Paul Cobb

Vanderbilt University | Vander Bilt · Department of Teaching and Learning

Research on the teaching and learning of mathematics has made significant progress in recent years. However, this work has had only limited impact on classroom instruction in many countries. We report on an eight-year project in which we partnered with several large urban school districts in the US that were attempting to support mathematics teache...

This study aims to compare teachers’ self-efficacy across Turkish and American in-service middle-school mathematics teachers. The samples consist of 379 Turkish and 245 American in-service middle-school mathematics teachers. The self-efficacy questionnaire of the Middle-school Mathematics and the Institutional Setting of Teaching (MIST) scale was u...

Two cases show the value of reflecting on data about students’ perspectives on their experiences of classroom conversations in professional learning settings.

The notion of a coherent instructional system builds on the Newmann, Smith, Allensworth, and Bryk’s concept of instructional program coherence, which the authors define as “a set of interrelated programs for students and staff that are guided by a common framework for curriculum, instruction, assessment, and learning climate” (Instructional program...

Principals and instructional coaches are asked to organize their schools to support teachers’ ongoing professional learning. Prior studies have examined what principals do to support coaches rather than the ways they work together to support instructional improvement. We build on prior studies by examining how principals and coaches coordinate thei...

We report on five-year professional development collaboration with a group of middle-school mathematics teachers during which their views of what constitutes a productive classroom statistical activity changed. The teachers’ statistics instruction was initially typical in the US context and focused on producing calculations and following convention...

Instructional improvement initiatives in many districts include instructional coaching as a primary form of job-embedded support for teachers. However, the coaching literature provides little guidance about what activities coaches should engage in with teachers to improve instruction. When researchers do propose activities, they rarely justify why...

Purpose: This study examines the content and efficacy of instructional leaders’ expectations and feedback (press) in relation to the improvement of middle school mathematics teachers’ instruction in the context of coherent systems of supports. Research Method/Approach: This mixed methods study is a part of a larger, 8-year longitudinal study in fou...

Instructional improvement initiatives in many districts include instructional coaching as a primary form of job-embedded support for teachers. However, the coaching literature provides little guidance about what activities coaches should engage in with teachers to improve instruction. When researchers do propose activities, they rarely justify why...

Research on the teaching and learning of mathematics has made significant progress in recent years. However, this work has had only limited impact on classroom instruction in many countries. We report on an eight-year project in which we partnered with several large urban school districts in the U.S. that were attempting to support mathematics teac...

Many districts are using content-focused coaching as a strategy to provide job-embedded support to teachers. However, the current coaching literature provides little guidance on what coaches need to know and be able to do to engage teachers in activities that will support their development of ambitious instructional practices. Furthermore, little i...

Many districts are using content-focused coaching as a strategy to provide job-embedded support to teachers. However, the current coaching literature provides little guidance on what coaches need to know and be able to do to engage teachers in activities that will support their development of ambitious instructional practices. Furthermore, little i...

District leaders often feel that working with researchers is not mutually beneficial. Researchers don’t provide enough practical guidance, and they’re often unable to present their findings in time to inform district decision making. Research-practice partnerships (RPPs) are a potential new strategy for addressing these challenges. RPPs are long-te...

In this article, the authors present an analysis of two views of culture reflected in equity scholarship and their implications on research and mathematics teaching. In doing so, they draw on two interrelated theoretical orientations to describe instructional practices that support equitable learning opportunities in mathematics classrooms. These t...

The importance of teachers developing adaptive instructional practices consistent with metaphor of whole-class scaffolding has been well documented. However, teachers’ development of such practices is currently not well understood. We draw on a 5-year professional development (PD) design experiment in which a group of middle school mathematics teac...

In this chapter, we describe a methodology for conducting educational design research to support system-wide instructional improvement in mathematics and draw on one of the few design studies that does this as an illustrative case. Design studies conducted at the level of an educational system are interventionist in nature, and can address both the...

In this paper, we frame the dissemination of the products of classroom design studies as a process of supporting the learning of large numbers of teachers. We argue that high-quality pull-out professional development is essential but not sufficient, and go on to consider teacher collaboration and one-on-one coaching in the classroom as additional s...

We examined the extent to which mathematics program evaluations that have been conducted according to methodologically rigorous standards have attended to the theories underlying the programs being evaluated. Our analysis focused on the 37 reports of K-12 mathematics program evaluations in the last two decades that have met standards for inclusion...

Student success on tougher assessments from the Common Core and rigorous mathematics standards requires school leaders to have a firm grasp of those standards of the instruction needed to prepare students. Available at: http://www.kappancommoncore.org/schooling-leaders-on-the-common-core/

A key aspect of supporting teachers’ learning on a large scale concerns mathematics leaders’ practices in designing for and leading high-quality professional development. We report on a retrospective analysis of an initial design experiment aimed at supporting the learning of three math leaders who were charged with supporting the learning of middl...

