Abstract
The crisis in mathematics education is likely to grow. One of the targets for reform is the math textbook, which largely defines the math curriculum. Several aspects of math textbooks that strongly influence student learning are explained: the organization of lessons, the use of time, the rate of introducing new concepts, the quality of instructional activities, the nature of the examples, and the provision of guided and independent practice. Excerpts from math texts illustrate these factors. Research findings on an alternative to basais, represented by the Direct Instruction math curriculum, illustrate how conceptual understanding and proficiency can be developed for a full spectrum of students.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anrig, G. R., & LaPointe, A. E. (1989). What we know about what students don't know.Educational Leadership, 47(3), 4–9.
Baroody, A. J. (1989). Manipulatives don't come with guarantees.Arithmetic Teacher. October, 4–5.
Behr, M. J., Wachsmuth, I., Post, J. R., & Lesh, R. (1984). Order and equivalence of rational numbers: A clinical teaching experiment.Journal for Research in Mathematics Education.15(5), 323–241.
Carnine, D. (1980). Preteaching versus concurrent teaching of the component skills of a multiplication algorithm.Journal of Research in Mathematics Education, 11(5), 375–378.
Carnine, D. (1980). Relationships between stimulus variation and the formation of misconceptions.Journal of Educational Research, 74, 106–110.
Carnine, D. (in press). Direct instruction in mathematics. In J. W. Lloyd, N. N. Singh, & A. C. Repp (Eds.),The regular education initiative: Alternative perspectives on concepts, issues, and methods. Sycamore, IL: Sycamore Publishing Co.
Carpenter, T. P., Coburn, T. G., Reys, R. E., & Wilson, J. W. (1976). Notes from the national assessment: Problem solving.Mathematics Teacher, 32, 389–393.
Darch, C., Carnine, D., & Gersten, R. (1984). Explicit instruction in mathematics problem solving.Journal of Educational Research, 77(66), 350–359.
Durkin, D. (1978–1979). What classroom observation reveals about reading instruction.Reading Research Quarterly, 14(4), 481–533.
Englemann, S., & Carnine, D. (1991).Connecting Math Concepts. Chicago: Science Research Associates.
Evans, D. G. (1990). Comparison of three instructional strategies for teaching borrowing in subtraction. Doctoral Dissertation, University of Oregon.
Gersten, R., Becker, W., Heiry, T., & White, W. A. (1984). Entry I.Q. and yearly academic growth of children in Direct Instructional Programs: A longitudinal study of low SES children.Educational Evaluation and Policy Analysis, 6(2) 109–121.
Gersten, R., & Carnine, D. (1984). Direct Instruction mathematics: A longitudinal evaluation of low SES elementary students.Elementary School Journal, 84(4), 395–407.
Gleason, M., Carnine, D., & Boriero, D. (in press). Improving CAI effectiveness with attention to instructional design in teaching story problems to mildly handicapped students.Journal of Special Education Technology.
Good, T. L., & Grouws, D. A. (1979). The Missouri Mathematics Effectiveness Project: An experimental study of fourth-grade classrooms.Journal of Educational Psychology, 71, 355–362.
Good, T. L., Grouws, D. A., & Ebmeier, H. (1983).Active Mathematics Teaching. New York: Longman.
Hamann, M. S., & Ashcraft, M. H. (1986). Textbook presentation of basic addition facts.Journal of Cognition and Instruction, 3(3), 173–192.
Haney, W. (1977). Reanalysis of Follow Through parent and teacher data. Boston: Huron Institute.
International Association for the Evaluation of Educational Achievement (1987).The underachieving of curriculum: Assessing U.S. school mathematics from an international perspective. Urbana, IL: University of Illinois.
Kameenui, E., & Carnine, D. (1986). Preteaching versus concurrent teaching of the component skills of a subtraction algorithm to skill-deficient second graders: A component analysis of Direct Instruction.The Exceptional Child, 33(2), 103–115.
Kameenui, E., Carnine, D., Darch, D., & Stein, M. (1986). Two approaches to the development phase of mathematics instruction.Elementary School Journal, 86(5), 633–650.
Kelly, B., Carnine, D., Gersten, R., & Grossen, B. (1986). The effectiveness of videodisc instruction in teaching fractions to learning-handicapped and remedial high school students.Journal of Special Education Technology, 8(2), 5–17.
LaPointe, A. E., Mead, N. A., & Phillips, G. W. (1989).A world of difference: An international assessment of mathematics and science. Princeton, NJ: Educational Testing Service.
Moore, L., & Carnine, D. (1989). Evaluating curriculum design in the context of active teaching.Remedial and Special Education, 10, 28–37.
National Council of Teachers of Mathematics (1989).Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.
New York Times, (April 11, 1990). Study: Workers lack math training, Eugene, OR: Register-Guard, p. 13D.
Paine, S., Carnine, D., & White, W. A. T., & Walters (1982). Effects of fading teacher presentation structure (covertization) on acquisition and maintenance of arithmetic problem-solving skills.Education and Treatment of Children, 5(2), 92–107.
Porter, A. (1989). A curriculum out of balance: The case of elementary school mathematics.Educational Researcher, 18 (5), 9–15.
Resnick, L. B., & Omanson, S. F. (1987). Learning to understand arithmetic. In R. Glasser (Ed.),Advances in Instructional Psychology. Hillsdale, NJ.: Erlbaum.
Stebbins, L. B., St. Pierre, R. G., Proper, E. C., Anderson, R. B., & Cerva, T. R. (1977). Education as experimentation: A planned variation mode). Vols. 4A, 4C.An Evaluation of Follow Through. Cambridge, MA.
Steely, D., Carnine, D., & Engelmann (in press). Making connections in mathematics.Journal of Learning Disabilities.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Carnine, D. Reforming mathematics instruction: The role of curriculum materials. J Behav Educ 1, 37–57 (1991). https://doi.org/10.1007/BF00956753
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00956753