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Small-Group Learning and Teaching in Mathematics

A Selective Review of the Research

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Learning to Cooperate, Cooperating to Learn

Abstract

Since the late 1960s, a variety of types of cooperative learning procedures have been used in teaching many different mathematics courses, ranging from elementary school through graduate school. The procedures include small-group interaction in which students work together in groups of three to six members, partner learning taking place in dyads, and a peer-tutoring variation of partner learning in which one student is assigned to tutor another. Peer tutoring includes both same-age tutoring and cross-age tutoring, in which an older student tutors a younger one.

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References

  • Aronson, E. The Jigsaw classroom. Beverly Hills, Calif.: Sage, 1978.

    Google Scholar 

  • Brechting, Sister M. C., & Hirsch, C. R. The effects of small-group discovery learning on student achievement and attitudes in calculus. American Mathematics Association of Two-Year Colleges Journal, 1977, 2, 77–82.

    Google Scholar 

  • Briggs, K. & Briggs Myers, I. Myers-Briggs Type Indicator. Palo Alto, Calif.: Consulting Psychologists Press, 1977.

    Google Scholar 

  • Chakerian, G. D., Crabill, C. D., & Stein, S. K. Geometry: A guided inquiry. Boston: Houghton Mifflin, 1972.

    Google Scholar 

  • Chang, P-T. On relationships among academic performance, sex difference, attitude and persistence of small groups in developmental college level mathematics courses. Doctoral dissertation, Georgia State University, School of Education, Atlanta, Georgia, 1977. (a)

    Google Scholar 

  • Chang, P-T. Small group instruction: A study in remedial mathematics. American Mathematics Association of Two-Year Colleges Journal, 1977, 2, 72–76. (b)

    Google Scholar 

  • Davidson, N. The small-group discovery method as applied in calculus instruction. American Mathematical Monthly, August-September 1971, 789–91. (a)

    Google Scholar 

  • Davidson, N. The small-group discovery method of mathematics instruction as applied in calculus. Doctoral dissertation, University of Wisconsin, 1970. Technical Report No. 168. Wisconsin Research and Development Center for Cognitive Learning, Madison, 1971. (b)

    Google Scholar 

  • Davidson, N. The small-group discovery method: 1967–77. In Problem Solving Studies in Mathematics. J. Harvey & T. Romberg (Eds.), Wisconsin Research and Development Center for Individualized Schooling, University of Wisconsin, Madison, 1979.

    Google Scholar 

  • Davidson, N., & Gulick, F. Abstract algebra: An active learning approach. Boston: Houghton Mifflin, 1976.

    Google Scholar 

  • Davidson, N., McKeen, R. & Eisenberg, T. Curriculum construction with student input. The Mathematics Teacher, 1973, 66(3), 271–275.

    Google Scholar 

  • Deutsch, M. The effects of cooperation and competition upon group process. In D. Cart-wright & A. Zander (Eds.), Group Dynamics: Research and theory (2nd ed.). New York: Harper & Row, 1960.

    Google Scholar 

  • Devin-Sheehan, L., Feldman, R., & Allen V. L. Research on children tutoring children: A critical review. Review of Educational Research, 1976, 46, 335–385.

    Article  Google Scholar 

  • Dewey, John. Democracy and education. New York: Free Press, 1966. (Originally published, 1916.)

    Google Scholar 

  • Dewey, John. Experience and education. New York: Collier, 1963. (Originally published, 1938.)

    Google Scholar 

  • Edwards, K. J., & DeVries, D. L. Learning games and student teams: Their effects on student attitudes and achievement. Center for Social Organization of Schools, The Johns Hopkins University, 1972, Report No. 147.

    Google Scholar 

  • Edwards, K. J., & DeVries, D. L. The effects of Teams-Games-Tournaments and two structural variations on classroom process, student attitudes, and student achievement. Center for Social Organization of Schools, The Johns Hopkins University, 1974, Report No. 172.

    Google Scholar 

  • Edwards, K. J., DeVries, D. L., & Snyder, J. P. Games and teams: A Winning combination. Simulation and Games 1972, 3 247–269.

    Article  Google Scholar 

  • Gallicchio, A. The effects of brainstorming in small group mathematics classes. Doctoral dissertation, University of Maryland, College Park, 1976.

    Google Scholar 

  • Gilmer, G. F. Effects of small discussion groups on self-paced instruction in a developmental algebra course. Doctoral dissertation, Marquette University, Milwaukee, Wis., 1978.

