Running head: PAUL COBB BIOGRAPHY
Biography of a Researcher: Paul Cobb
Kathleen Matson
George Mason University
EDCI 858, Fall 2015
Dr. Jennifer Suh
1

Running head: PAUL COBB BIOGRAPHY 2
Table of Contents
Biographical Information
...................................................................................................................... 3
Major Projects and Themes
.................................................................................................................. 4
Radical Constructivism
..................................................................................................................................... 4
Learning in Interaction
..................................................................................................................................... 5
Instructional Design
........................................................................................................................................... 7
Classroom Mathematical Practices
................................................................................................................ 9
Diversity and Equity
....................................................................................................................................... 10
The Institutional Setting
................................................................................................................................. 11
Methodology
........................................................................................................................................... 12
Research Trajectory
............................................................................................................................. 14
What have I learned about the nature of mathematical research?
........................................... 15
What questions does this raise?
......................................................................................................... 17
What do I take away from Paul Cobb’s work?
.............................................................................. 18
References
............................................................................................................................................... 21

Running head: PAUL COBB BIOGRAPHY 3
This biography of Paul Cobb begins with a brief overview of his education, the universities where he worked and a summary of his awards and publications. I have framed the rest of the paper chronologically and use one or two specific publications to focus on each of the different phases of Cobb’s evolving research trajectory. Along with the synthesis of these papers, I have included specific reflections that Cobb published about his own research. The paper concludes with my own reflections of what I have learned, questions raised, and what I take away from Paul Cobb’s work.
Biographical Information
Paul Cobb was educated at Bristol University, UK where he received an honors degree in mathematics and completed a one-year course for teaching mathematics. After teaching secondary mathematics for two years he moved to the United States where he attended the
University of George and completed his master’s degree and Ph.D. studies. His first faculty position was at Purdue University in 1983. In 1992 he moved to Vanderbilt University in
Nashville where he still works today. Paul Cobb is the co-author and co-editor of seven books and author or co-author of 150 articles and book chapters. He received the award for outstanding article published in Journal for Research in Mathematics Education in 1996 and was elected to the National Academy of Education 2002. He was awarded the Hans Freudenthal Medal for cumulative research over prior 10 years from the International Commission on Mathematics
Instruction (ICMI) in 2005 and the Sylvia Scribner Award from the American Educational
Research Association in 2010 for research over the past ten years that contributes to our understanding of learning and instruction. He is an Invited Fellow of the Center for Advanced
Studies in the Behavioral Sciences and currently holds the Peabody Chair in Teaching and
Learning at Vanderbilt University.

Running head: PAUL COBB BIOGRAPHY 4
Major Projects and Themes
Radical Constructivism
When Cobb started as a graduate student at the university of Georgia, he intended to focus on the teaching and learning of algebra. However, after reading an article by Ernst von
Glaserfeld, given to him by a fellow student, he developed an interest in radical constructivism as an epistemology and a theory of learning. Based on this interest, he asked to work with his mentors, Leslie Steffe and Ernst von Glaserfeld, on their research project that focused on early number learning. This changed the direction of his studies and he left his focus on algebra behind. Cobb’s dissertation grew out of this work and reflected the strong commitment he had made at the time to the radical constructivist view of mathematical learning. His dissertation focused on young children’s construction of thinking strategies using a known sum or difference to find an unknown sum or difference (Cobb, 1983).
An article co-authored with Leslie Steffe while Cobb was a doctoral student provides a view of Cobb’s early work and his perspectives (Cobb & Steffe, 1983). Cobb and Steffe conducted a constructivist teaching experiment with the purpose of advancing the scientific understanding of children’s early understanding of numbers. The article they published in 1983,
The Constructivist Researcher as Teacher and Model Builder, focused on the role of perturbation as instigating children’s reorganization of their thinking in order to resolve conflicts in their understanding. In this article Cobb and Steffe focus explicitly on the individual psychological context in which a six-year old child, Jason, constructs his counting scheme. In this research,
Steffe and Cobb acted as teachers and researchers. They engaged in extensive teaching in order to gain insight into the development of the student’s mathematical reasoning and to test and revise conceptual models of the student’s mathematical reasoning. Cobb and Steffe built on this

