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This article was downloaded by: [University of Kent]On: 23 November 2014, At: 17:54Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number:1072954 Registered office: Mortimer House, 37-41 Mortimer Street,London W1T 3JH, UK
Mathematical Thinking andLearningPublication details, including instructionsfor authors and subscription information:http://www.tandfonline.com/loi/hmtl20
Book review of ThinkingPractices in Mathematicsand Science LearningGerald KulmPublished online: 18 Nov 2009.
To cite this article: Gerald Kulm (1999) Book review of Thinking Practices inMathematics and Science Learning, Mathematical Thinking and Learning, 1:4,315-320, DOI: 10.1207/s15327833mtl0104_3
To link to this article: http://dx.doi.org/10.1207/s15327833mtl0104_3
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MATHEMATICAL THINKING AND LEARNING, 1(4), 3 15-320 Copyright O 1999, Lawrence Erlbaum Associates, Inc.
BOOK REVIEW
James G. Greeno and Shelley V. Goldman (Eds.), Thinking Practices in Mathematics and Science Learning, Mahwah, NJ: Lawrence Erlbaum Associates, Inc., 1998, 429 pp. ISBN 0-8058-1 659-3 (cloth); ISBN 0-8058-1 660-7 (paper).
Reviewed by Gerald Kulm Department of Educational Curriculum and Instruction
Texas A M University
The title of this book: is intriguing and of potential interest to nearly anyone in mathematics or scieme education. The notion of an in-depth treatment of some- thing so basic and important as how people think about mathematics and science or how they think when they are learning or doing mathematics or science is in- deed important.
A key challenge in reviewing an edited book is to give a sense of how well the book works as a whole in achieving a purpose above and beyond the presentation of a set of chapters. 111 addition, of course, most readers are interested in the con- tents, strengths, and weaknesses of individual chapters. The first part of this re- view outlines the puxpose, organization, and potential barriers. The second part provides highlights aid comments on the chapters themselves.
The preface to thehook provides ahint ofthe purpose, stating that, instead ofindi- vidual thinking activiiy, the content deals with thinking as an aspect of social prac- tice, integrating theories of thinking with theories of social interaction in considering students' study of mathematics and science. Bringing together two ar- eas of work in this wa.y has had significant dividends for mathematics and science education inthe past. For example, the effort in themid- to late-1 970s to integrate the methodology and theories of teaching experiments and interviews with emerging theories in mathematics problem solving, numerical understanding, and rational number learning led to new areas of research and classroom practice. Similarly, the integration oftheories and practice of cognitive science with several areas ofworkin
Requests for reprints st~ould be sent to Gerald Kulrn, Texas A&M University, Harrington Tower, MS4232, College Station, TX 77843. E-mail: [email protected]
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mathematics and science learning has led to important advances in our understand- ing ofhow children develop and construct meaning in mathematics and science and how people use their knowledge to solve problems in these disciplines.
It is, of course, far too early to speculate whether, as the editors believe, the inte- gration of theories proposed in this book has the potential of these earlier efforts to become a coherent body of research and practice. The editors, along with some of the chapter authors, had key roles in the earlier work, integrating useful theories and methods, then extending and building the ideas to develop new theories and findings. Given this background, it is natural for the reader to have very high ex- pectations for this book. On the other hand, there are also some built-in barriers that can dampen f'le potential impact of a book such as this one. Although the edi- tors can help the reader to negotiate these barriers, some are more difficult than others. The ideas presented in the introduction to the book are clear and compel- ling; however, there are variations in how well they are illustrated, discussed, and implemented in the individual chapters.
The book was tieveloped through a project directed by the editors, consisting of a series of meetings attended by the authors and culminating with papers prepared for a final symposium. Unlike some previous similar efforts, these authors are not representatives of two relatively distinct research communities. Most of them are researchers whose work in mathematics or science teaching or learning already fits reasonably well ullder a thinking-practices umbrella. Although one or two chap- ters report new or ongoing work that was done as part of the project, the intent seems mainly to explore, reinterpret, and possibly tighten the relation of each au- thor's work with thinking-practice theory. The organization of the book attempts to continue the conversations and collaborations that were begun in the syrnpo- sium. The chaptens are divided into two parts: One set of four chapters deals with how students and teachers participate in communities of thinking practice, and the other set of seven chapters illustrates cases of thinking practices in different set- tings. After every lwo or three chapters, the editors or other authors offer an inter- pretive chapter to help clarify and point out important ideas and contrasts.
