A comparative analysis of number sense instruction in reform-based and traditional mathematics textbooks

Journal of Special Education

Volumn 41, Issue 3, 2007, Pages 145-157

  Sood, Sheetal ^a   Jitendra, Asha K ^a  

^a LEHIGH UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 36148962841     PISSN: 00224669     EISSN: None     Source Type: Journal    
DOI: 10.1177/00224669070410030101     Document Type: Article

References (102)

1. Ambridge, B. M., Theakston, A. L., Lieven, E. V. M., & Tomasello, M. M. (2006). The distributed learning effect for children's acquisition of an abstract syntactic construction. Cognitive Development, 21, 174-193.
2. Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215-241.
3. Baker, S., Gersten, R., & Lee, D. (2002). A synthesis of empirical research on teaching mathematics to low-achieving students. Elementary School Journal, 103, 51-73.
4. Ball, D. L. (2003, February 6). Mathematics in the 21st century: What mathematical knowledge is needed for teaching mathematics? Paper presented at the Secretary's Summit on Mathematics, U.S. Department of Education, Washington, DC.
5. Baxter, J., Woodward, J., & Olson, D. (2001). Effects of reform-based mathematics instruction in five third grade classrooms. Elementary School Journal, 101(5), 529-548.
6. Baxter, J., Woodward, J., Voorhies, J., & Wong, J. (2002). We talk about it, but do they get it? Learning Disabilities Research & Practice, 17(3), 173-185.
7. Brenner, M. E., Mayer, R. E., Moseley, B., Brar, T., Duran, R., Reed, B. S., et al. (1997). Learning by understanding: The role of multiple representations in learning algebra. American Educational Research Journal, 34, 663-689.
8. Britton, B. K., Woodward, A., & Binkley, M. (1993). Learning from textbooks: Theory and practice. Hillsdale, NJ: Erlbaum.
9. Brosvic, G. M., Dihoff, R. E., Epstein, M. L., & Cook, M. L. (2006). Feedback facilitates the acquisition and retention of numerical fact series by elementary school students with mathematics learning disabilities. The Psychological Record, 56(1), 35-54.
10. 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 & Practice, 18, 99-111.
11. Carnine, D. (1997). Instructional design in mathematics for students with learning disabilities. Journal of Learning Disabilities, 30, 130-141.
12. Carnine, D. W., Dixon, R. C., & Silbert, J. (1998). Effective strategies for teaching mathematics. In E. Kameenui & D. Carnine (Eds.), Effective teaching strategies that accommodate diverse learners. Upper Saddle River, NJ: Prentice Hall.
13. Carnine, D., Jitendra, A., & Silbert, J. (1997). A descriptive analysis of mathematics curricular materials from a pedagogical perspective. Remedial and Special Education, 18, 66-81.
14. Case, R. (1998, April). A psychological model of number sense and its development. Paper presented at the annual meeting of the American Educational Research Association, San Diego.
15. Chandler, D. G., & Brosnan, P. A. (1994). Mathematics textbook changes from before to after 1989. Focus on Learning Problems in Mathematics, 16(4), 1-9.
16. Chatterji, M. (2002). Models and methods for examining standards-based reforms and accountability initiatives: Have the tools of inquiry answered pressing questions on improving schools? Review of Educational Research, 72, 345-386.
17. Chard, D. J., & Kameenui, E. J. (1995). Mathematics instruction for students with diverse learning needs: Heeding the message of the Cheshire Cat. Focus on Learning Problems in Mathematics, 17, 24-38.
18. Cunningham, R. F. (2005). Algebra teachers' utilization of problems requiring transfer between algebraic, numeric, and graphic representations. School Science and Mathematics, 105, 73-81.
19. Dempster, F. N. (1991). Synthesis of research on reviews and tests. Educational Leadership, 4(7), 71-76.
20. Dempster, F. N., & Farris, R. (1990). The spacing effect: Research and practice. Journal of Research and Development in Education, 23, 97-101.
21. Fenneil, F., & Landis, T. E. (1994). Number sense and operation sense. In C. A. Thornton & N. S. Bley (Eds.), Windows of opportunity: Mathematics for students with special needs (pp. 187-203). Reston, VA: National Council of Teachers of Mathematics.
22. Findell, C. (1991). Mathematics education then and now: The need for reform. Journal of Education, 178(2), 3-13.
23. Fischer, F. (1990). A part-part-whole curriculum for teaching number to kindergarten. Journal for Research in Mathematics Education, 21, 207-215.
24. Flevares, L. M., & Perry, M. (2001). How many do you see? The use of non-spoken representations in first-grade mathematics lessons. Journal of Educational Psychology, 93, 330-345.