Running head: PAUL COBB BIOGRAPHY 5 work of understanding young children’s conceptual understanding of numbers in later work and used it to provide a framework for a developmental learning trajectory (Steffe, Cobb, & von
Glaserfeld, 1988). This process of building on his earlier work in order to create new frameworks of understanding can be seen throughout Cobb’s career. We see below, for example, how his early radical constructivist stance changed to a more social view of learning as
Cobb’s work moved from a focus on an individual child to a classroom of children.
Learning in Interaction
This shift in
Paul Cobb’s theories of learning, from a radical constructivist theory of learning to a social constructivist view, can be evidenced in the 1989 article,
Young Children’s
Emotional Acts While Engaged in Mathematical Problem Solving, published with Erna Yackel and Terry Wood. Cobb and his colleagues showed that considering learning at the classroom level and at the individual student level together can be productive. This assertion would later prove to be strong methodological claim seen throughout much of Cobb’s work. In the 1989 work with Yackel and Wood, Cobb’s focus shifts from a single individual’s understanding to a focus on the role of social norms in the classroom. Moreover, this phase of Cobb’s research demonstrates extending the constructivist teaching methodology of one-to-one interactions between researcher and a single child to examine the interactions in a classroom.
The theoretical perspective of this research was on the neo-Piagetian focus of interpersonal conflicts giving rise to intrapersonal cognitive perturbations for individual students.
This contrasts with his earlier work where perturbations were looked at only from an intrapersonal perspective. From a constructivist viewpoint, it is these disturbances that trigger individual learning (Cobb, Yackel, & Wood, 1989). Social interactions were viewed as giving rise to an individual student’s cognitive development. As the study progressed, the researchers

Running head: PAUL COBB BIOGRAPHY 6 noted that the expectations the classroom teacher in the study had for her students to explain their thinking ran counter to their previous experiences in school (Cobb et al., 1989). Thus, they observed the teacher initiating a mutual process of negotiating the social norms of the mathematics classroom with her students (Cobb et al., 1989). In this process she established a supportive context where doing mathematics was seen as a problem solving activity and where mistakes were seen as normal and as opportunities for learning. The positive nature of the teaching environment that was established together with the various ways in which the classroom teacher observed that her students reasoning developed, led to extending the project to the entire school year. The instructional materials created in this study were later used to support the practices of about 20 second-grade teachers in the district. As mentioned above, we will see how extending this work to other teachers in the district planted the seeds of a future change in
Cobb’s research trajectory.
In this study conducted with Yackel and Wood, the analysis of social norms drew on previous work drawn from both outside and within mathematics education (Cobb et al., 1989) and was a first attempt to treat the classroom as a social context established jointly by the students and the teacher (Cobb & Yackel, 2011). The study differentiated between the social and cognitive aspects of the classroom and assumed that some aspects of the classroom are inherently social and some are inherently cognitive (Cobb & Yackel, 2011). Later, Cobb and Yackel came to the view that any aspect of the classroom can be analyzed from either a cognitive or a social perspective. They credit many of the advances they made in this research to the strengths of the mathematics teacher they worked with in this study (Cobb & Yackel, 2011).
The above research completed by Cobb, Yackel, and Wood in 1989 led to a collaboration with Heinrich Bauersfeld, Gotz Krummheuer, and Jorg Voigt with the goal of formulating an

Running head: PAUL COBB BIOGRAPHY 7 approach that integrated both the social and cognitive perspectives on mathematical learning
(Cobb & Yackel, 2011). Despite much work back and forth across the ocean, the group was not able to agree on an overarching set of constructs that could integrate these differing theoretical perspectives (Cobb & Yackel, 2011). However, the collaboration resulted in a coordination of these perspectives through the publication of a book edited by Cobb and Baursfeld. This book contained analyses of the same children from Cobb, Yackel and Wood’s study in the same classroom but viewed these through different theoretical lenses (Paul Cobb & Bauersfeld, 1995).
This collaboration was fruitful in giving rise to the ideas of symbolic interactionism and ethnomethodology that were key to some of Cobb’s later work (Cobb & Yackel, 2011).
Another of the results of expanding on these ideas was the later development of the notion of sociomathematical norms (Yackel & Cobb, 1996). The study published in 1989 by
Cobb, Yackel and Wood analyzed the social norms characterized by explanation, justification and argumentation that developed in a classroom. This work was extended to focus to norms that were specific to students’ mathematical activities and defined as sociomathematical norms
(Yackel & Cobb, 1996). For example, the understanding that students are expected to justify their thinking is a social norm whereas understanding what counts as a mathematical justification is considered a sociomathematical norm. The development of Paul Cobb’s theoretical view that mathematical learning is not only individual construction but includes the participation in mathematical practices (Yackel & Cobb, 1996) is seen in this study.
Instructional Design
One of the significant influences on Paul Cobb’s thinking came from his interests in
Realistic Mathematics Education (RME) through reading a book on designing instructional sequences by Adrian Treffer, Three Dimensions: A Model of Goal and Theory Description in

