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Dialogic and Direct Instruction: Two Distinct Models of Mathematics Instruction and the Debate(s) Surrounding Them


by Charles Munter, Mary Kay Stein & Margaret S. Smith — 2015

Background/Context: Which ideas should be included in the K–12 curriculum, how they are learned, and how they should be taught have been debated for decades in multiple subjects. In this article, we offer mathematics as a case in point of how new standards-related policies may offer an opportunity for reassessment and clarification of such debates.

Purpose/Objective: Our goal was to specify instructional models associated with terms such as “reform” and “traditional”—which, in this article, we refer to as “dialogic” and “direct”—in terms of perspectives on what it means to know mathematics, how students learn mathematics, and how mathematics should be taught.

Research Design: In the spirit of “adversarial collaboration,” we hosted a series of semi-structured discussions among nationally recognized experts who hold opposing points of view on mathematics teaching and/or learning. During those discussions, the recent consensus regarding what students should learn—as represented by the Common Core State Standards for Mathematics (CCSSM)—was taken as a common goal, and additional areas of agreement and disagreement were identified and discussed. The goal was not to reach consensus but to invite representatives of different perspectives to clarify and come to agreement on how they disagree.

Findings/Results: We present two instructional models that were specified and refined over the course of those discussions and describe nine key areas that distinguish the two models: (a) the importance and role of talk; (b) the importance and role of group work; (c) the sequencing of mathematical topics; (d) the nature and ordering of mathematical instructional tasks; (e) the nature, timing, source, and purpose of feedback; (f) the emphasis on creativity (i.e., authoring one’s own learning; mathematizing subject matter from reality); (g) the purpose of diagnosing student thinking; (h) the introduction and role of definitions; and (i) the nature and role of representations. Additionally, we elaborate a more nuanced description of the ongoing debate, as it pertains to particular sources of difference in perspective.

Conclusions/Recommendations: With this article, we hope to advance ongoing debates in two ways: (a) discrediting false assumptions and oversimplified conceptions of the “other side’s” arguments (which can obscure both the real differences and real similarities between different models of instruction), and (b) framing the debates in a manner that allows for more thoughtful empirical investigation oriented to understanding learning in the discipline.



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Cite This Article as: Teachers College Record Volume 117 Number 11, 2015, p. 1-32
http://www.tcrecord.org ID Number: 18115, Date Accessed: 3/24/2017 12:05:48 PM

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About the Author
  • Charles Munter
    University of Pittsburgh
    E-mail Author
    CHARLES MUNTER is an Assistant Professor of Mathematics Education in the School of Education at the University of Pittsburgh. His research focuses on defining high-quality mathematics instruction and understanding and supporting its enactment at scale. Recent publications include: Munter, C. (2014). Developing visions of high-quality mathematics instruction. Journal for Research in Mathematics Education, 45(5), 584-635; and Munter, C., Wilhelm, A. G., Cobb, P., & Cordray, D. S. (2014). Assessing Fidelity of Implementation of an Unprescribed, Diagnostic Mathematics Intervention. Journal of Research on Educational Effectiveness, 7(1), 83–113.
  • Mary Kay Stein
    University of Pittsburgh
    E-mail Author
    MARY KAY STEIN holds a joint appointment at the University of Pittsburgh as Professor of Learning Sciences and Policy, and Senior Scientist at the Learning Research and Development Center. Her research focuses on mathematics and science teaching and learning in classrooms and the ways in which policy. Recent publications include: Kaufman, J., Stein, M. K., & Junker, B. (in press). How district context influences the accuracy of teachers’ survey reports about their mathematics instruction. Elementary School Journal; and Tekkumru Kisa, M., & Stein, M.K. (2015). Teachers’ learning to see STEM instruction in new ways: A foundation for maintaining cognitive demand. American Educational Research Journal, 52(1), 105–136.
  • Margaret Smith
    University of Pittsburgh
    E-mail Author
    MARGARET S. SMITH is a Professor in the Department of Instruction and Learning in the School of Education and a Senior Scientist at the Learning Research and Development Center, both at the University of Pittsburgh. Her work focuses on developing research-based materials for use in the professional development of mathematics teachers and studying what teachers learn from the professional development in which they engage. Recent publications include: Steele, M. D., Hillan, A. F., & Smith, M. S. (2013). Developing Mathematical Knowledge for Teaching in a Methods Course: The Case of Function. Journal of Mathematics Teacher Education, 16(6), 451–482; and Marrongelle, K., Sztajn, P., & Smith, M. S. (2013). Scaling Up Professional Development in an Era of Common State Standards. Journal of Teacher Education, 64(3), 202–211.
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