Dancing at two weddings: A case study of mathematics reform

Karen J Rothschild, University of Pennsylvania

Abstract

Recent years have seen an ongoing effort to reform mathematics education spearheaded by the National Council of Teachers of Mathematics (NCTM). However, NCTM neither offers curricula nor clearly outlines the theoretical structure of the reform. This dissertation addresses theoretical and practical questions about the reform by proposing a conceptual perspective and analytical framework for understanding mathematics curriculum and instruction. Using the proposed framework, one reformed 7th grade math course was studied. Data for the study were collected using ethnographic methods including observation and audio taping of class sessions, interviews, and collection of classroom artifacts.^ Four major arguments are made. The first is that school mathematics can be understood in terms of a paradigm that includes a body of knowledge as well as generally unspoken social norms that govern how work in the discipline is conducted (Kuhn, 1970). The proposed analytical framework divides mathematical activity into four major categories, labeled knowledge, ways of thinking, beliefs and values, and stance, derived from Kuhn, from research on mathematics education, and from empirical observation. Knowledge encompasses what is usually considered the 'content' of a course. Ways of thinking include reasoning processes such as exploring, conjecturing, modeling, symbolizing, explaining, arguing, proving, and critiquing. Beliefs and values refer to ideas about what kinds of knowledge and practice are considered legitimate and important within the discipline. Stance refers to affective states which influence students' work.^ The second and third arguments, derived from the empirical study, claim that the observed course was consistent with NCTM's goals for reform and that it immersed students in a mathematical paradigm different from and sometimes in conflict with the paradigm implicit in traditional school math. The final argument claims that because this course was unique, students in the class were unfairly asked to do mathematics in two often conflicting paradigms, one in the observed course and another underlying all their other math courses.^ In sum, this dissertation provides an analytical framework for understanding classroom mathematical activity as well as a description and analysis of one model of reform in practice. Implications for students and educators are discussed. ^

Subject Area

Education, Mathematics|Education, Administration|Education, Curriculum and Instruction|Education, Philosophy of

Recommended Citation

Karen J Rothschild, "Dancing at two weddings: A case study of mathematics reform" (January 1, 1997). Dissertations available from ProQuest. Paper AAI9727288.
http://repository.upenn.edu/dissertations/AAI9727288

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