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Mathematics Instruction – The Wikobas Project, 1987. This book explained the instructional design work and classroom experimentation that had been conducted through the Freudenthal
Institute in the Netherlands and illustrated design theory of RME (Cobb, Gravemeijer, & Yackel,
2011). Out of the insights gained from Treffer’s book and his interest in RME came a 10-year collaboration Koeno Gravemeijer, the Research Coordinator at the Freudenthal Institute.
This influence and collaboration can be seen in his article, Learning From Distributed
Theories of Intelligence, (1998) where Cobb describes the intentional development of coherent instructional sequences. Here, we see Cobb’s evolution of instructional design from an individualistic perspective of psychological constructivism to a design that makes sense of what goes on in the classroom through sociocultural and sociolinguistic theories (Paul Cobb, 1998).
He described how the basic tenets of the RME approach to design were adapted to fit with his emerging collectivist view of mathematics learning. The first adaptation was to frame the instructional goals in terms of the student’s socially situated mathematical experience. Secondly, the RME approach was adapted by reframing individual learning trajectories in a more collectivist way as teachers and students enacted mathematical practices together. The instructional design presented in this paper (Paul Cobb, 1998) proposes selecting initial instructional goals as a basis for student mathematization as a model for informal mathematical activity leading to a model for mathematic reasoning.
This method of analysis of mathematical learning represented a major shift in Cobb’s position when compared to the radical constructivist position at the beginning of his career by considering the classroom practices (Cobb et al., 2011). Furthermore, considering the mathematical learning of the classroom community as well as of the individual student challenged the predominant view of viewing mathematical learning in the realm of cognitive and

Running head: PAUL COBB BIOGRAPHY 9 developmental psychology that was prevalent during this time. Though the ideas of hypothetical and actual learning trajectories had little impact at the time the 1998 article was published, the ideas of classroom social norms and sociomathematical norms presented by Cobb and developed together with his collaborating researchers were taken up and widely used in mathematics education research (e.g. Healy & Sacristán, 2014; Hino, 2015; Penuel, Allen, Coburn, & Farrell,
2015; Straehler-Pohl, Fernández, Gellert, & Figueiras, 2014).
Classroom Mathematical Practices
While Cobb’s early work with classroom mathematical practices was “largely intuitive”
(Cobb et al., 2011) , his study, Participating in Classroom Mathematical Practices, published in
2001 with Michelle Stephan, Kay McClain, and Koeno Gravemeijer presents collective learning in the classroom as an explicit methodology for analyzing collective learning. This study is grounded in the authors’ work in classroom-design research and in their views of an individual student’s mathematical reasoning as an act of participating in collective practices. Under this view, the participation provides the conditions for the possibility of mathematical learning. The article is explicit in characterizing mathematical practice as comprising of three inter-related types of mathematical norms: (1) taken-as-shared purpose of engaging in mathematical activity,
(2) taken-as-shared forms of mathematical argumentation, and (3) taken-as-shared ways of reasoning with tools and symbols. Each of these norms built on extensions of prior work (e.g.
Yackel & Cobb, 1996) and theories (e.g. RME) (Cobb, Gravemeijer, et al., 2011).
In addition to being explicit about the nature of classroom mathematical practice, the
2001 study examined how new practices in a classroom emerge as a reorganization of prior practices (Cobb, Stephan, McClain, & Gravemeijer, 2001). The study also illustrated the reflexive relation between collective learning and individual learning. Collectively, the taken-as-

