Tell me with whom you're learning, and I'll tell you how much you've learned: Mixed-ability versus same-ability grouping in mathematics

In this article we report on 3 studies in which we investigated the effects of teaching mathematics in a mixed-ability setting on students' achievements and teachers' attitudes. The findings of the first 2 studies indicate that the achievements of students need not be compromised in a heterogeneous setting; on the contrary, the achievements of our average and less able students proved to be significantly higher when compared to their peers in the same-ability classes, whereas highly able students performed about the same. In the 3rd study we show that participating in the project workshops had a positive effect on teachers' attitudes toward teaching in mixed-ability mathematics classes.

[1]  C. Hirsch Curriculum and Evaluation Standards for School Mathematics , 1988 .

[2]  Deborah R. Dillon Chapter 7: The Wider Social Context of Innovation in Mathematics Education , 1993 .

[3]  J. Oakes,et al.  Keeping Track: How Schools Structure Inequality. , 1986 .

[4]  Walter G. Secada,et al.  New directions for equity in mathematics education , 1995 .

[5]  T. Cook,et al.  Quasi-experimentation: Design & analysis issues for field settings , 1979 .

[6]  R. Slavin Synthesis of Reseach on Grouping in Elementary and Secondary Schools. , 1988 .

[7]  S. Sarason Parental Involvement and the Political Principle: Why the Existing Governance Structure of Schools Should Be Abolished , 1995 .

[8]  Angie Su,et al.  National Council of Supervisors of Mathematics , 1999 .

[9]  Ellen Goldring,et al.  Classroom diversity and teachers' perspectives of their workplace , 1994 .

[10]  H. Abadzi Ability Grouping Effects on Academic Achievement and Self-Esteem: Who Performs in the Long Run as Expected , 1985 .

[11]  Peter J. Denning,et al.  A nation at risk: the imperative for educational reform , 1983, CACM.

[12]  S. Sarason The predictable failure of educational reform : can we change course before it's too late? , 1990 .

[13]  Paul M. Wortman,et al.  School Desegregation and Black Achievement , 1985 .

[14]  J. Oakes The reproduction of inequity: The content of secondary school tracking , 1982 .

[15]  George M. A. Stanic,et al.  Chapter 1 Mathematics curriculum reform in the united states: A historical perspective , 1992 .

[16]  Paul Cobb,et al.  Small-group interactions as a source of learning opportunities in second-grade mathematics. , 1991 .

[17]  Jorg Voigt,et al.  Negotiation of mathematical meaning and learning mathematics , 1994 .

[18]  Teri Rysz Professional Standards for Teaching Mathematics in a Two-Year College Classroom. , 1999 .

[19]  M. Apple Do the Standards Go Far Enough? Power, Policy, and Practice in Mathematics Education. , 1992 .

[20]  Anne Wheelock,et al.  The Case for Untracking. , 1992 .

[21]  Paul Cobb,et al.  Learning mathematics : constructivist and interactionist theories of mathematical development , 1994 .

[22]  Dilafruz R. Williams The Predictable Failure of Educational Reform: Can We Change Course Before It's Too Late? , 1992 .

[23]  Edwin W. Schreiber The National Council of Teachers of Mathematics , 1936 .

[24]  T. Power Perceptions of Competence: How Parents and Teachers View Each Other. , 1985 .

[25]  A Framework for Appraising Educational Reforms , 1996 .

[26]  A. Bandura Self-efficacy mechanism in human agency , 2024, Psihologìâ ì suspìlʹstvo.

[27]  S. Swap Developing Home-School Partnerships: From Concepts to Practice , 1993 .

[28]  L. Resnick,et al.  Assessment as the Catalyst of School Reform. , 1993 .

[29]  Kenneth Ruthven,et al.  Ability stereotyping in mathematics , 1987 .

[30]  Torsten Husén,et al.  Educational research and educational change : the case of Sweden , 1967 .

[31]  J. Fey Change in mathematics education since the late 1950's — Ideas and realisation U.S.A. , 1978 .

[32]  H. Abadzi Ability Grouping Effects on Academic Achievement and Self-Esteem in a Southwestern School District , 1984 .

[33]  Robert L. Crain,et al.  The Effect of Research Methodology on Desegregation-Achievement Studies: A Meta-Analysis , 1983, American Journal of Sociology.

[34]  Adam Gamoran,et al.  Alternative Uses of Ability Grouping in Secondary Schools: Can We Bring High-Quality Instruction to Low-Ability Classes? , 1993, American Journal of Education.

