SPEAKER: Dr. Joseph Tripp, Assistant Professor, Department of Mathematics
TITLE: Some Characteristics of a Radically Reformed College-Level
Franke et al. (1997) say that “the vision of mathematics portrayed in the reform documents requires students to think differently from the way they currently do about the nature of mathematical knowledge” (p. 8). For example, as McLeod (1992) points out, “current efforts at curriculum reform place special emphasis on solving non-routine problems, on applying mathematics in new situations, and on communication regarding mathematical problems” (p. 591). In addition, according to Romberg (1995), “the central feature of the current reform efforts involves an epistemological shift from the mastery of a set of concepts and procedures to mathematical power” (p. vii). Romberg’s notion of mathematical power is consistent with the concept as it is presented in the NCTM Standards (1989). In the Standards, mathematical power refers to “an individual’s abilities to explore, conjecture, and reason logically, as well as the ability to use a variety of mathematical methods effectively to solve non-routine problems. This notion is based on the recognition of mathematics as more than a collection of concepts and skills to be mastered; it includes methods of investigating and reasoning, means of communication, and notions of context. In addition, for each individual, mathematical power involves the development of personal self-confidence” (p. 5).
Based on the vision for students to attain mathematical power, reform-based mathematics classrooms must reflect a dramatic change in curriculum. Koch (1994) suggests that a classroom characterized by students working in small groups on non-textbook problems, students writing out and discussing detailed descriptions of what was involved for them in solving the problems, and instructors listening to individual and small groups of students while they work on problems is reflective of a reform-based mathematics classroom.
In the Fall of 1996, the Basic Algebra course offered at Syracuse University was radically reformed. Prior to the change, basic algebra at Syracuse had been taught in a traditional lecture based format for several years. The emphasis in the traditional approach had been on learning procedures and developing basic algebra skills. The reformed approach to teaching basic algebra, however, is based on the philosophy that students will effectively learn mathematics as they engage in problem solving activities in the context of cooperative learning groups. The emphasis in the reformed version of the course is on gaining conceptual understanding of the content of the course. The mathematics embedded in the problem solving activities constitutes the content of the course and is learned by becoming engaged in the activities. There is, therefore, little transmission of knowledge from the teacher to the student. Ideally, when a student asks the teacher a question, the teacher’s task is to turn the question back to the student or the student’s group. In this reformed approach to teaching, the teacher serves as a facilitator of student learning rather than the expert who transmits knowledge to the students.
The use of advanced technology is a significant feature of the reformed algebra course at Syracuse. During my involvement with the course, the Texas Instruments TI-92 was used in learning and doing mathematics both in and out of class. This calculator was also used on all quizzes and exams.
I began teaching the reformed algebra course at Syracuse during the Spring 97 semester. Whereas I had previously taught about a dozen different mathematics courses, this was to be my first experience teaching a radically reformed course in mathematics. Consequently, I felt some degree of trepidation as I considered how the students in my class were going to learn the content without me teaching them. In my presentation, I will discuss some of the characteristics of the reform-based mathematics course that I was involved in developing and teaching while I was a graduate student at Syracuse University.
Franke, M., & Carey, D. (1997). Young Children's Perceptions of Mathematics in Problem-Solving Environments. Journal for Research in Mathematics Education, 28(1), 8-25.
McLeod, D. (1992). Research on Affect in Mathematics Education: A Reconceptualization. In D. Grouws (Ed.). Handbook of Research on Mathematics Teaching and Learning. (pp. 575-596). New York, NY: Macmillan Publishing Company.
Romberg, T. (1995). Reform in School Mathematics and Authentic Assessment. Albany, NY: State University of New York Press.
National Council of Teachers of Mathematics. (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, Va: The Council.
Koch, L. (1994). Reform in College Mathematics. Research on Teaching in Developmental Education, 10(2), 101-108.
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