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**SPEAKER:** **Dr. Joseph Tripp, Assistant
Professor, Department of Mathematics**

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**TITLE: ***Some
Characteristics of a Radically Reformed College-Level *

*Mathematics Course*

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**ABSTRACT:**

*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.

**References**

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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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**REFRESHMENTS: 11:00am, STARR 138**

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**Please visit Math Colloquium
website at**

**http://www.ferris.edu/htmls/colleges/artsands/Math/MATH_COLLOQUIUM/ColloquiumWeb/index.html**