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Teachers’ Views of Students’ Mathematical Capabilities: Challenges and Possibilities for Ambitious Reform


by Kara Jackson, Lynsey Gibbons & Charlotte J. Sharpe — 2017

Background: Research suggests that teachers’ views of their students’ capabilities matter when attempting to accomplish instructional reform, particularly in settings serving historically marginalized groups of students. However, to date, this issue has received minimal attention in the scholarship and practice of mathematics instructional reform.

Purpose: This study offers a large-scale snapshot of middle-grades teachers’ views of their students’ mathematical capabilities in the context of instructional reform. It contributes to the field’s understanding of the learning demands for teachers inherent in achieving a vision of high-quality mathematics instruction and suggests potentially critical foci for professional learning opportunities.

Setting: The study took place in two large urban districts pursuing ambitious reform in middle-grades mathematics.

Participants: Participants included 122 middle-grades mathematics teachers.

Research Design: The study consisted of a qualitative analysis of semistructured interviews conducted with each of 122 teachers regarding their perspectives on the district’s reform efforts, including their views of their students’ mathematical capabilities in relation to the reform. Conceptually, we approached our analysis of teachers’ views of their students’ mathematical capabilities by attending to how they framed a common problem of practice—students facing difficulty in mathematics—diagnostically (i.e., how they explained the source of students’ difficulty) and prognostically (i.e., what they described doing to support students facing difficulty). Analysis also focused on patterns in the relations between teachers’ diagnostic and prognostic framings.

Findings: On the whole, most teachers did not view all of their students as capable of participating in rigorous mathematical activity. Most teachers attributed at least some of their students’ difficulty to inherent traits of the students or deficits in their families or communities, and most described lowering the cognitive demand of an activity if they perceived that students were facing difficulty. Moreover, our analysis of the relations between teachers’ diagnostic and prognostic framing revealed that even when teachers explained students’ difficulty in terms of instructional opportunities, thereby taking responsibility for their students’ learning, they did not necessarily respond in ways that would enable students to participate substantially in rigorous mathematical activity.

Conclusions: Findings suggest that a significant challenge in accomplishing ambitious reform entails supporting shifts in how teachers view their students’ capabilities along two dimensions: how teachers explain the source of students’ difficulties in mathematics and how they address such difficulties. Implications for designing professional learning opportunities to support productive shifts in teachers’ views of their students’ capabilities are discussed.



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Cite This Article as: Teachers College Record Volume 119 Number 7, 2017, p. -
http://www.tcrecord.org ID Number: 21791, Date Accessed: 5/27/2017 5:23:09 PM

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About the Author
  • Kara Jackson
    University of Washington
    E-mail Author
    KARA JACKSON is an associate professor of mathematics education at the University of Washington. Her research focuses on specifying forms of practice that support all learners in participating in rigorous mathematics and reorganizing educational contexts to support teachers in developing such forms of practice. Recent publications include: Jackson, K., Cobb, P., Wilson, J., Webster, M., Dunlap, C., & Appelgate, M. (2015). Investigating the development of mathematics leaders' capacity to support teachers' learning on a large scale. ZDM Mathematics Education, 47(1), 93–104; and Jackson, K., Garrison, A., Wilson, J., Gibbons, L., & Shahan, E. (2013). Exploring relationships between setting up complex tasks and opportunities to learn in concluding whole-class discussions in middle-grades mathematics instruction. Journal for Research in Mathematics Education, 44(4), 646–682.
  • Lynsey Gibbons
    Boston University
    E-mail Author
    LYNSEY GIBBONS is an assistant professor of mathematics education at Boston University. Her research focuses on the challenge of organizing school- and district-level contexts to support teachers’ development of high-quality instructional practices that are productive for student learning. Recent publications include: Gibbons, L. K., & Cobb, P. (2016). Examining content-focused coaching knowledge and practices implicated in designing coaching activities. Elementary School Journal, 117(2), 237–259.
  • Charlotte Sharpe
    Vanderbilt University
    E-mail Author
    CHARLOTTE J. SHARPE is a postdoctoral fellow in elementary mathematics education at Syracuse University. Her research focuses on how teachers come to develop ambitious instructional practices in both teacher education and school settings, and how the vision and practice of others in these settings shapes teachers’ opportunities to learn. Recent publications include: Dunlap, C., Webster, M., Jackson, K., & Cobb, P. (2015). Schooling leaders on the common core. Available at www.kappancommoncore.org.
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