Running head: PAUL COBB BIOGRAPHY 10 shared experiences of a classroom support and/or constrain individual learning. Individually, the ways in which individuals participate in collective practices change as the individual student learns, resulting in the unfolding of the collective taken-as-shared practices.
As in other previous studies and areas of research, the observations and limitations that came out of the 2001 study discussed above, led to a further evolution of Paul Cobb’s research focus. Cobb and his collaborators conjecture in this article that one of the uses of the analytic approach based on classroom practices was a means of supporting the development of professional teaching communities. Furthermore, they note the need to look beyond the classroom and take into account the school as a social institution and community factors that may foster inequity due to race, gender, class and economic status (Cobb et al., 2001). Paul
Cobb’s next areas of research addressed these two issues.
Diversity and Equity
In an analysis of two groups of teachers, one in an inner city setting and a one rural/suburban setting, Paul Cobb and Erna Yackel found that the core assumptions and values of mathematics reform recommendations conflicted with those of the inner city teachers (Cobb &
Yackel, 1996). Against this backdrop, Cobb began collaboration with Lynn Hodge to explore how a focus on “diversity and equity can become part and parcel of mainstream research that involves the development of instructional designs and the analysis of the learning and teaching of significant mathematical ideas” (Cobb & Hodge, 2007, p. 159). Cobb and Hodge elaborated an interpretive scheme where diversity and equity were seen as emerging from students participation in the mathematics classroom, their home and the wider society (Cobb,
Gravemeijer, et al., 2011). The definition of equity in schooling was formulated in terms of three aspects: (1) enabling student’s participation in significant out-of-school practices, (2) providing

Running head: PAUL COBB BIOGRAPHY 11 students with access to future mathematics courses, and (3) explicitly cultivating students’ mathematical interests as an instructional goal (Cobb & Hodge, 2007). Within this definition, student identities were seen in terms of three primary interrelated constructs: normative identity, core identity and personal identity. The strength of this scheme, argue Cobb and Hodge, is as a tool to inform instructional design and teaching and to move the issues of equity to become a routine aspect of mainstream research in mathematics education (Cobb & Hodge, 2007).
The Institutional Setting
The work done with Yackel and Wood in the late 1980’s to support second-grade teachers’ instructional practices (see above section Explaining Learning in Interaction) had unintended results when the newly elected school board for the district began to question the changes that were being made in mathematics instruction (Cobb, Dean, Lamberg, Visnovska, &
Zhao, 2011). A 2-year struggle between the teachers and the school board ensued, with the end result being more autonomy for the teachers to make curricular and instructional decisions in mathematics (Cobb, Dean, et al., 2011). The process served to draw the attention of Cobb and his colleagues to the importance of taking into account the school and district settings when working with teachers (Cobb & McClain, 2001). This led to further work where Cobb and colleagues observed and reflected on how school leaders support teachers’ opportunities to learn in interaction with each other. Furthermore, it served as an impetus to research ways of scaling up the work done with individual and small groups of teachers.
In a research study completed in 2006 with Kay McClain, The collective mediation of a high-stakes accountability program: communities and networks of practice , Cobb developed a way to document institutional settings in which groups of teachers work. This approach situated teachers’ instructional practices within the schools and districts where they worked and showed

Running head: PAUL COBB BIOGRAPHY 12 the key role school and district leaders play in mediating high-stakes accountability policies.
Moreover, Cobb and McClain analyzed the significance of developing a common vision of mathematics instruction between teachers and school and district leaders. In the urban district where this study was conducted, the middle-school teachers and the district leaders had a common vision for high-quality mathematics instruction. They viewed mathematics instruction as a means by which to address a state-mandated, high-stakes accountability program. It took only three months of work with these teachers before they were able to become a full-fledged professional teaching community focused on improving instructional practices.
Cobb’s similar work with groups of middle-school teachers in another urban school district provided an informative comparison to the 2006 study referenced above (Cobb et al.,
2003). In this case, the district leaders viewed mathematics instruction as routine activity and viewed accountability in terms of test scores. Here, it took 19 months for the teachers in this district to establish a professional teaching community that supported the improvement of instructional practices. It was only after understanding the effect of the institutional setting on their instructional practices that teachers were able to move to collaborating to improve their practices. Results of these studies indicated that not only can analysis of institutional settings account for teachers’ activities in the classroom and in professional development programs but that these analyses can also support teacher learning. Cobb continues to work in this area of teacher development with the goal of improving the quality of mathematics teaching on a large scale (e.g. Cobb & Jackson, 2012).
Methodology
One of the most often cited publications written by Paul Cobb and colleagues is the article describing the nature of design experiments in educational research (Paul Cobb, Confrey,

