# Kay McClain's research while affiliated with Arizona State University and other places

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## Publications (44)

Accepting the importance of Jim Greeno’s work, not just in this volume but throughout his career, I offer this commentary
from the position of a researcher who first worked “from the inside out” and who now works “from the outside in.” My identity is that of a mathematics educator with a theoretical commitment to design research. To clarify, for al...

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...

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 paper we provide an analysis of the work of a video-based case development team whose goal was to produce didactic objects to be used the professional development of secondary mathematics teachers. In order to generate artifacts for use in the creation of the cases, the research team conducted a classroom intervention in an Algebra I classr...

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

This paper provides an analysis of the evolution of the statistical understandings related to exploratory data analysis of a cohort of middle-school mathematics teachers. The analysis is grounded in a design experiment in the context of teacher development where the teachers' understandings of statistical data analysis, in particular distribution,...

In this paper, we document the iterative cycles of design research conducted to support the learning of a group of middle school mathematics teachers. The goal of the research team was to support the teachers' ability to reason statistically about data. In this process, understanding the teachers' instructional reality became crucial for conducting...

During the past two years, we have been engaged in a collaborative effort focused on improving middle-grades statistics instruction in the Madison School District in Phoenix, Arizona. Part of our work has entailed rethinking what might constitute an instructional “unit” that highlights the importance of students' engaging in genuine data analysis w...

This article provides an analysis of a teaching experiment conducted in the context of teacher education designed to support preservice teachers' understandings of place value and multidigit addition and subtraction. The experiment addresses the following research question: Can the results from research conducted in elementary mathematics classroom...

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...

This paper reports the analysis of performance assessment tasks administered in a seventh-grade classroom. The purpose of the assessments was to obtain data on students’ current statistical understandings that would then inform future instructional design decisions in a classroom teaching experiment that focused on statistical data analysis. The ta...

The 2 episodes featured in this issue provide a rich setting in which to investigate not only the influence but also the confluence of students' and teacher's understandings on the quality of whole class discussions. In particular, I focus on the communication between the students and myself as the teacher in the classroom. This unique perspective...

The analysis reported in this paper contributes to the effort to understand how mathematics teachers might proactively support their students' mathematical learning by documenting one first-grade teacher's role in guiding the development of sociomathematical norms in her classroom. We highlight the learning opportunities that arose for both the tea...

The purpose of this paper is to describe the role of an instructional sequence and two accompanying computer-based tools in supporting students' developing understandings of statistical data analysis. In doing so, we also take account of the role of the data creation process in supporting students' ability to engage in genuine data analysis. Data i...

Our purpose in this chapter is to outline a general approach to collaborating with teachers in order to support the establishment of a professional teaching community. As will become apparent, our goal is to help teachers develop instructional practices in which they induct their students into the ways of reasoning of the discipline by building sys...

The classroom that is the focus of the analysis reported in this paper was the site for a year-long first-grade teaching experiment. The goal of the classroom teaching experiment was to investigate ways to proactively support students' ability to develop strategies for adding and subtracting quantities. In addition, the project also focused on the...

The National Council of Teachers of Mathematics has been advocating the importance of effective communication in classrooms since the release of its Standards documents (NCTM 1989, 1991). This emphasis is echoed in Richards's (1991) description of an inquiry classroom (see also, e.g., Ball [1993]; Cobb, Wood, and Yackel [1991]; Lampert [1990]). In...

In this article, we describe an approach for documenting students' mathematical development in the social context of a classroom over a prolonged period of time. Our theoretical perspective is based on the view that the ways in which children participate in classroom discussions are influenced by their views of themselves as members of the classroo...

Ongoing discussions about students' experiences with data analysis include debates about the role of graphical representations in supporting students' understandings (Shaughnessy 1992; Lehrer and Romberg, in press; Hancock, Kaput, and Goldsmith 1992). More specifically, do students first need to know how to construct various types of graphs before...

The analysis in this paper focuses on the relationship between classroom discourse and math- ematical development. We give particular attention to reflective discourse, in which mathematical activity is objectified and becomes an explicit topic of conversation. We differentiate between students' development of particular mathematical concepts and t...

The analysis in this paper focuses on the relationship between classroom discourse and mathematical development. We give particular attention to reflective discourse, in which mathematical activity is objectified and becomes an explicit topic of conversation. We differentiate between students' development of particular mathematical concepts and the...

In this article, we describe an analytic approach for situating teachers’ instructional practices within the institutional settings of the schools and school districts in which they work. In doing so, we draw on an ongoing collaboration with a group of teachers in an urban school district to illustrate both the approach and its usefulness in guidin...

In this paper we document the importance of institutional context in both constraining and enabling the work of mathematics teachers. We build from our current and ongoing collaborative efforts with middle-grades mathematics teachers to provide an analytic approach and resulting analysis that clarifies the critical role of institutional context in...

