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Scaling Up Mathematics: The Interface of Curricula with Human and Social Capital

Lauren Resnick

Carrie Leana, Mary Kay Stein, Brian Gill


Background: This project seeks to understand:

  • How human and social capital within schools interact to affect the breadth, depth and endurance of curricular implementation;
  • How the characteristics of the curriculum moderate the relationship between human and social capital and implementation;
  • How district strategies influence the human and social capital in schools via the structure and organization of professional development opportunities and curriculum roll-out strategy;
  • How the breadth, depth and endurance of implementation of a research-based curriculum influence student achievement.

    Purpose: The project is organized into four subprojects:

    1. The Capital in Schools group studies the effects of human and social capital on outcomes such as student achievement in 200 urban schools implementing the Everyday Math curriculum. [Leader: Carrie Leana]
    2. The Capital and Curriculum group examines the different ways in which human and social capital effects play out for different curricula and contrasts the implementation of Everyday Math and Investigations in urban settings. [Leader: Mary Kay Stein]
    3. The Edison Schools and District Strategy group studies the role of human and social capital in a for-profit school management setting. This group also will provide a theoretically-based analysis of the key elements of scale up strategies and their impact. [Leader: Brian Gill]
  1. The Coordination group organizes seminars and conferences aimed at integrating the project's various components [Leader: Lauren Resnick]

    Intervention: We are studying the role of human and social capital in school districts implementation of two major, conceptually-oriented math programs, Investigations and Everyday Math. In addition, we are studying the effects of different district strategies in the implementation of these programs. The impact of all of these factors on student learning gains is also investigated.

    Setting: We study teachers, math coaches, support teachers and school administrators in six urban schools districts (New York City Regions 2, 4, 5, 7 and 8, the Cartwright School District in Phoenix Arizona) and in 24 Edison Schools in four states (Illinois, Nevada, New York, and Pennsylvania).

    Research Design: This is a longitudinal study with multiple measures, both quantitative and qualitative. Measures include surveys of teachers and principals; interviews with teachers, coaches, principals and district leaders; and observations of classroom and professional development activities. We will use multiple modeling approaches to examine causal effects of human and social capital, as well as district policies, on student learning.

    The Capital in Schools group surveyed over 6,000 classroom teachers in 200 New York City public elementary schools in March 2004 and March 2005. This represents approximately 90% of the eligible teacher population in NYC Districts 2, 4, 5 and 7. In 2005 the CIS group added approximately 200 special education teachers to their sample. The CIS project also collected student achievement data from over 10,000 third, fourth, and fifth grade students in NYC Districts 2, 4, 5 and 7.

    The Capital in Curriculum group is working in New York City s Region 8 and in the Cartwright district in Phoenix AZ. It has administered 1,500 teacher surveys and performed 600 classroom observations, 60 professional development observations, 580 interviews with school level personnel and 40 interviews with district level personnel.

    The Edison Schools group has surveyed over 300 teachers.

    The District Strategy group has conducted 45 interviews with district and region level staff in New York City and Phoenix, AZ.

    Capital in Schools [For more information:]

    All the survey data have been collected for Time 1 (2004) and Time 2 (2005), and Time 1 student achievement data have been received and matched to teachers. Preliminary analysis suggests several findings of interest.

    • Social capital: Despite the plethora of experts, consultants, coaches, and other specialists hired by the districts, by a factor of approximately two to one teachers report that they get their information on math instruction from one another rather than from various experts or administrators.
    • Human capital: There is a good deal of variability in teachers self-reports of their ability to teach particular subjects in math such as fractions, probability, and geometry. Teacher preparation varies both by district and, more pronounced, by grade level, with teachers at lower grades reporting lower levels of efficacy in teaching math. There is also a good deal of variability in objective assessments of teachers mathematical teaching ability.
    • Student Achievement: Variance in student achievement is predicted by student characteristics and teacher human capital, as expected. It is also predicted by social capital at multiple levels of analysis (social capital of individual teacher; collective social capital of the grade team). Contrary to assertions in the education literature, teacher ideology regarding math instruction (i.e., teacher beliefs regarding how students best learn math) does not significantly predict student achievement.
  • Teacher turnover: Teachers who leave their jobs have higher human capital in the form of experience and efficacy, and lower social capital in the form of the intensity of their interactions within the school. Teachers who work in schools characterized by strong social capital are significantly less likely to leave their jobs. Contrary to the organizational demography literature, the degree to which a teacher is demographically (i.e., race, age) or ideological (i.e., beliefs regarding how students best learn math) distinct from her peers is not a significant predictor of turnover, nor are demographic and ideological diversity within the grade teams.