25. Fraivilling, J., Murphy, L., & Fuson, K. (1999). Advancing children's mathematical thinking in Everyday Mathematics classrooms. Journal for Research in Mathematics Education, 30, 148-170.
26. Garner, R. (1992). Learning from school texts. Educational Psychologist, 27, 53-63.
27. Gersten, R., & Baker, S. (1998). Real world use of scientific concepts: Integrating situated cognition with explicit instruction. Exceptional Children, 65, 23-35.
28. Gersten, R., & Chard, D. (1999). Number sense: Rethinking arithmetic instruction for students with mathematical disabilities. The Journal of Special Education, 33, 18-28.
29. Greenes, C. (1996). Investigations: Vehicles for learning and doing mathematics. Journal of Education, 178(2), 35-49.
30. Griffin, S. (2003). Laying the foundation for computational fluency in early childhood. Teaching Children Mathematics, 9, 306-309.
31. Griffin, S. (2004a). Building number sense with number worlds: A mathematics program for young children. Early Childhood Research Quarterly, 19, 173-180.
32. Griffin, S. (2004b). Teaching number sense. Educational Leadership, 61, 39-41.
33. Griffin, S., & Case, R. (1997). Rethinking the primary school math curriculum: An approach based on cognitive science. Issues in Education, 4, 1-51.
34. Griffin, S., Case, R., & Siegler, R. (1994). Rightstart: Providing the central conceptual prerequisites for first formal learning of arithmetic to students at risk for school failure. In K. McGilly (Ed.), Classroom lessons integrating cognitive theory in classroom practice (pp. 24-29). Cambridge, MA: MIT Press.
35. Hegarty, M., & Kozhevnikov, M. (1999). Types of visual-spatial representations and mathematical problem solving. Journal of Educational Psychology, 91, 684-689.
36. Hiebert, J. (1986). Conceptual and procedural knowledge: The case of mathematics. Hillsdale, NJ: Erlbaum.
37. Hiebert, J. (1999). Relationships between research and the NCTM standards. Journal for Research in Mathematics Education, 30, 3-19.
38. Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., et al. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational Researcher, 25, 12-21.
39. Isaacs, A. C., & Carroll, W. M. (1999). Strategies for basic-facts instruction. Teaching Children Mathematics, 5, 508-514.
40. Jitendra, A., Carnine, D., & Silbert, J. (1996). Descriptive analysis of fifth grade division instruction in basal mathematics programs: Violations of pedagogy. Journal of Behavioral Education, 6, 381-403.
41. Jitendra, A. K., Deatline-Buchman, A., & Sczesniak, E. (2005). A comparative analysis of third-grade mathematics textbooks before and after the 2000 NCTM standards. Assessment for Effective Intervention, 30(2), 47-62.
42. Jitendra, A. K., Griffin, C., Deatline-Buchman, A., Sczesniak, E., Sokol, N. G., & Xin, Y. P. (2005). Adherence to mathematics professional standards and instructional design criteria for problem-solving in mathematics. Exceptional Children, 71, 317-335.
43. Jitendra, A. K., Salmento, M., & Haydt, L. (1999). A case study of subtraction analysis in basal mathematics programs: Adherence to important instructional design criteria. Learning Disabilities Research & Practice, 14, 69-79.
44. Jones, G. A., Langrall, C. W., Thornton, C. A., & Nisbet, S. (2002). Elementary students' access to powerful mathematical ideas. In L. English, M. B. Bussi, G. A., Jones, R. A. Lesh, & D. Tirosh (Eds.), Handbook of international research in mathematics education (pp. 113-141). Mahwah, NJ: Erlbaum.
45. Kame'enui, E. J., Carnine, D. W., Dixon, R. C., Simmons, D. C., & Coyne, M. D. (2002). Effective teaching strategies that accommodate diverse learners (2nd ed.). Upper Saddle River, NJ: Merrill/Prentice Hall.
46. King-Sears, M. E. (2001). Three steps for gaining access to the general education curriculum for learners with disabilities. Intervention in School and Clinic, 37, 67-76.
47. Kroesbergen, E. H., & Van Luit, J. E. H. (2003). Mathematical interventions for children with special educational needs. Remedial and Special Education, 24, 91-114.
48. Kroesbergen, E. H., Van Luit, J. E. H., & Maas, C. J. M. (2004). Effectiveness of explicit and constructivist mathematics instruction for low-achieving students in the Netherlands. Elementary School Journal, 104, 233-251.
49. Larkin, M. J. (2001). Providing support for student independence through scaffolded instruction. Teaching Exceptional Children, 24(1), 30-34.
50. Leinhardt, G. (1989). Math lessons: A contrast of novice and expert competence. Journal for Research in Mathematics Education, 20, 52-75.