Running head: PAUL COBB BIOGRAPHY 13 diSessa, Lehrer, & Schauble, 2003). According to Google Scholar, this article has been cited
2,288 times. While Cobb’s epistemology and theory of learning evolved over the span of his career, the methodology used in his research was primarily design experiments. He and his colleagues used design experiments in a variety of settings. In his early work, he used this methodology with a one-on-one teacher-experimenter and student and examined a single student in depth and detail (Paul Cobb & Steffe, 1983). This methodology was also used in his classroom design experiments where the researchers collaborated with a teacher to understand the instruction in the classroom (Cobb et al., 1989). The work done with groups of teachers to develop a professional community is another example of this type of methodology (Cobb &
McClain, 2001).
Cobb’s work in mathematical research using design experiments points to the crosscutting features common to this type of methodology. First, as seen above, he developed theories on learning of and the means of learning of individuals, classroom communities, groups of teachers and schools or school districts. Next, his research involved direct intervention in the types of learning he was investigating. This can be seen from the intensive teaching of a single six-year old (Cobb & Steffe, 1983) to the development of professional learning communities with teachers (Cobb & McClain, 2006). The third feature is the prospective and reflective nature of design experiments as can be seen in the classroom study with Yackel and Wood where the initial conjectures about instructional tasks were revised due to the observed interactions between the teacher and her students (Cobb et al., 1989). This leads to the fourth feature of design experiments, the iterative nature of revising a conjecture based on evidence leading to a continuation of the inquiry, as represented in Cobb’s work with Stephan, McClain, and

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Gravemeijer (Cobb et al., 2001). Lastly, Cobb’s work addressed the pragmatic nature of research that addresses the specific needs of practitioners in their work.
Research Trajectory
The importance of context can be seen throughout Cobb’s work. His early work focused on the context of learning as “the context within which the child constructs mathematical knowledge” (Paul Cobb & Steffe, 1983, p. 84) and referred to the individual psychological context for a particular child. His ongoing work showed a shift in this notion of context to include social context of the classroom (e.g. Paul Cobb, 1998), cultural context (e.g. Nasir &
Cobb, 2002) and the institutional context where teachers develop their practices (e.g. Cobb,
McClain, Lamberg, & Dean, 2003).
While Cobb continued to value the insights on students mathematical reasoning made through constructivist analyses, his work evolved to understand those experiences as socially and culturally situated (Cobb, 2011; Cobb, 1998; Yackel & Cobb,
1996). He grew to believe that “any event in a classroom can be considered productively both by focusing on the practices that are enacted collectively and on the participation of individuals in those practices” (E. Yackel, Gravemeijer, & Sfard, 2011, p. vii).
Underlying the shift in his work was the shift in his fundamental epistemology from radical constructivism to pragmatic realist (Cobb, 2011). He stated that though his basic assumptions about the process of mathematical learning significantly changed over time, there are several recurrent themes that run throughout his career (Cobb, 2011). These themes are (1) the importance of sustained and direct involvement with the phenomena being investigated, (2) a commitment to the view that people’s practices are reasonable from their perspective as a prerequisite to developing effective designs to support their learning, (3) the value of making distinctions in mathematical reasoning between different mathematical domains, (4) the

Running head: PAUL COBB BIOGRAPHY 15 importance of the core tenets of constructivist teaching experiment methodology as a precursor to design experiments, and (5) the importance of context on learning (Cobb, 2011).
What have I learned about the nature of mathematical research?
I have learned that mathematical research is an evolving field. While a researcher may make contributions based on a single paradigm, Paul Cobb demonstrates a life-long learner whose work is characterized by shifts in perspectives and methodology in order to address practical issues arising through his research (Cobb, Gravemeijer, et al., 2011). Furthermore, in looking at the work of Paul Cobb I see that mathematical research begins in a small way. Paul
Cobb began as an apprentice researcher when a graduate student at University of Georgia and developed his foundation and grounding by asking to work with his mentors (Cobb, 2011). This highlights to me the importance of taking initiative to learn from the professors that I am privileged to work with and of the importance of spending time working within my field.
Though I learned a good deal through my initial graduate research assistantship, it was not in my field and I missed the opportunity of much of the intangible learning from mentors within my field.
Paul Cobb states that his initial interest in coming to the U.S. to study at the University of
Georgia included the desire of seizing the opportunity to travel Georgia (Cobb, 2011). This wanderlust perspective combined with my own love of travel leads me to use the travel analogy proposed by Anna Sfard (Sfard, 2011), to further describe what I have learned about mathematical research.

Mathematical research is always framed in terms of what has already been done in the field. Don’t leave on a trip without consulting with those who have been there before.