    Capital and Curriculum [For more information:]

    Data collection is on-going.

    Stein & Coburn (2005) used qualitative social network techniques to map the networks of teachers, coaches, and principals in 4 case-study schools. The findings suggested the development of authentic communities of practice, in which discussions centered on mathematical content, in the Investigations schools. In the Everyday Math schools, on the other hand, there were few examples of discussions beyond the requirements of formal roles, and conversations were mostly centered on how to coordinate and use instructional materials. Possible explanations were probed for these differences, including the nature of district policy messages and the characteristics of the two different curricula.

    Stein & Kim's (2006) analyses of Investigations and Everyday Mathematics revealed that while both curricula are primarily comprised of high-level, cognitively demanding tasks, Investigations has more open-ended, unstructured problems while Everyday Mathematics has more procedurally based, conceptually oriented problems. The authors hypothesize that this would be associated with Investigations placing greater demands on teacher learning. However, their analyses also revealed that Investigations contained more opportunities for teacher learning, including more transparency (i.e., explication of the mathematical rationales behind the tasks with which students engage) and more examples of how students typically approach the tasks.

    In an analysis of 121 classroom observations conducted during the first two years of the project, Stein, Kim, & Seeley (2006) found that the majority of the Investigations teachers were able to keep the cognitive demands of the tasks at a high level during classroom implementation whereas the majority of the Everyday Mathematics teacher's lessons declined into purely algorithmic exercises. Their analyses revealed that when teachers made use of the opportunities for teacher learning provided in the curricula, they were better able to maintain high levels of cognitive demand.

    District Strategy [For more information:]

    Preliminary findings based on the district design case study work indicate that implementation approaches vary with respect to district context and curricular program. In both New York and Cartwright, the district office made strategic choices with respect to rolling out the program, altering the curriculum through supplementation, allowing some schools to opt out of the implementation, and creating staff positions to support the implementation. However, many of these choices eventually changed in response to new contingencies in the district context. These findings suggest that district leaders believed that the curricula were not sufficient alone for at least two reasons: first, the perceived gap between the human and social capital demands of the curriculum and the extant human and social capital of the teachers; and second, the district context, including the political demands placed on the district, including from the community as well as from the teachers' union.


    Capital in Schools [For more information:]


    Leana, C. & Pil, F. (2006) Social capital and organizational performance: Evidence from urban public schools. Organization Science, 13(3), 1-14.

    Pil, F. & McEvily, S. (2006) The influence of modularity and complexity on innovation, imitation, and sustained competitive advantage. Academy of Management Review, 31(4).

    Conference Presentations:

    Ghitulescu, B. & Leana, C. Job crafting in educational settings. National meeting of the Academy of Management, Atlanta, 2006.

    Ghitulescu, B., Pil, F. & Leana, C. Exploring the idiosyncratic nature of work: Antecedents and consequences of employee job crafting. Labor and Employment Relations Association (formerly IRRA), 58th National Conference, Boston, 2006.

    Leana, C., Ghitulescu, B. & Pil, F. A multi-level analysis of turnover in urban public schools, National meeting of the Academy of Management, Honolulu, Hawaii, 2005.

    Working Papers and Doctoral Dissertations:

    Ghitulescu, B. & Leana, C. Customizing work: How individuals and groups alter their work and working conditions. Katz Graduate School of Business, University of Pittsburgh.