    Google Scholar 

  • Golton, R. F. The effect of student interaction on computer-assisted instruction in mathematics at the sixth grade level. Doctoral dissertation, University of California, Berkeley, Calif., 1975.

    Google Scholar 

  • Grant, S. The effects of three kinds of group formation using FIRO-B compatibility, sociometric choice with group dynamics exercises, and in-class choice on mathematics classes taught by the small-group discovery method. Doctoral dissertation, University of Maryland, College Park, 1975.

    Google Scholar 

  • Huber, G., Bogatzki, W., & Winter, M. Cooperation: Condition and goal of teaching and learning in classrooms. Unpublished manuscript, University of Tübingen, West Germany, 1982.

    Google Scholar 

  • Hulten, B. H., & DeVries, D. L. Team competition and group practice: Effects on student achievement and attitudes. Center for Social Organization of Schools, Johns Hopkins University, 1976, Report No. 212.

    Google Scholar 

  • Jackins, H. The human side of human beings (2nd ed.). Seattle: Rational Island Publishers, 1978.

    Google Scholar 

  • Janicki, T. C. Aptitude-treatment interaction effects of variations in direct instruction. Unpublished doctoral dissertation, University of Wisconsin, Madison, 1979.

    Google Scholar 

  • Johnson, D. W., & Johnson, R. T. Instructional goal structure: Cooperative, competitive, or individualistic. Review of Educational Research, 1974, 44, 213–240.

    Article  Google Scholar 

  • Johnson, D. W., & Johnson, R. T. Learning together and alone. Englewood Cliffs, N.J.: Prentice-Hall, 1975.

    Google Scholar 

  • Johnson, D. W., Johnson, R. T., & Scott, L. The effects of cooperative and individualized instruction on student attitudes and achievement. Journal of Social Psychology, 1978, 104, 207–216.

    Article  Google Scholar 

  • Klingbeil, D. An examination of the effects of group testing in mathematics courses taught by the small-group discovery method. Doctoral dissertation, University of Maryland, College Park, 1974.

    Google Scholar 

  • Loomer, N. J. A multidimensional exploratory investigation of small-group heuristic and expository learning in calculus. Doctoral dissertation, University of Wisconsin, Madison, 1976.

    Google Scholar 

  • Madden, N. A., & Slavin, R. E. Effects of cooperative learning on the social acceptance of mainstreamed academically handicapped students. Journal of Special Education, 1983, 17, 171–182.

    Article  Google Scholar 

  • Pence, B. M. J. Small group review of mathematics: A function of the review organization, structure, and task format. Doctoral dissertation, Stanford University, Stanford, Calif., 1974.

    Google Scholar 

  • Perry, W. G. Forms of intellectual and ethical development in the college years: A scheme. New York: Holt, Rinehart and Winston, 1970.

    Google Scholar 

  • Peterson, P. L., & Janicki, T. C. Individual characteristics and children’s learning in large-group and small-group approaches. Journal of Educational Psychology, 1979, 71, 677–687.

    Article  Google Scholar 

  • Peterson, P. L., Janicki, T. C., & Swing, S. R. Ability × treatment interaction effects on children’s learning in large-group and small-group approaches. American Educational Research Journal, 1981, 18, 453–473.

    Google Scholar 

  • Polya, G. Mathematical discovery, Vol. 2. New York: Wiley, 1965.

    Google Scholar 

  • Robertson, L. Integrated goal structuring in the elementary school: Cognitive growth in mathematics. Unpublished doctoral dissertation, Rutgers University, New Brunswick, N.J., 1982.

    Google Scholar 

  • Schutz, W. C. The interpersonal underworld. Palo Alto, Calif.: Science and Behavioral Books, 1966.

    Google Scholar 

  • Shearn, E. L. Adapting the developmental instruction model, based on Perry’s theory, to a mathematics content course for preservice elementary teachers to enhance attitudes toward mathematics, cognitive development, and achievement. Unpublished doctoral dissertation, University of Maryland, College Park, 1982.

    Google Scholar 

  • Slavin, R. E. Cooperative learning. Review of Educational Research, 1980, 50, 315–342 (a).