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
Mathematical research is collaborative. Most of Paul’s work was collaborative and he had a number of lengthy and productive collaborations e.g. with Yackel and Wood, with
Gravemeijer and RME, etc. Don’t travel alone.

Mathematical research needs to be experienced firsthand. Paul Cobb stresses the importance of staying close the events and facts which one is investigating (Cobb, 2011;
Paul Cobb, Confrey, diSessa, Lehrer, & Schauble, 2003b). “There is no substitute for sustained, first-hand engagement with the phenomena that we seek to understand.”
(Cobb, 2011, p. 11). Paul Cobb’s development as a researcher can be seen as choices driven by the reality of his investigations with students, teachers and institutions (Cobb,
Gravemeijer, et al., 2011). If you want to understand a different culture or place you need to go there yourself.

Mathematical research is a process built on experiences. For example the constructs of classroom mathematical practices grew out of Cobb’s design work with instructional sequences. The interpretations of classroom events then led to inform continued development of instructional efforts. A seasoned traveler is one who learns from previous experiences.
 Mathematical research is practical. “For us, the methodology is nothing more than a potentially revisable solution to the concrete problems and issues that we have encountered while experimenting in classrooms.” (Cobb et al., 2001, p. 154) Travel necessitates attending to the pragmatic. Never sacrifice sleep, nutrition, safety or
cleanliness.

Mathematical research needs to be integrated. In his awareness of issues of equity and diversity in mathematics education, Paul Cobb realized that though these issues are

Running head: PAUL COBB BIOGRAPHY 17 complex, they should become an “integral aspect of mainstream research in mathematics education” (Cobb & Hodge, 2007, p. 173). Travel broadens your perspectives and helps
you understand different people and cultures.
What questions does this raise?
As I reflect on the research trajectory of Paul Cobb, a number of questions arise. First, when I consider his evolution as a researcher alongside the development of the concepts and methods in the field of mathematics research I wonder about the interaction between new paradigms and working within existing paradigms. I wonder if Paul Cobb’s progression was part of the development of “normal science” (Kuhn, 2012) or if his work was a stimulus that moved the science forward. Perhaps it was a combination of both. Certainly, his contributions to the field of mathematics research have been significant but at the same time, others worked in the field both individually and in collaboration with him to advance mathematics education.
Secondly, I wonder how my own evolution of a researcher will evolve. I have already seen changes in my research interests during my short time as a doctoral student. As I become more knowledgeable about the research in mathematics education and become further immersed in the field will my interests evolve together with the field?
Related to this, I wonder about the research trajectory from individual student learning in particular mathematical domains to the development of learning environments in specific classrooms, to the learning that takes place in professional teaching communities, to viewing school and district settings where teachers develop their practices. Cobb’s views on learning have tracked this progression as they moved from a radical constructivist viewpoint to a sociocultural and situated perspective. Will the focus of mathematical research circle back around to the individual? Has it before? Is the progression from the individual to the organizations a

Running head: PAUL COBB BIOGRAPHY 18 function of an individual’s (Paul Cobb’s) experience and maturity or is it the direction of the field? Of course, I realize that there are broad distinctions within current mathematics research but I am focusing on what may be the general trend.
Lastly, I wonder how I can build on what has already been done by researchers such as
Paul Cobb? While I recognize that he began in a small way while a doctoral student at the
University of Georgia, the corpus of his work seems daunting. There is benefit in being able to build on the foundation of understanding of mathematical learning and teaching that has been established. At the same time, it is a challenge to make significant contributions that can make a difference in the field.
What do I take away from Paul Cobb’s work?
There are a number of important concepts that I take away from the examination of Paul
Cobb’s work. First are the insights about what makes research scientific, productive and how it can improve educational practice. His explicit descriptions of design experiment methodology are fleshed out in his research projects providing a deep understanding of what makes this type of research scientific. His work also demonstrates the useful nature of mathematical research. I appreciate the pragmatic emphasis Cobb places on the nature of research stating that it should directly address the work of practitioners.
Secondly, as mentioned above, I realize that my own theoretical position and interests may change over time (as it has even in a short time in this PhD program) based on practical experience. Research foci do not need to be fixed. My areas of interest will change in response to experiences and to what I continue to learn. In the same way that educational views and practices in the field evolve over time, so too will my own views.