    Leana, C. & Pil, F. "Predictors of teacher turnover: a longitudinal study." Katz Graduate School of Business, University of Pittsburgh.

    Leana, C. & Pil, F. The effects of teacher human and social capital on student achievement. Katz Graduate School of Business, University of Pittsburgh.

    Shevchuk, I., Leana, C., Mittal, V. & Pil, F. "Moderators of the relationship between school commitment and teacher turnover." University of Pittsburgh.

    Ghitulescu, B. Job crafting in organizations: Exploring why and how individuals shape tasks and relationships at work. Doctoral dissertation, University of Pittsburgh Katz Graduate School of Business, expected completion: summer 2006.

    Shevchuk, I. Predictors and moderators of teacher turnover. Doctoral dissertation, University of Pittsburgh Katz Graduate School of Business, expected completion: summer 2007.

    Gong, B. Managing interruptions: The role of fit between task demands and capacity among public school principals. Doctoral dissertation, University of Pittsburgh Katz Graduate School of Business, expected completion: fall 2006.

    Survey Instrumentation:

    2004 Teacher Survey

    Edison Schools Survey

    2005 Teacher Survey

    2005 Special Education Teacher Survey

    Capital and Curriculum [For more information:]


    Stein, M.K., Smith, M.S., & Remillard, J. (In Press). How curriculum influences student learning. In F.K. Lester (Ed.), Second handbook of research on mathematics teaching and learning. Greenwich, CT: Information Age Publishing.

    Conference Presentations:

    Coburn, C. E., & Russell, J.L. Exploring the determinants of teacher social networks. Annual Conference of the American Sociological Association, Montreal, August 2006.

    Stein, M.K., Remillard, J., & Smith, M.S. How curriculum influences student learning.
    Paper presented at the research pre-session of the annual meeting of the National Council of
    Teachers of Mathematics, Anaheim, CA. 2005.

    Stein, M.K., & Coburn, C. E. Districts use of instructional guidance systems in
    mathematics. Paper presented at the annual meeting of the American Educational Research
    Association, Montreal, 2005 .

    Stein, M.K. Improving instruction at scale: Teacher learning as situated within schools and
    Districts. Presentation at Michigan State University, March, 2005.

    Stein, M.K., & Kim, G. (2006). The role of mathematics curriculum in large-scale urban reform: An analysis of demands and opportunities for teacher learning, AERA Conference San Francisco, April 2006.

    Stein, M.K., Kim, G., & Seeley, M. (2006). The enactment of reform mathematics curricula in urban settings: A comparative analysis, AERA Conference San Francisco, April 2006.

    Sutherland, S. Facilitating organizational learning: Understanding social networks in
    schools. Presented at the American Evaluation Association, Toronto, ON. 2005.

    Sutherland, S., with Castleton, L, Denison, M., Glanz, K., Silvestre, G., & Smith, J. (2006). The development of social capital by school leaders, AERA Conference San Francisco, April 2006.


    Implementation of Innovative Mathematics Curricula in Elementary Schools (IIMCES) 2005 Teacher Survey (NYC)

    Implementation of Innovative Mathematics Curricula in Elementary Schools (IIMCES) 2005 Teacher Survey (AZ)

    Scaling Up Mathematics Teacher Protocol Interview - (2004, 2005)

    Scaling Up Mathematics Principal Protocol Interview - (2004, 2005)

    Scaling Up Mathematics Coach Protocol Interview - (2004, 2005)

    Scaling Up Mathematics Non Focal Teacher (Social Capital) Protocol Interview - (2004, 2005)

    Scaling Up Mathematics Classroom Observation Instrument - (2004, 2005)

    District Strategy [For more information:]

    Working Papers:

    Chun, M. & Nelson, C. "Strategies for Scaling Up Mathematics Curricula in Three Districts," RAND.

    Conference Presentations:

    Chun, M., Nelson, C., with Ferguson, K., Developing a conceptual model of district strategy for curricular scale-up in urban schools, AERA Conference, San Francisco, April 2006.