Among the diverse domains of human knowing, mathematics stands out as a hothouse for insights about teaching and learning in general. This chapter summarizes the ways that research on mathematics learning contributes to our understanding of how people learn. We begin with a brief historical overview, which explains what it is about mathematics that...

This article draws on previously employed methods for conducting fidelity studies and applies them to an evaluation of an unprescribed intervention. We document the process of assessing the fidelity of implementation of the Math Recovery first-grade tutoring program, an unprescribed, diagnostic intervention. We describe how we drew on recent concep...

We examine classroom video recordings as a means of supporting the learning of teacher communities. Drawing on a longitudinal professional development program for middle years mathematics teachers in the USA, we first outline two contrasting episodes in which the teachers analyzed same segments of classroom video in two different points in the prog...

Mathematics Recovery (MR) is designed to identify first graders who are struggling in mathematics and provide them with intensive one-to-one tutoring. We report findings from a 2-year evaluation of MR conducted in 20 elementary schools across five districts in two states. The design allowed for the estimation of the counterfactual growth trajectory...

In this commentary, we discuss the lessons we learned from case studies of two African American mathematics teachers, thereby endorsing the claim made by the contributors to this special issue that the insights they gained are not restricted to mathematics teaching in nonselective urban schools but can also inform the field more generally. We then...

Consider four important elements of setting up challenging mathematics problems to support all students' learning.

In this chapter, we draw on a 5-year interventionist professional development study that we conducted with a group of middle-school mathematics teachers in the United States. The fifth and final year of the study involved a performance assessment in which the teachers collectively designed an instructional unit on statistics that aimed both to buil...

In this article we describe and illustrate an analytical perspective in which educational policies are viewed as designs for supporting learning. From the learning design perspective, a policy comprises 3 components that we term the what, how, and why of policy: the goals for the learning of members of the group targeted by the policy, the supports...

The authors comment on Porter, McMaken, Hwang, and Yang's recent analysis of the Common Core State Standards for Mathematics by critiquing their measures of the focus of the standards and the absence of an assessment of coherence. The authors then consider whether the standards are an improvement over most state mathematics standards by discussing...

This article presents an analytical approach for documenting the identities for teaching that mathematics teachers negotiate as they participate in 2 or more communities that define high-quality teaching differently. Drawing on data from the first 2 years of a collaboration with a group of middle school mathematics teachers, the article focuses on...

The authors comment on Porter, McMaken, Hwang, and Yang’s recent analysis of the Common Core State Standards for Mathematics by critiquing their measures of the focus of the standards and the absence of an assessment of coherence. The authors then consider whether the standards are an improvement over most state mathematics standards by discussing...

Problem: Ernst von Glasersfeld's radical constructivism has been highly influential in the fields of mathematics and science education. However, its relevance is typically limited to analyses of classroom interactions and students' reasoning. Methods: A project that aims to support improvements in the quality of mathematics instruction across four...

In his chapter, Clancey develops his transactional perspective by taking an interactional viewpoint as his primary point of reference. In this chapter, I argue that the distinction that Clancey draws between the interactional and transactional perspectives is a difference that makes a difference when theorizing about learning and practice. I first...

The analysis reported in this article is grounded in the practice of classroom-based developmental or transformational research and focuses on the distributed views of intelligence developed by Pea (1993) and by Hutchins (1995). The general areas of agreement with this theoretical perspective include both the nondualist orientation and the critical...

This article describes an analytic approach for situating teachers’ instructional practices within the institutional settings of the schools and school districts in which they work. The approach treats instructional leadership and teaching as distributed activities and involves first delineating the communities of practice within a school or distri...

In this article, we frame issues of equity in term of the relations between the specifically mathematical practices established in the classroom on the one hand, and the practices of students’ local, home communities and of the broader groups to which they belong in wider society on the other hand. In the first part of the article, we discuss how t...

The constructivist teaching experiment is used in formulating explanations of children’s mathematical behavior. Essentially, a teaching experiment consists of a series of teaching episodes and individual interviews that covers an extended period of time—anywhere from 6 weeks to 2 years. The explanations we formulate consist of models—constellations...

In this article, we describe a methodology for analyzing the collective learning of the classroom community in terms of the evolution of classroom mathematical practices. To develop the rationale for this approach, we first ground the discussion in our work as mathematics educators who conduct classroom-based design research. We then present a samp...

The analysis reported in this chapter focuses on a second-grade classroom in which the children typically displayed positive emotional acts as they attempted to solve personally challenging mathematics problems. We argue that, within the microculture established in a particular classroom, certain emotional acts but not others are appropriate in sit...

Our purpose in this article is to propose a comprehensive, empirically grounded theory of action for improving the quality of mathematics teaching at scale. In doing so, we summarize current research findings that can inform efforts to improve the quality of mathematics instruction on a large scale, and identify questions that are yet to be address...

I completed my dissertation studies with Les Steffe and Ernst von Glasersfeld at the University of Georgia in 1983 and then accepted a faculty position at Purdue University in Indiana. The first study that I conducted at Purdue University was built on my dissertation work and focused on the psychological contexts within which young children interpr...