Running head: PAUL COBB BIOGRAPHY 19
Related to this, I realize that there is nothing new under the sun. What I mean by this is that the field does not progress with blinding flashes of revelation of new knowledge about the teaching and learning of mathematics. Instead, it progresses by the methodical extension and elaboration of ideas and beliefs. Achievements (and understanding) are cumulative and the way mathematics teaching and learning is viewed today is a product of the work done over the past decades and a product of the past centuries. With this in mind, each new development of conceptual and methodological resources can be used as a building block in the next challenge or stage.
Another strong impression I have from examining the work of Paul Cobb is the collective effort of researchers in the field of mathematics education. There is a real sense of common vision and goals for improving mathematics education that is garnered from the work of Paul
Cobb with colleagues all over the world. Instead of viewing my interests and goals from an individual perspective, I have a sense of a community working together for a common good.
Along these lines is the concept of scaling up the efforts of improving mathematical teaching and learning. I see Cobb’s trajectory as a process of discovery of theories and principles on a small scale propelling him to research ways to support teaching and learning on a large scale. This presents a challenge, as I consider moving ahead with my research interests. It gives rise to a sense of responsibility to use what I know to make a difference.
Lastly, I am impressed by Cobb’s humility in approaching his research. He consistently approached his research with an attitude of learning and an openness to what he could garner from his colleagues and those he collaborated with.
Paul Cobb is a remarkable contributor of mathematics education research. I really enjoyed your presentation and your biography paper. I love how you reflected on the social norms that he and

Running head: PAUL COBB BIOGRAPHY 20 his colleagues defined as being critical to bringing out the process standards like communication,
Connections, problem solving, reasoning and representations. Their of three inter-related types of mathematical norms: (1) taken-as-shared purpose of engaging in mathematical activity, (2) taken-as-shared forms of mathematical argumentation, and (3) taken-as-shared ways of reasoning with tools and symbols are the ones that we want to see in our math classrooms.
I am also very interested in his study, Participating in Classroom Mathematical Practices, with
Michelle Stephan, Kay McClain, and Koeno Gravemeijer that presents collective learning in the classroom as an explicit methodology for analyzing collective learning. This method would be interesting to use in our classroom based studies. In your narrative, you are very reflective of his work and consider ways your research orientation and agenda is shaping as you are continuing in the program. I am looking forward to following your journey as a mathematic educator and researcher.

Running head: PAUL COBB BIOGRAPHY 21
References
Cobb, P. (1998). Learning From Distributed Theories of Intelligence. Mind, Culture, and
Activity, 5(3), 187–204. http://doi.org/10.1207/s15327884mca0503_4
Cobb, P. (2011). Introduction. In E. Yackel, K. Gravemeijer, & A. Sfard (Eds.), A journey in
mathematics education research: insights from the work of Paul Cobb (pp. 9–17).
Dordrecht: Springer.
Cobb, P. A. (1983). Children’s strategies for finding sums and differences (thinking,
Abstraction) (Educat.D.). University of Georgia, United States -- Georgia. Retrieved from http://search.proquest.com.mutex.gmu.edu/docview/303153663/28304DE212A0
4867PQ/1
Cobb, P., & Bauersfeld, H. (1995). The emergence of mathematical meaning: Interaction in
classroom cultures. Psychology Press. Retrieved from https://books.google.com/books?hl=en&lr=&id=yr3y27cSuEQC&oi=fnd&pg=PR1& dq=emergence+of+mathematical+meaning:+interaction+in+classroom+cultures+co bb+bauersfeld&ots=wDyQTsPp7I&sig=3plMAHvuL3NsUQKswjQe0m0HYzU
Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design Experiments in
Educational Research. Educational Researcher, 32(1), 9–13. http://doi.org/10.3102/0013189X032001009
Cobb, P., Dean, C., Lamberg, T., Visnovska, J., & Zhao, Q. (2011). Introduction. In E. Yackel, K.
Gravemeijer, & A. Sfard (Eds.), A journey in mathematics education research: insights
from the work of Paul Cobb (pp. 199–205). Dordrecht: Springer.