What barriers might there be to this book making a compelling case for the importance of ma1,hematics and science thinking practices as an emerging field of study? It is difficult for the printed word to convey the context, shared experi- ences, and thinking practices from the meetings and symposia. A prerequisite is that the reader understand the theories themselves, in this case, theories on thinking as social practice and theories on how to foster students' thinking in mathematics and science. The naive reader must work hard to appreciate the full import and implications of an unfamiliar field of study. The editors acknowledge this, introducing the book by saying that readers may not have heard of thinking practices. Although the introductory chapter attempts to provide a primer on the subject, mentioning key ideas and results, there are many new ideas for the reader to considex and pull together.
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The collection of authors in an edited book provides opportunities for interest- ing and insightful ideas as well as--especially for a volume that combines new theories-the potential jbr variations in style and message that can interfere with a reader's focus on the central purpose of the book. The frequent interpretive chap- ters can help to ameliorzite these variables or even distract the flow, but the success of the book lies mainly in the individual chapters themselves.
In an attempt to illusixate a variety of implications for the ideas, there is the dm- ger that none of them is sufficiently developed. In addition to addressing both mathematics and science, which themselves have a limited history of cooperative work on teaching and learning, the book includes attention to teacher develop- ment, classroom discourse, conceptual change, problem solving, teacher demon- strations, and electronic tools. A special challenge for writing about the social aspects of thinking prrtctices is communicating the richness and complexity of thinking in classrooms, among groups of teachers, or on the Internet. The reliance on transcripts, excerpts from student work, summaries of meetings, and reflective reports all present difficulties that can be only partially overcome by careful selec- tion of examples and clear organization and interpretation by the author or editor of the chapter.
The following discu,ssion of individual chapters follows their order in the book and the editor's organi;:ational scheme, providing a sense of how the chapters were intended to present key ideas related to the notion of thinking practices. Nearly ev- ery chapter offers useful ideas, and most of them offer new ideas or at least new perspectives on familiar ideas about learning and teaching mathematics and sci- ence. Nonetheless, the chapters are somewhat uneven in offering clarity and focus for the notion ofthinking practices. There is sometimes a "now you see it, now you don't" feeling across the chapters. The intervening discussant chapters are some- what helpful, especial iy in providing information about the early discussions that led to the papers and ir. extending the interpretation of the papers in the light of the- ories of thinking. Overall, the book is probably most effective if the related chap- ters are read together. Connections across the chapters are less clear, and it is even possible to get the impression that the construct thinking practices is such a broad idea that it can mean ;ilmost anything.
For those readers who know Silver's QUASARproject and the work ofLampert, their chapters offer a familiar starting point in the book and serve to illustrate two ex- amples of thinking pritctices by mathematics teachers. Stein, Silver, and Smith use the perspective of thinking practices to describe, in case-study fashion, the thinking and developing culture of a group of teachers in one school district who imple- mented QUASAR over a period of 5 years. Their focus is first on the teacher who provided leadership, then on how teachers became old-timers and on how newcom- ers were brought into the community, and finally, on how they participated in the practice of reform. One particular aspect of thinking practice used in the chapter is storytelling, which, according to theory, can be important in supporting the forma-
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tion of acohesive community. The chapter documents several types of storytelling, from classroom anecdotes to professional presentations, that characterized the in- duction and acceptance ofteachers into the project. The authors conclude with sev- eral implications for the contribution of the idea of a community of practice for teacher education, including the support of individual teachers, multiple sources of teacher learning, and motivation for teacher change.
Lampert's offering seems to best reflect the idea of thinking practices in mathe- matics classrooms. Her discussions of the language of fifth graders as they learn mathematics embocly many of the ideas suggested by the anthropological and so- ciological roots of tlhe theory. Although Lampert's primary focus is on the mathe- matics being learned, the development of a community with a common language is evident. In her chapter, Lampert reflects on shifting the focus, considering her own roles as a teacher and researcher, along with her thinking about the nature of math- ematics, the teaching of mathematics, and the responsibility to communicate re- sults of research. Slie discusses the paradox of being both inside and outside the practice of teaching: One learns to teach mathematics only by engaging in teach- ing, but what is known cannot be taught except to others who know it. Lampert concludes that, despite the paradox, teachers must form communities of practice if they are to implement the reforms that are necessary in mathematics education.
The next two chitpters conclude Part I and, according to the discussant, empha- size the importance of lived experience to science, a description that is a creative feat in finding comrnon ground in two very different papers. Similar to the detailed self-reflections of ],ampert, the chapter by O'Connor, Godfrey, and Moses de- scribes a classroorrl incident in which a sixth-grade class deals with what to do about one student who forgot to record a data point that was to be used to construct a graph containing the 20 students' data from an experiment. Detailed excerpts from transcripts of two class periods, along with exhaustive interpretations of stu- dents' conversations, illustrate the authors' concerns about developing students' scientific habits of mind. According to O'Connor et al., this development needs school lab experimc:nts to be realistic in requiring common knowledge, authentic- ity, and equal participation by students no matter how long they take or how far they are from the omtent learning goal. The chapter explores the extreme condi- tions necessary for achieving some of the characteristics of thinking practice rather than imposing meaning on students.