[35]  Etienne Wenger,et al.  Situated Learning: Legitimate Peripheral Participation , 1991 .

[36]  P. Elliott Assessment Standards for School Mathematics , 1995 .

[37]  Jenz Holger Lorenz On some psychological aspects of mathematics achievement assessment and classroom interaction , 1982 .

[38]  M. Foucault,et al.  Power/Knowledge: Selected Interviews and Other Writings 1972-1977 , 1980 .

[39]  Diana Lambdin Kroll,et al.  An Overview of Research on Cooperative Learning Related to Mathematics. , 1991 .

[40]  Yehezkel Dar Teachers' attitudes toward ability grouping: Educational considerations and social and organizational influences , 1985 .

[41]  C. Willie Diversity, School Improvement, and Choice , 1990 .

[42]  R. Mare,et al.  Secondary School Tracking and Educational Inequality: Compensation, Reinforcement, or Neutrality? , 1989, American Journal of Sociology.

[43]  Thinking More Politically about the Challenges before Us: A Response to Romberg. , 1992 .

[44]  Thomas J. Cooney The Issue of Reform: What Have We Learned from Yesteryear?. , 1988 .

[45]  Thomas L. Good,et al.  Grouping for instruction in mathematics: A call for programmatic research on small-group processes. , 1992 .

[46]  P. Appelbaum,et al.  Popular Culture, Educational Discourse, and Mathematics , 1995 .

[47]  Robert E. Slavin,et al.  Achievement Effects of Ability Grouping in Secondary Schools: A Best-Evidence Synthesis , 1990 .

[48]  R. Crain Making Desegregation Work: How Schools Create Social Climates , 1981 .

[49]  L. Linchevski,et al.  The cumulative effect of ability grouping on mathematical achievement: A longitudinal perspective , 1996 .

[50]  Annette Lareau,et al.  Home Advantage: Social Class and Parental Intervention in Elementary Education. , 1991 .

[51]  Walter G. Secada Agenda setting, enlightened self‐interest, and equity in mathematics education , 1989 .

[52]  Maureen T. Hallinan,et al.  Effects of Ability Grouping on Growth in Academic Achievement , 1986 .

[53]  Lynn Balster Liontos At-Risk Families & Schools: Becoming Partners , 1992 .

[54]  Douglas A. Grouws,et al.  Handbook of research on mathematics teaching and learning , 1992 .

[55]  A. Gamoran,et al.  The Effects of Stratification in Secondary Schools: Synthesis of Survey and Ethnographic Research , 1987 .

[56]  A. C. Kerckhoff,et al.  Effects of Ability Grouping in British Secondary Schools. , 1986 .

[57]  J. P. Smith,et al.  Efficacy and Teaching Mathematics by Telling: A Challenge for Reform. , 1996 .

[58]  Michael W. Apple,et al.  Teachers and Texts: A Political Economy of Class and Gender Relations in Education , 1988, History of Education Quarterly.

[59]  Richard Lynn,et al.  STREAMING IN THE PRIMARY SCHOOL , 1971 .

[60]  Alan H. Schoenfeld,et al.  Ideas in the air: Speculations on small group learning, environmental and cultural influences on cognition, and epistemology , 1989 .

[61]  Thomas A. Romberg Further Thoughts on the Standards: A Reaction to Apple. , 1992 .

[62]  J. Price,et al.  President's Report: Building Bridges of Mathematical Understanding for All Children. , 1996 .

[63]  M. Fine [Ap]parent Involvement: Reflections on Parents, Power, and Urban Public Schools , 1993, Teachers College Record: The Voice of Scholarship in Education.

[64]  M. Poster Michel Foucault: Beyond Structuralism and Hermeneutics , 1984, Telos.

[65]  D. Peressini Parents, Power, and the Reform of Mathematics Education , 1996 .

[66]  Thomas A. Romberg,et al.  School Mathematics: Options for the 1990s. Proceedings of the Conference (Madison, Wisconsin, December 5-8, 1983). [Volume 2]. , 1984 .

[67]  C. Carver,et al.  Control theory: a useful conceptual framework for personality-social, clinical, and health psychology. , 1982, Psychological bulletin.

[68]  A. Henderson,et al.  A New Generation of Evidence: The Family Is Critical to Student Achievement , 1994 .

[69]  Leon W. Cohen,et al.  Conference Board of the Mathematical Sciences , 1963 .

[70]  A. Collins,et al.  Situated Cognition and the Culture of Learning , 1989 .