My career as a mathematics education researcher began in 1978 when I entered the master’s program in mathematics education at the University of Georgia. Prior to moving to Georgia with my wife Jenny, I had completed my undergraduate degree in mathematics at Bristol University in England and was a secondary math teacher for 2 years. Our primary reas...

The emergent perspective described in Chapter 4 serves to orient the analysis of the teacher’s and students’ actions and interactions in particular mathematics classrooms. As noted in Chapter 4, this framework was developed while analyzing the data generated in the course of two year-long classroom design experiments (an initial experiment conducte...

The notion of a classroom mathematical practice was introduced in the reprinted chapter in the last part. It is fair to say in retrospect that my initial use of this construct was largely intuitive: I had not defined a classroom mathematical practice with any precision or clarified how other researchers might identify the mathematical practices int...

Supporters of US current reform recommendations argue that the classroom instructional practices they advocate are more equitable than traditional instructional practices in giving all students access to significant mathematical ideas. The approach to instructional design outlined in the previous part of this book is broadly compatible with the inf...

We report on our 5-year collaboration with a group of teachers whose statistics instruction initially concerned producing graphs and calculations. Towards the end of the collaboration, the teachers routinely planned for statistical activities in which generation and analysis of data were driven by a need to gain insight in a specific problem at han...

This article focuses on 3 conceptual challenges that we sought to address while conducting a design experiment in which we supported the learning of a group of middle school mathematics teachers. These challenges involved (a) situating teachers' activity in the institutional setting of the schools and district in which they worked, (b) developing a...

This presentation will focus on an interpretive scheme for documenting the identities that students are developing as they participate in mathematics classrooms. As we clarify, the approach that we propose is grounded in the context of conducting design research at the classroom level. We first consider how the basic tenets of classroom design meth...

Our primary purpose in this article is to propose an interpretive scheme for analyzing the identities that students develop in mathematics classrooms that can inform instruc- tional design and teaching. We first introduce the key constructs of normative iden- tity and personal identity, and then illustrate how they can be used to conduct empir- ica...

In this response to Foundations for Success: The Final Report of the National Mathematics Advisory Panel (2008), the authors argue that the Panel's assumption that only experimental research studies can produce scientific evidence limits the power of the Panel's recommendations to improve mathematics teaching and learning. The authors first discuss...

This article focuses on the critical role of design theory in our work as mathematics educators. We give particular attention to a specific design theory, Realistic Mathematics Education (RME). We first clarify the enduring contributions of RME to design in mathematics education and then discuss three adaptations that we made to RME theory while co...

Background to the Design ExperimentInstructional TasksThe Classroom Activity StructureTool UseClassroom DiscourseDemocratic Participation and EquityConclusion

The analysis reported in this paper investigates ways in which aspects of the classroom can support students' access to identities and competence in the context of statistical data analysis. This retrospective analysis explores how and in what ways norms of participation, the role of the teacher, instructional activities, and classroom discourse af...

In this paper we discuss the considerations and challenges in designing instructional tasks that support both students' mathematical engagement and their developing mathematical competence. We draw on Dewey's work and take the perspective that cultivating students' content-related interests should be an instructional goal in their own right rather...

We use our experiences from a five-year collaboration with a group of middle-school mathematics teachers to ground the discussion of building on mathematics teachers' current instructional practices to achieve a professional-development (PD) agenda. Researchers working with teachers argue for pragmatic importance of positioning teachers as professi...

Our overall objective in this paper is to share a few observations made and insights gained while conducting a recently completed teaching experiment. The experiment had a strong pragmatic emphasis in that we were responsible for the mathematics instruction of a second grade class (7 year-olds) for the entire school year. Thus, we had to accommodat...

In this paper, our goal is to address a conceptual challenge that arises as researchers conduct design experiments to support and understand teachers' learning. This challenge centers on articulating the relations between teachers' learning in professional development and their practice in the classroom. In our view, designs for supporting teachers...

In this article, we argue that conceptions of content should be broadened beyond the ideas, skills, and proficiencies of particular subject matter disciplines. We frame mathematics teaching as a paradigm case in which to argue that a focus on pedagogy should also include an explicit concern for the kinds of dispositions that students are developing...

The motivation for this article is our belief that theory is critically important but currently underplayed in design research studies. We seek to characterize and illustrate a genre of theorizing that seems to us strongly synergistic with design-based research. We begin by drawing contrasts with kinds of theory that are relevant but, we contend, b...

In this article, we report on a design experiment conducted in an 8th grade classroom that focused on students' analyhsis of bivariate data. Our immediate goal is to document both the actual learning trajectory of the classroom community and the diversity in the students' reasoning as they participated in the classroom mathematical practi...

In this article, the authors first indicate the range of purposes and the variety of settings in which design experiments have been conducted and then delineate five crosscutting features that collectively differentiate design experiments from other methodologies. Design experiments have both a pragmatic bent—“engineering” particular forms of learn...