Ellice Ann Forman

Orchestrating the Multiple Voices and Inscriptions of a Mathematics Classroom

The purpose of this article is to explore how inscriptions are used to create argumentative positions in the 2 classroom episodes, Batteries and AIDS. This activity is similar to a prominent practice of scientific communities: the use of inscriptions to advance knowledge claims. We begin by discussing the meaning and function of inscriptions in scientific communities and then apply some notions from the history and sociology of science to our analyses of the case study data in the 2 episodes. In addition, we address some of the challenges for teachers in incorporating scientific practices into their classroom activities. Among these challenges is the need to alter the nature of the problems and inscriptions used as well as change classroom discourse structures. In our analyses of the 2 episodes, we found that the classroom activities resembled those of scientific communities in several ways: Real-world, dilemma-driven problems were presented; students evaluated the inscriptions offered in terms of their adequacy for advancing particular knowledge claims; and the teachers helped their students reflect on, clarify, expand, evaluate, oppose, or integrate each others explanations into their argumentative positions. We also found that the teachers legitimated student contributions to the discussion by revoicing their arguments. Despite the positive findings from our analyses, we were able to identify and illustrate one additional challenge for future design experiments: How do we orchestrate the multiple voices of the classroom in an equitable fashion while pursuing our instructional goals?

The Multiple Voices of a Mathematics Classroom Community

Several mathematics educators have expressed their concern about conflicting visions of educational reform among parents and teachers, which could result in the emergence of multiple voices in discussions of achievement and instruction. The aim of this article is to examine the multiple voices of educational reform in the discourse of a third grade classroom community. In order to achieve our aim, we integrated the social and the individual as well as the past, present, and future in our analysis of the discourse in this classroom community using theoretical frameworks and methods from cultural psychology. Although our analyses focused on the classroom teacher, we employed units of analysis capable of bridging the individual and her social context. We began our analysis by focusing on a sample of whole-class discussions of students’ strategies for solving multidigit word problems. This analysis isolated two distinct voices: one that occurred during discussions of students’ invented strategies and the other that emerged during talk about standard algorithms. We extended our analysis to include information about the historical, social, and institutional context of the classroom community in order to understand the origins and functions of these two voices. This additional information helped us appreciate the interconnections between the teacher’s personal feelings, beliefs, recollections, and expectations; and her interpersonal transactions with her students, their parents, and other educators. We concluded with a discussion of the implications of the study for understanding one of the dilemmas of educational reform and for advancing research in classroom discourse.

Learning what counts as a mathematical explanation

Abstract Instructional practices are being transformed in many mathematics classrooms as a result of reform efforts in the United States and Europe. For example, students are being asked to take a more active role in explaining their problem solution strategies. In order to achieve these changes in student activity, teachers are being encouraged to restructure the communication patterns in their classrooms. The goal of this article is to examine, in detail, the discourse of one teacher and three of her middle school students during a single lesson on area measurement. Some concepts from sociocultural theory (e.g., authoritative versus internally persuasive discourse) are used to organize and interpret our analysis. The teacher observed in this study, tried to share responsibility and authority for explaining and evaluating mathematical problems with her students. We found that two of the three students initially tried to present explanations that differed from that used by the teacher on a previous day. Each time these students offered an alternative solution strategy, the teacher overlapped her speech with theirs. Eventually both students employed the teachers explanation. The third student who used the teachers explanation from the beginning did not encounter her overlapping speech. As a result of our analyses, we concluded that the teacher did achieve one of her goals for this lesson, the sharing of responsibility for providing explanations, but not the goal of sharing authority. The theoretical and instructional implications of our analysis for research on educational reform are addressed.

Assisting Teachers and Students to Reform the Mathematics Classroom.

This study examines the usefulness of selected aspects of Tharp and Gallimores (1988) theory of assistance as a theoretical framework for describing and analyzing change efforts in a middle school mathematics reform project. Drawing upon Tharp and Gallimores redefinition of teaching as assisting performance and learning as the result of assisted performance, the social organization of a school-based mathematics reform effort in which teacher educators, mathematics teachers, and students both assist and are assisted is analyzed. In addition, one particular classroom assistance activity is presented and analyzed in terms of characteristics of assistance that, according to the theory, should lead to significant learning.

Discourse Analysis A Sociocultural Perspective

Discourse analysis is one of the principal methodologies of sociocultural research in education. sociocultural research focuses on understanding how cognitive, social, cultural, affective, and communicative factors influence instruction. we review how sociocultural theory conceptualizes teaching and learning, some fundamental constructs of both the theory and the methodology, and the basic guidelines for discourse analysis. we discuss the applications of sociocultural theory and discourse analysis to remedial and special education by focusing on three areas of research: the social construction of disability, contingent instruction between adults and learners, and miscommunication between adults and working class or minority students.

