A. K., Hoff, K., & Beck, M. M. (1999). Teaching middle school students with learning disabilities to solve word problems using a schema-based approach. Remedial and Special Education, 20(1), 50-64.
42. Jones, E. D., Wilson, R., & Bhojwani, S. (1998). Mathematics instruction for secondary students with learning disabilities. In D. P. Rivera (Ed.), Mathematicseducation for students with learning disabilities: Theory to practice (pp. 155-176). Austin, TX: Pro-Ed.
43. Kauffman, J. M. (2001). Characteristics of emotional and behavioral disorders of children and youth (7th ed.). Upper Saddle River, NJ: Merrill, Prentice-Hall.
44. Lamon, S. J. (1999). Teaching fractions and ratios for understanding. Hillsdale, NJ: Lawrence Erlbaum.
45. Lee, J., Grigg, W., & Dion, G. (2007). The nation's report card: Mathematics 2007 (NCES 2007-494). Washington, DC: National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education.
46. Loveless, T. (2004). The Brown Center report on American education: How well are American students learning? Washington, DC: The Brookings Institution.
47. Maccini, P., & Gagnon, J. C. (2006). Mathematics instructional practices and assessment accommodations by secondary special and general educators. Exceptional Children, 72, 217-234.
48. Maccini, P., & Hughes, C. A. (2000). Effects of a problem-solving strategy on the introductory algebra performance of secondary students with learning disabilities. Learning Disabilities Research and Practice, 15, 10-21.
49. Maccini, P., Mulcahy, C. A., & Wilson, M. G. (2007). A follow-up of mathematics interventions for secondary students with learning disabilities. Learning Disabilities Research and Practice, 22, 58-74.
50. Mack, N. K. (1993). Learning rational numbers with understanding: The case of informal knowledge. In T. P. Carpenter, E. Fennema, & T. A. Romberg (Eds.), Rational numbers: An integration of the research (pp. 85-105). Hillsdale, NJ: Lawrence Erlbaum.
51. Mastropieri, M. A., Scruggs, T. E., & Shiah, S. (1991). Mathematics instruction for learning disabled students: A review of research. Learning Disabilities Research and Practice, 6, 89-98.
52. Means, B., & Knapp, M. S. (1991). Cognitive approaches to teaching advanced skills to educationally disadvantaged students. Phi Delta Kappan, 73, 282-289.
53. Miller, S. P., & Hudson, P. J. (2007). Using evidencebased practices to build mathematics competence related to conceptual, procedural, and declarative knowledge. Learning Disabilities Research and Practice, 22, 47-57.
54. Montague, M., Bos, C., & Doucette, M. (1991). Affective, cognitive, and metacognitive attributes of eighthgrade mathematical problem solvers. Learning Disabilities Research and Practice, 6, 145-151.
55. Muth, K. D. (1984). Solving arithmetic word problems: Role of reading and computational skills. Journal of Educational Psychology, 76, 205-210.
56. National Center on Education and the Economy. (2007). Tough choices or tough times: The report of the new commission on the skills of the American workforce. Washington, DC: NCEE.
57. National Research Center for Career and Technical Education. (2006). Building academic skills in context: Testing the value of enhanced math learning in CTE. The Ohio State University: Columbus, OH.
58. National Research Council (NRC). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
59. O'Donnell, C. L. (2008). Defining, conceptualizing, and measuring fidelity of implementation and its relationship to outcomes in K-12 curriculum intervention research. Review of Educational Research, 78, 33-84.
60. Pashler, H., Bain, P., Bottge, B., Graesser, A., Koedinger, K., ⋯ Metcalfe, J. (2007). Organizing instruction and study to improve student learning (NCER 2007-2004). Washington, DC: National Center for Education Research, Institute of Education Sciences, U.S. Department of Education. Retrieved from http://ncer.ed.gov
61. Planty, M., Hussar, W., Snyder, T., Provasnik, S., Kena, G., ⋯ Kemp, J. (2008). The Condition of Education 2008 (NCES 2008-031). Washington, DC: National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education.
62. Post, T. R., Wachsmuth, I., Lesh, R., & Behr, M. J. (1985). Order and equivalence of rational number concepts. Journal for Research in Mathematics Education, 16, 18-36.
63. Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods (2nd ed.). Newbury Park, CA: Sage.
64. Raudenbush, S. W., Bryk, A. S., Cheong, Y. F., & Congdon, R. T. (2004). Hierarchical linear and nonlinear modeling. Lincolnwood, IL: Scientific Software International.
65. Rittle-Johnson, B., & Alibali, M. W. (1999). Conceptual and procedural knowledge of mathematics: Doesone lead to the other? Journal of Educational Psychology, 91, 175-189.
66. Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93, 346-363.
67. Schoenfeld, A. H. (2006). Mathematics teaching and learning. In P. A. Alexander & P. H. Winne (Eds.), Handbook of educational psycholog y (2nd ed.; pp. 479-544). Mahwah, NJ: Erlbaum Associates.
68. Smith, J. P. (2002). The development of students' knowledge of fractions and ratios. In B. Litwiller & G. Bright (Eds.), Making sense of fractions, ratios, and proportions (pp. 3-17). Reston, VA: National Council of Teachers of Mathematics.
69. Star, J. R. (2005). Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36, 404-411.
70. Steffe, L. P. (2004). On the construction of learning trajectories of children: The case of commensurate fractions. Mathematical Thinking and Learning, 204, 129-162.
71. Stodden, R. A., Galloway, L. M., & Stodden, N. J. (2003). Secondary school curricula issues: Impact on postsecondary students with disabilities. Exceptional Children, 70, 9-25.
72. Sulzer-Azaroff, B., & Mayer, G. R. (1977). Applying behavior analysis procedures with children and youth. New York, NY: Holt, Rinehart &Winston.
73. University of Iowa. (2001). The Iowa Tests of Basic Skills (ITBS, Form A). Thousand Oaks, CA: Sage.
74. Wagner, M., Newman, L., Cameto, R., Levine, P., & Garza, N. (2006). An overview of findings from wave 2 of the National Longitudinal Transition Study-2 (NLTS-2). (NCSER 2006-3004). Menlo Park, CA: SRI International.
75. Washington State Legislature. (2009). Definition and eligibility for specific learning disability (WAC 392-172-126). Olympia, WA: Author. Retrieved from http://apps.leg.wa.gov/WAC/default.aspx?cite=392-172A-03070
76. Witzel, B. S., Mercer, C. D., & Miller, M. D. (2003). Teaching algebra to students with learning difficulties: An investigation of an explicit instruction model. Learning Disabilities Research and Practice, 18, 121-131.
77. Woodward, J. (2004). Mathematics education in the United States: Past to present. Journal of Learning Disabilities, 37, 16-31.
78. Woodward, J., Baxter, J., & Robinson, R. (1999). Rules and reasons: Decimal instruction for academically low achieving students. Learning Disabilities Research and Practice, 14, 15-24.
79. Xin, Y. P., Jitendra, A. K., & Deatline-Buchman, A. (2005). Effects of mathematical word problem-solving instruction on middle school students with learning problems. The Journal of Special Education, 39, 181-192.