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Cobb, P., Gravemeijer, K., & Yackel, E. (2011). Introduction. In A. Sfard, K. Gravemeijer, & E.
Yackel (Eds.), A Journey in Mathematics Education Research (pp. 1–5). Dordrecht:
Springer Netherlands. Retrieved from http://link.springer.com/10.1007/978-90-
481-9729-3
Cobb, P., & Hodge, L. L. (2007). Culture, identity, and equity in the mathematics classroom.
In N. S. Nasir & P. Cobb (Eds.), Improving access to mathematics: Diversity and equity
in the classroom (pp. 159–171). New York: Teachers College Press.
Cobb, P., & Jackson, K. (2012). Analyzing educational policies: A learning design perspective. Journal of the Learning Sciences, 21(4), 487–521.
Cobb, P., & McClain, K. (2001). An approach for supporting teachers’ learning in social context. In F. L. Lin & T. Cooney (Eds.), Making sense of mathematics teacher
education (pp. 207–232). Dordrecht, The Netherlands: Kluwer.
Cobb, P., & McClain, K. (2006). The collective mediation of a high-stakes accountability program: Communities and networks of practice. Mind, Culture, and Activity, 13(2),
80–100. http://doi.org/10.1207/s15327884mca1302_2
Cobb, P., McClain, K., Lamberg, T., & Dean, C. (2003). Situating teachers’ instructional practices in the institutional setting of the school and school district. Educational
Researcher, 32(6), 13–24.
Cobb, P., & Steffe, L. P. (1983). The Constructivist Researcher as Teacher and Model Builder.
Journal for Research in Mathematics Education, 14(2), 83. http://doi.org/10.2307/748576

Running head: PAUL COBB BIOGRAPHY 23
Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (2001). Participating in Classroom
Mathematical Practices. Journal of the Learning Sciences, 10(1-2), 113–163. http://doi.org/10.1207/S15327809JLS10-1-2_6
Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31(3-4), 175–190. http://doi.org/10.1080/00461520.1996.9653265
Cobb, P., & Yackel, E. (2011). Introduction. In E. Yackel, K. Gravemeijer, & A. Sfard (Eds.), A
journey in mathematics education research: insights from the work of Paul Cobb (pp.
33–40). Dordrecht: Springer.
Cobb, P., Yackel, E., & Wood, T. (1989). Young Children’s Emotional Acts While Engaged in
Mathematical Problem Solving. In D. McLeod & V. M. Adams (Eds.), Affect and
Mathematical Problem Solving (pp. 117–148). Springer New York. Retrieved from http://link.springer.com/chapter/10.1007/978-1-4612-3614-6_9
Healy, L., & Sacristán, A. I. (2014). Towards an understanding of the shaping of research outcomes by contextual issues: reflections on the contributions of the ReMath project. Educational Studies in Mathematics, 85(3), 423–435. http://doi.org/10.1007/s10649-014-9538-2
Hino, K. (2015). Comparing multiple solutions in the structured problem solving:
Deconstructing Japanese lessons from learner’s perspective. Educational Studies in
Mathematics, 90(2), 121–141. http://doi.org/10.1007/s10649-015-9626-y
Kuhn, T. S. (2012). The structure of scientific revolutions (Fourth edition). Chicago ; London:
The University of Chicago Press.

Running head: PAUL COBB BIOGRAPHY 24
Nasir, N. S., & Cobb, P. (2002). Diversity, Equity, and Mathematical Learning. Mathematical
Thinking and Learning, 4(2-3), 91–102. http://doi.org/10.1207/S15327833MTL04023_1
Penuel, W. R., Allen, A.-R., Coburn, C. E., & Farrell, C. (2015). Conceptualizing Research–
Practice Partnerships as Joint Work at Boundaries. Journal of Education for Students
Placed at Risk (JESPAR), 20(1-2), 182–197. http://doi.org/10.1080/10824669.2014.988334
Sfard, A. (2011). Epilogue: On the importance of looking back. In E. Yackel, K. Gravemeijer,
& A. Sfard (Eds.), A journey in mathematics education research: insights from the
work of Paul Cobb (pp. 231–239). Dordrecht: Springer.
Steffe, L., Cobb, P., & von Glaserfeld, E. (1988). Construction of arithmetical meanings and
strategies. New York: Springer-Verlag.
Straehler-Pohl, H., Fernández, S., Gellert, U., & Figueiras, L. (2014). School mathematics registers in a context of low academic expectations. Educational Studies in
Mathematics, 85(2), 175–199. http://doi.org/10.1007/s10649-013-9503-5
Yackel, E., & Cobb, P. (1996). Sociomathematical Norms, Argumentation, and Autonomy in
Mathematics. Journal for Research in Mathematics Education, 27(4), 458–477. http://doi.org/10.2307/749877
Yackel, E., Gravemeijer, K., & Sfard, A. (Eds.). (2011). A journey in mathematics education
research: insights from the work of Paul Cobb. Dordrecht: Springer.