“Nothing's a Gift, It's All on Loan”: Remembering Randi Engle

We are sad to report that Randi Engle died at the age of 45 at home in Berkeley, California on October 26, 2012 after more than two years of battling with pancreatic cancer. She had served as an Associate Professor in Cognition and Development in the Graduate School of Education at the University of California, Berkeley and published many influential papers in prominent journals in the learning sciences. Her survivors include her husband, Thomas Kuhn, and their two daughters, Rebecca Engle and Gwendolyn Kuhn; her brother, mother, father, and stepmother. Randi made outstanding contributions to the learning sciences. We two were privileged to have the pleasure and good fortune to collaborate with her at different times in her life. Thus, we decided to write separate parts of this professional memorial to Randi’s career.

The Dialectic between Embodied Experiences and Mathematical Concepts

In their article, Saxe, de Kirby, Kang, Le, and Schneider [this issue] address a crucial issue in children’s mathematical development: how to understand the dialectic between everyday (embodied experiences) and scientific concepts (verbally defined, specialized disciplinary vocabulary). In other words, how can we conceptualize the interplay between bottom-up and top-down learning processes in a classroom community? Although this issue was identified by Vygotsky [1987] 80 years ago, detailed descriptions of its microgenesis 1 are rare. In addition to articulating the dynamics of this dialectic, Saxe and his colleagues demonstrate how it was used to support students’ understanding of several mathematics concepts that have been shown to be difficult to learn (e.g., equivalent fractions). To illustrate their analytic approach, Saxe et al. draw from a corpus of data collected over 19 lessons in one fifth-grade classroom located in California. Despite their single case study design, they argue that the process by which they conceptualized students’ learning could generalize to other classrooms and other content areas. To support this claim, they mention Saxe’s previous research in culture and cognition

Reassessing the Nature of Learning in a Science or Mathematics Classroom

The nature of learning, dominated by behaviourist models in the first half of the 20th century, became more complicated in the second half with the cognitive revolution (Harre & Gillett, 1994). In the 21st century, new paradigms for learning are emerging, making the nature and evolution of learning a site of controversy. For example, Sfard (1998) presents two metaphors for learning mathematics— learning as acquisition versus learning as participation. Others have also proposed alternative models of learning (e.g., Kirshner, 2002; Lehrer & Schauble, 2006).

Engendering a Learning Motive in East Harlem

Once upon a time, at a New York City after-school program in East Harlem, there was a teaching experiment conducted by several researchers in collaboration with an elementary school teacher. Before the teach-to-the-test accountability fervor of the early 21st century in the United States, these teacher-researchers, like their less theoretically grounded peers engaged with similar ideas, were inspired to design and implement a social studies curriculum that built on children’s interest in and knowledge of their own local community and its historical origins. The original experiment, reported in this book, entailed a little less than 40 hourly sessions from September to May and involved approximately fi fteen children from 8 to 12 years of age. The two authors of this book were involved in the teaching experiment as were several other researchers [see Pedraza & Ayala, 1996]. This teaching experiment was derived from a theoretical perspective on children’s learning and development originally articulated by several Russians: Vygotsky, El’konin, and Davydov. It was also based on similar work that had been conducted in Denmark [Hedegaard, 1998]. Is this another example of a laborand resource-intensive progressive teaching experiment, which fl ourished for a brief time in an unexpected environment and then sank from sight (except as an item in several academic resumes)? Or is this a project that had strong enough legs (suffi cient theoretical grounding and empirical support) to travel? How does it compare with other on-going educational design experiments? These were the questions I asked myself when I began reading the book, and these are the questions I address in this essay review. I begin by explaining the authors’ notion of radical-local teaching and learning and summarizing its application to the East Harlem after-school project. Then, I compare this short-term after-school project with two other long-term and in-school projects to see whether its major innovations continue elsewhere, perhaps in a more sustainable fashion.

The Practice Turn in Learning Theory and Science Education

Recent developments in learning theory, referred to as the “practice turn” have suggested incorporation of disciplinary practices into classroom instruction. Instead of relying on a set of disembodied laboratory procedures and teacher-centered didactic instruction, advocates of this pedagogy propose that teachers and students create a new activity system that supports an epistemic culture for authentic scientific inquiry. It introduces students to the creative aspects of scientific practices through engagement in activities that involve representing, explaining, persuading, testing models, and making sense of scientific inquiry. Research in learning theory, science studies, and science education that has been used to articulate the practice turn in science education is reviewed and critiqued in this chapter.