After a brief introduction to the idea of what it means to be even a peripheral member of a learning community, Star's chapter explores the inverse-namely, experiences by core members of a community who do not fit with the central con- cerns of their work. Star employs an autobiographical approach to describe an eclectic series of science-related anecdotes and experiences that occurred during an illness she had while writing her dissertation in sociology of medical science. Her conclusion is that experience in communities of practice should include writ-
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ings and biographies that go beyond conforming to a uniform voice or way of thinking about science.
The first three chapters of Part I1 provide instances of thinking practices in vari- ous contexts in which students are learning mathematics or science. The chapter by diSessa and Minstrel1 clescribes benchmark lessons as a genre of teacher-instigated full-class discussions aimed at promoting conceptual change in students. The au- thors claim that such lessons are a genre used by teachers who focus on classroom processes rather than facts. After providing a list of maxims for how these bench- mark lessons are different fiom other lessons, diSessa and Minstrel1 offer a case study of a lesson in physics for a small group of sixth graders. Curiously, although the lesson was spontan,eous (i.e., not teacher instigated) and the class was not typi- cal of its school, the authors insist that the situation should not be viewed as excep- tional. DiSessa and Minstrell progress to a detailed analysis of the lesson transcript, in which they apply benchmark lesson criteria to conclude that develop- ing a student's ability to make judgments and scientific sense should be favored over getting the right imswer.
In their chapter, Hall and Rubin-using video excerpts and journals supplied by Lampert--explore the: structure of classroom participation during a unit on rate. They use specific types of language, activities, and representations established by Lampert as a structure: for analyzing students' participation in classroom thinking practices. Specifically, a special way of representing rates on a number line is used to illustrate how knowledge moves fiom private to local (small group) to public (whole class) settings. The authors conclude that, for these transformations in thinking practice to take place, the participation structures as well as the teacher-researcher stance taken by Lampert are necessary.
The chapter by Saxe and Guberman describes students' thinking as they play an educational game designed to help them learn and practice place-value ideas. The game was invented a; a setting to investigate the notion of emergent goals (i.e., goals formed by children as they bring their knowledge to bear on problems) as a construct for studying how children form their own learning environments. The fo- cus of studying the inieraction of pairs of students playing the game was the nature of problems attempted, the strategies used, and the type of support given or sought by individual members of the pairs. Saxe and Guberman describe some prelimi- nary findings about how students of different ages help one another form goals and solve problems.
The next two chapters deal with the question of what mathematics and science are and what contexl:~ can be used to provide experiences with or examples of mathematical and scientific thinking. A chapter by Lynch and Macbeth promises to address what it means to act and speak scientifically and then uses two cases of teachers demonstratiilg science experiments to students as examples. As the au- thors admit, the dilemmas of concentrating on formal presentation and attempting
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experiences with scientific phenomena are fraught with difficulty. Neither has much chance of helping students learn about scientific thinking.
A more promising approach to making these ideas accessible is given in Schoenfeld's chapter, in which analogies are drawn between learning to cook and learning to think mathematically. In an autobiographical description of how he learned to make pasta and bread, Schoenfeld illustrates parallels to the develop- ment of skills, the role of examples, and memory and representation in doing math- ematics. (The chapter appendix includes his recipes for goat cheese ravioli with red pepper cream sauce and for spaghetti with prawn and chile pesto, making this volume perhaps thle first one to combine mathematics and science education with a cookbook.)
The final two chapters extend the idea of thinking practices via electronic me- dia. Brown, Elleqi, and Campione describe features of a community of learners classroom, with special attention given to the role of experts and novices through e-mail interaction. Using transcripts of e-mail exchanges, the authors describe and categorize various examples of experts providing different types of information and guidance to students who are learning science. Brown et al. conclude with some conditions that are conducive to the use of e-mail in communities of learners.
Another type of electronic interaction is described by Riel, whose chapter on electronic networking focuses on learning circles, which are geographically di- verse classrooms joined by the selection of a curricular theme. A cycle of activities for opening the circle, interacting and exchanging information, and then closing the circle is described and exemplified by excerpts of exchanges among schools conducting a projt:ct on pollution. The chapter includes a discussion of implica- tions for knowledge construction, teacher development, and workforce skills.
Fresh and clear perspectives are needed to study and interpret the complex world of teachers' and children's thinking as they communicate about and learn mathematics and science. The editors and authors of this book have succeeded in bringing together a diverse and important set of ideas that can provide these new perspectives. The use of social interaction theories appears to have promise for guiding the analysis and interpretation of the rich and complex data that arises from classroom observations, videotape studies, interviews, and similar research methods.
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