51. Leinhardt, G., & Putnam, R. T. (1987). The skill of learning from classroom lessons. American Educational Research Journal, 24, 557-587.
52. Lemke, M. A., Sen, E., Pahlke, L., Partelow, D., Miller, T., Williams, D., et al. (2004). International outcomes for learning in mathematics literacy and problem solving: Pisa 2003 results from the U.S. perspective. Washington, DC: U.S. Department of Education, National Center for Education Statistics.
53. Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 33-41). Hillsdale, NJ: Erlbaum.
54. Lhyle, K. G., & Kulhavy, R. W. (1987). Feedback processing and error correction. Journal of Educational Psychology, 79, 320-322.
55. Lubinksi, C. A., & Otto, A. D. (2002). Meaningful mathematical representations and early algebraic reasoning. Teaching Children Mathematics, 9, 76-80.
56. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum.
57. Markovits, Z., & Sowder, J. T. (1994). Developing number sense: An intervention study in grade 7. Journal for Research in Mathematics Education, 25, 4-29.
58. Mayer, R. E., Sims, V., & Tajika, H. (1995). A comparison of how textbooks teach mathematical problem solving in Japan and the United States. American Educational Research Journal, 32, 443-460.
59. McCarty, D. (1998, February). Books + manipulatives + families = A mathematics lending library. Teaching Children Mathematics, 368-375.
60. McCoy, L. P., Baker, T. H., & Little, L. S. (1996). Using multiple representations to communicate: An algebra challenge. In P. C. Elliot & M. J. Kenney (Eds.), Communication in mathematics, K-12 and beyond (pp. 40-44). Reston, VA: National Council of Teachers of Mathematics.
61. McIntosh, A., Keys, B. J., & Reys, R. E. (1992). A proposed framework for examining basic number sense. Learning of Mathematics, 12(3), 2-8.
62. McLeskey, J., Henry, D., & Axelrod, M. I. (1999). Inclusion of students with learning disabilities: An examination of data from reports to Congress. Exceptional Children, 6, 55-66.
63. Miller, S. P., & Mercer, C. D. (1993). Using data to learn about concrete-semi-concrete-abstract instruction for students with math disabilities. Learning Disabilities Research and Practice, 8, 89-96.
64. Montague, M. (2005). Math problem solving for primary elementary students with disabilities. The Access Center: Improving Outcomes for All Students K-8. Retrieved August 10, 2006, from http://www.k8accesscenter.org/ training_resources/mathprimaryproblemsolving.asp
65. Moreno, R., & Mayer, R. E. (2005). Role of guidance, reflection, and interactivity in an agent-based multimedia game. Journal of Educational Psychology, 97, 117-128.
66. Morocco, C. C. (2001). Teaching for understanding with students with disabilities: New directions for research on access to the general education curriculum. Learning Disability Quarterly, 24, 5-13.
67. Mullis, I. V. S., Martin, M. O., Gonzalez, E. J., & Chrostowski, S. J. (2004). TIMSS 2003 international mathematics report: Findings from IEA's Trends in International Mathematics and Science Study at Fourth and Eighth Grade. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College. Retrieved June 15, 2006, from http://timss.bc.edu/timss2003i/ intl_reports.html
68. Nathan, M. J., Long, S. D., & Alibali, M. W. (2002). The symbol precedence view of mathematical development: A corpus analysis of the rhetorical structure of textbooks. Discourse Processes, 33(1), 1-21.
69. National Center for Education Statistics. (2003). Highlights from the TIMSS 1999 video study of eighth-grade mathematics teaching. Washington, DC: U.S. Department of Education.
70. National Center for Education Statistics. (2006). National assessment of educational progress: The nation's report card: Mathematics 2005. U.S. Department of Education, Institute of Education Sciences. Retrieved from http://nces.ed.gov/nationsreportcard/mathematics/
71. National Council of Teachers for Mathematics. (1989). The curriculum and evaluation standards for school mathematics. Reston, VA: Author.
72. National Council of Teachers for Mathematics. (2000). The curriculum and evaluation standards for school mathematics. Reston, VA: Author.
73. National Research Council. (1989). Everybody counts. A report to the nation on the future of mathematics education. Washington, DC: National Academy Press.
74. National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, and B. Findell (Eds.), Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.
75. Nolet, V., & McLaughlin, M. J. (2005). Accessing the general curriculum: Including students with disabilities in standards-based reform (2nd ed.). Thousand Oaks, CA: Corwin Press.
76. Noss, R., Healy, L., & Hoyles, C. (1997). The construction of mathematical meanings: Connecting the visual with the symbolic. Educational Studies in Mathematics, 33, 203-233.