    Article  Google Scholar 

  • Slavin, R. E. Using student team learning (rev. ed.), Baltimore, Md.: Center for Social Organization of Schools, The Johns Hopkins University, 1980. (b)

    Google Scholar 

  • Slavin, R. E. Cooperative learning. New York: Longman, 1983. (a)

    Google Scholar 

  • Slavin, R. E. When does cooperative learning increase student achievement? Psychological Bulletin, 1983, 94, 429–445. (b)

    Article  Google Scholar 

  • Slavin, R. E., & Karweit, N. L. Cognitive and affective outcomes of an intensive student team learning experience. Journal of Experimental Education, 1981, 50, 29–35.

    Google Scholar 

  • Slavin, R. E., & Karweit, N. L. Student teams and mastery learning: An experiment in urban Math 9 classes. Paper presented at the Annual Convention of the American Educational Research Association, New York, March 1982.

    Google Scholar 

  • Slavin, R. E., Leavey, M., & Madden, N. A. Combining student teams and individualized instruction in mathematics: An extended evaluation. Paper presented at the Annual Convention of the American Educational Research Association, Montreal, April 1983.

    Google Scholar 

  • Slavin, R. E., Leavey, M., & Madden, Nancy A. Combining cooperative learning and individualized instruction: Effects on student mathematics achievement, attitudes, and behaviors. Elementary School Journal, 1984, 84, 409–422.

    Google Scholar 

  • Slavin, R. E., Madden, N. A., & Leavey, M. Effects of cooperative learning and individualized instruction on mainstreamed students. Exceptional Children, 1984, 50, 434–443. (a)

    PubMed  Google Scholar 

  • Slavin, R. E., Madden, N. A., & Leavey, M. Effects of Team Assisted Individualization on the mathematics achievement of academically handicapped and non-handicapped students. Journal of Educational Psychology, 76, 813–819, 1984 (b).

    Article  Google Scholar 

  • Stam, P. J. The effect of sociometric grouping on task performance in the elementary classroom. Doctoral dissertation, Stanford University, Stanford, Calif. 1973.

    Google Scholar 

  • Stein, S., & Crabill, C. Elementary algebra: A guided inquiry, Boston: Houghton Mifflin, 1972.

    Google Scholar 

  • Stein, S., & Crabill, C. Elementary algebra: A guided inquiry, Boston: Houghton Mifflin, 1972.

    Google Scholar 

  • Webb, N. M. Learning in individual and small-group settings. Technical Report No. 7. Stanford, Calif.: Aptitude Research Project, School of Education, Stanford University, 1977.

    Google Scholar 

  • Webb, N. M. An analysis of group interaction and mathematical errors in heterogeneous ability groups. British Journal of Educational Psychology, 1980, 50, 1–11. (a)

    Article  Google Scholar 

  • Webb, N. M. Group process: The key to learning in groups. New Directions for Methodology of Social and Behavioral Science: Issues in Aggregation, 1980, 6, 77–87. (b)

    Google Scholar 

  • Webb, N. M. A process-outcome analysis of learning in group and individual settings. Educational Psychologist, 1980, 15, 69–83. (c)

    Article  Google Scholar 

  • Webb, N. M. Group composition, group interaction and achievement in cooperative small groups. Journal of Educational Psychology, 1982, 74, 475–484. (a)

    Article  Google Scholar 

  • Webb, N. M. Student interaction and learning in small groups: Research summary. Paper presented at the Meeting of the International Association for the Study of Cooperation in Education, Provo, Utah, 1982. (b)

    Google Scholar 

  • Weissglass, J. Mathematics for elementary teaching: A small-group laboratory approach. American Mathematical Monthly, May 1977, 377–382.

    Google Scholar 

  • Weissglass, J. Exploring elementary mathematics: A small-group approach for teaching. San Francisco: W. H. Freeman, 1979.

    Google Scholar 

  • White, R., & Lippitt, R. Leader behavior and member reaction in three “Social Climates”. In D. Cartwright & A. Zander (Eds.), Group dynamics: Research and theory. New York: Harper & Row, 1960.

    Google Scholar 

  • Widick, C., Knefelkamp, L., & Parker, C. The counselor as a developmental instructor. Counselor Education and Supervision, 1975, 14, 286–296.

    Article  Google Scholar 

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Davidson, N. (1985). Small-Group Learning and Teaching in Mathematics. In: Slavin, R., Sharan, S., Kagan, S., Hertz-Lazarowitz, R., Webb, C., Schmuck, R. (eds) Learning to Cooperate, Cooperating to Learn. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-3650-9_8

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  • DOI: https://doi.org/10.1007/978-1-4899-3650-9_8

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-3652-3

  • Online ISBN: 978-1-4899-3650-9

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