This paper provides an analysis of a Teacher Development Experiment (Simon, 2000) designed to support teachers' understandings of statistical data analysis. The experiment addresses the following research question: Can the results from research conducted in a middle-grades mathematics classroom be used to guide teachers' learning? In both cases, ac...

DISCUSSIONS of the role of algorithms in the elementary school curriculum give rise to conflicting notions of how algorithms should be approached in the classroom. These views range from encouraging students to invent their own algorithms with minimal guidance to teaching students to perform traditional algorithms. In this paper, we will discuss an...

School District pschmitt@msd38.org The lack of current theories to guide analyses of the interplay between teaching and texts (cf., Ball and Cohen, 1999; Goldsmith and Schifter, 1997; Simon, 1997) became problematic in our ongoing professional development work with teachers. In order to address this problem, we began the development of an interpret...

## Citations

... analyzed the extent to which the intellectual authority in the classroom was vested in mathematical reasoning rather than the teacher or text. A learning environment embodying the norm of accountability to the discipline regularly encourages students to account for how their ideas make contact with those of other mathematical authorities, both inside and outside the classroom (Cobb et al. 1997;Lampert 1990). Each lesson was assigned a score of from 0 to 2, depending on the extent to which the majority of the students had such opportunities, where 0 meant that judgments of correctness derived from the teacher or the text and 2 meant that judgments of correctness derived from mathematical reasoning. ...

... The second point for the redesign is to pay more attention to reasoning with the simulated sampling distribution in various situations and not automatically use the 95% area. Discussion on students' analyses and not only on the results will support students' development of strong mathematical arguments (McClain, McGatha, & Hodge, 2000). ...

... For a time, however, some of the aspects of these programmes remained implicit and were not theorised, even as they were essential to making the transformation possible. These included changes in the norms of a classroom discourse (McClain & Cobb, 1998), or the role that an alignment of the goals of the research programme with the school's curricular goals played (Franke, Carpenter, & Battey, 2008). Instead, the success was primarily attributed to sharing with the teachers the analysis of mathematics involved, and of how students may come to reason with it. ...

... Rather, research work that follows the socio-constructivist paradigm has used the classroom as a unit of analysis, and has shown the effectiveness of group-work and classroom discourse in promoting students' conceptual change and understanding (e.g. Cobb et al., 1991Cobb et al., , 1997Yackel, 1996). ...

... MethodSince the potentiality of PWWs for proof activities has remained so far conjectural, we decided to adopt the DBR paradigm as our main methodological underpinning(Cobb et al., 2001;Bakker, 2018). The DBR, organized in research cycles through which Content courtesy of Springer Nature, terms of use apply. ...

... Research studies show that the advancement of teacher knowledge is greatly enhanced by the efforts of school community to improve teacherstheir understandings of mathematics teaching and learning (e.g. Cobb, & McClain, 2001;Sherin, 2002). Mathematics teachers should be supported by everyone involved in mathematics education including policymakers, as well as students themselves to enhance students' mathematical proficiency (Anthony & Walshaw, 2009). ...

... Then the students were given several questions in the textbook, then mentions the data that the highest and lowest of data only, The problems encountered; the learning-based realistic mathematics education can be an alternative solution. This is evidenced by several studies that have been carried out by previous investigators, such as Mcgatha & Cobb (2016), Headlines an Analysis of Statistical student Understanding was able to create a statistical learning process interesting and meaningful learning. Then Walle (2013) titles of books and Middle Elementary School Mathematics Teaching Development. ...

... However, substantive research papers on the DNL are rare. We have found some interesting studies (e.g., Moss and Case, 1999;Misailidou and Williams, 2003;Corina, Zhao, Cobb and McClain, 2004;Orrill and Brown, 2012), but often the DNL plays only a small part in the research or the tasks used are not particularly well designed or implemented. ...

... But Chazan and Ball (1999) expressed "frustration at the current education discourse about the teacher's role in discussion-intensive teaching" (p. 2) highlighting that there are times when teachers need to tell things to their students, such as the conventional mathematical terminology that describes ideas students are proposing. McClain and Cobb (2001) followed a teacher who felt it was important to accept all student contributions equally, but at the cost of not contrasting contributions or indicating that some contributions might have different value than others. While it may be undesirable to tell students how to proceed, it may also be undesirable to validate everyone's solution method and thereby not guide the students' mathematical development. ...

... Formulas, and symbolic language in general, play a key role in creating, applying and communicating mathematical knowledge in classrooms (Cobb et al., 2000;Steinbring, 2005). This goes in particular for upper secondary teaching, where general relationships and formulas are set up, proven and applied in a variety of particular examples, contexts and problems (Kieran, 2007;Schou, 2017). ...