77. Osborne, J. H., Jones, B. F., & Stein, M. (1985). The case for improving textbooks. Educational Leadership, 42(1), 9-16.
78. Porter, A. (1989). A curriculum out of balance: The case of elementary school mathematics. Educational Researcher, 18(5), 9-15.
79. Prawat, R. S. (1989). Promoting access to knowledge, strategy, and disposition in students: A research synthesis. Review of Educational Research, 59, 1-41.
80. Remillard, J. T. (2005). Examining key concepts in research on teachers' use of mathematics curricula. Review of Educational Research, 7, 211-246.
81. Resnik, L. (1989). Treating mathematics as an ill-structured discipline. In R. I. Charles & E. A. Silver (Eds.), The teaching and assessing of mathematical problem solving (pp. 32-62). Hillsdale, NJ: Erlbaum.
82. Ritchhart, R. (1999). Generative topics: Building a curriculum around big ideas. Teaching Children Mathematics, 5(8), 462-467.
83. Rittle-Johnson, B., & Koedinger, K. R. (2005). Designing knowledge scaffolds to support mathematical problem solving. Cognition and Instruction, 23, 313-349.
84. Santoro, L. E., Coyne, M. D., & Simmons, D. C. (2006). The reading-spelling connection: Developing and evaluating a beginning spelling intervention for children at risk of reading disability. Learning Disabilities Research & Practice, 21, 122-133.
85. Schmidt, W. (2002). Missed opportunities: How mathematics education in the U.S. puts our students at a disadvantage and what can be done about it. Retrieved July 13, 2004, from www.epc.msu.edu
86. Schmidt, W. H., Jakwerth, P. M., & McKnight, C. C. (1998). Curriculum-sensitive assessment: Content does make a difference. International Journal of Educational Research, 29, 503-527.
87. Schoenfeld, A. H. (2002). Making mathematics work for all children: Issues of standards, testing, and equity. Educational Researcher, 31(1), 13-25.
88. Seabrook, R., Brown, G. D. A., & Solity, J. E. (2005). Distributed and massed practice: From laboratory to classroom. Applied Cognitive Psychology, 19(1), 107-122.
89. Smith, S. B., Simmons, D. C., Gleason, M. M., Kame'enui, E. J., Baker, S. K., Sprick, M., et al. (2001). An analysis of phonological awareness instruction in four kindergarten basal reading programs. Reading and Writing Quarterly, 17(1), 25-51.
90. Sowder, J., & Schappelle, B. (1994). Number sense-making. Arithmetic Teacher, 41, 342-346.
91. Suter, L. E. (2000). Is student achievement immutable? Evidence from international studies on schooling and student achievement. Review of Educational Research, 70, 529-545.
92. Swanson, H. L., & Hoskyn, M. (1998). A synthesis of experimental intervention literature for students with learning disabilities: A meta-analysis of treatment outcomes. Review of Educational Research, 68, 271-321.
93. Thompson, P. W. (1992). Notations, conventions, and constraints: Contributions of effectiveness of concrete materials in elementary mathematics. Journal for Research in Mathematics Education, 23, 123-147.
94. Thornton, C. A., & Tucker, S. C. (1989). Lesson planning: The key to developing number sense. Arithmetic Teacher, 36(2), 18-21.
95. Valverde, G. A., & Schmidt, W. H. (1997/1998). Refocusing U.S. math and science education. Issues in Science and Technology, 14, 60-66.
96. Van de Walle, J. A. (2007). Elementary and middle school mathematics (6th ed.). Longman: New York.
97. Van Garderen, D. (2006). Teaching visual representation for mathematics problem solving. In M. Montague & A. K. Jitendra (Eds.), Teaching middle school students with mathematics difficulties (pp. 72- 88). New York: Guilford Press.
98. Van Garderen, D., & Montague, M. (2003). Visual-spatial representation, mathematical problem solving, and students of varying abilities. Learning Disabilities Research & Practice, 18, 246-254.
99. Vaughn, S., Gersten, R., & Chard, D. J. (2000). The underlying message in LD intervention research: Findings from research syntheses. Exceptional Children, 67, 99-114.
100. Woodward, J., & Baxter, J. (1997). The effects of an innovative approach to mathematics on academically low achieving students in mainstreamed settings. Exceptional Children, 63, 373-388.
101. Yang, D. C. (2002). Teaching and learning number sense: One successful process-oriented activity with sixth grade students in Taiwan. School Science and Mathematics, 102(4), 152-157.
102. Yang, D. C., & Huang, F. Y. (2004). Relationships among computational performance, pictorial representation, symbolic representation and number sense of sixth-grade students in Taiwan. Educational Studies, 30, 373-389.