Mathematics Education: Exploring the Culture of Learning
reviewed by Vicky L. Kouba - 2005
Title: Mathematics Education: Exploring the Culture of Learning
Author(s): Barbara Allen and Sue Johnston-Wilder
Publisher: Routledge/Falmer, New York
ISBN: 0415327008, Pages: 245, Year: 2004
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Mathematics Education: Exploring the Culture of Learning is a collection of previously published articles intended as catalyst readings for post-graduate students and mathematics educators. The editors, Barbara Allen and Sue Johnston-Wilder from The Open University state that they do not envision that any reader would work their way through the book from start to finish (p. 4); but see the book more as one readers would dip into for particular interests and then read more widely around. Allen and Johnston-Wilder have made a judicious choice of fourteen articles and structured them into three sections (culture, communications, and perceptions) each with an introduction and a short list of suggested further readings. Ten of the articles were first published between 1997 and 2001. The remaining three articles were published in 1984, 1990, and 1994.
The book offers, in a readily accessible form, a sample of the core ideas from some of the leaders in the areas of the culture of mathematics classrooms (including equity and social justice by such authors as Ernst, Pollard, Povey and Burton, Watson, Cooper and Dunne, and Goos, Galbraith, and Renshaw ); communication in mathematics classrooms (including linguistics, representation, and technology by Zevenbergen, Morgan, Houssart, and Hoyles ); and pupils and teachers perceptions (such as conceptions of mathematics, the learning of mathematics, and agency/identity by Thompson, Boaler, Reay and Wiliam, and Allen). The majority of the chapter authors write from a UK perspective, but the topics and reported research have international links and implications.
Allen and Johnston-Wilder seem to view the structure of the book as beginning with the culture section that serves as an overview for aspects of culture in the classroom, followed by sections containing research on two major mediating variables of classroom culture communication and human perceptions. I see the collection of articles as being much more cohesive than Allen and Johnston-Wilder suggest. The first two articles in the first section provide a philosophy and action foundational perspective on the culture of mathematics classrooms. Ernst (pp. 12-25) provides the philosophical perspective on the need to change the negative image communicated by the mathematics classroom, and Pollard (pp. 26-42) provides the sociological perspective. Each concludes with actions to be taken. However, in contemplating the actions, one has to look more closely at the major players: the students (Povey and Burton with Angier and Boylan, pp. 43-56), the teachers (Watson, pp. 57-68), and the content (Cooper and Dunne, pp. 69-90). Thus, the emergent structure for the first section of the book could be seen as David Hawkins (1974/2002) classic I-thou-it triangular relationship among the student, the teacher, and the mathematics.
For me, the four articles in the second section, communication (Chapters 7-10), provide four different perspectives on voice as a theme. Zevenbergen (pp. 119-133) presents the case for working-class students who are denied access to the mathematics because they do not know how to find voice within the advantaged structures of discourse that dominate the mathematics classroom. Morgan (pp. 134-145) presents the case for students whose access to mathematics and mathematical explanation is through diagrams. When diagrams are valued less than verbal communication or are viewed as signs of low-ability (p. 135), the visual communicators in the classroom are silenced. Houssart (pp. 146-158 presents the story of the whisperers (p. 146), those students who find their voice in unsolicited, often whispered, comments that run as a parallel discourse beneath the regular classroom discourse. What is silenced for the whisperers is discussion and acknowledgement of the deeper understanding of the mathematics that their whispered comments demonstrate. Hoyles (pp. 159-172) addresses technology as a means for giving voice to students own development of proof. Hoyles makes the case that the proper computer software can give voice to students who have been reared in an investigative culture and who want to explain but lack the tools to do so.
The perspectives section examines the effects of teachers perceptions of mathematics, students and teachers perceptions of contrasting classroom settings, and students perceptions of self and mathematics as influenced by assessment. This structure returns to an I-thou-it frame but adds the dimension of context or classroom setting. Some might wonder at the inclusion of Alba Gomez Thompsons 1984 article (pp. 175-194) on the relationship of teachers conceptions of mathematics and teaching to instructional practice in the classroom, but the article was a pivotal one in the history of research on teachers conceptions. In the continuing debate on the effect of teachers conceptions and perceptions on instruction, one can hear echoed the questions Thompson (p. 192) raised in her recommendations for future research: whether differences in the composition of the class or content bore any relationship to differences in teachers professed conceptions and their characteristic instructional patterns whether or not teachers conceptions are likely to change whether or not differences in teachers conceptions have an effect on the conceptions of mathematics of their students. Boaler (pp. 195-218), Reay and William (pp. 219-232), and Allen (pp. 233-241) answer, to a certain extent, some of Thompsons questions. Students views of themselves as learners and their view of mathematics are effected by teachers perspectives, comments, assessments, and values sometimes subtly as in Bolars look at the complexity of ability-level tracking (setting and streaming) students; and sometimes painfully overtly as in Reays and Williams Ill be a nothing.
As a graduate school faculty member for master-level degree programs for teachers, and doctoral-level degree programs for teachers of teachers, I envision using the Allen and Johnston-Wilder book with How People Learn: Brain, Mind, Experience, and School (Bransford, Brown, and Cocking, 2000) and the mathematics chapters from How Students Learn: History, Mathematics and Science in the Classroom (Donovan and Bransford, 2005). In How People Learn, Bransford et al. posit four interrelated attributes of learning environments that need cultivation (p. 23): schools and classrooms should be learner-centered, content-centered, community-centered and assessment-centered. Although the Bransford et al. book has depth in the psychological perspective, it does not present the same level of depth in the sociological perspective. Mathematics Education: Exploring the Culture of Learning gives depth to the social and cultural aspects of the context for learning mathematics, while mapping well to the four interrelated environmental aspects listed above. I would then use Allens and Johnston-Wilders book as a foundation for doing a sociological examination of assumptions made about students and the culture of the classroom in the two chapters from How Students Learn. I think the articles in Mathematics Education: Exploring the Culture of Learning provide the language, theory, and structure needed to give students voice to their struggle to integrate what we know about the psychology of student learning into the very real and challenging culture of classrooms.
I found Mathematics Education: Exploring the Culture of Learning to be useful, coherent, and cogent.
Bransford, J.D., Brown, A. L., and Cocking, R.R. (Eds.) (2000). How people learn: brain, mind, experience, and school. Washington, DC: National Academy Press.
Donovan, M.S. and Bransford, J.D. (Eds.) (2005). How students learn: History, mathematics and science in the classroom. Washington, DC: National Academy Press.
Hawkins, D. (1974/2002). The informed vision: Essays on learning and human nature. New York: Agathon Press.