COUNTING ON COOPERATIVE LEARNING TO UNCOVER THE RICHNESS IN UNDERGRADUATE MATHEMATICS

Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, Mar 2004 by Kasturiarachi, A Bathi

ABSTRACT: The reform movement, with its bold and innovative approaches that focus on student-centered learning, has been able to uncover the richness in undergraduate mathematics. The most outstanding pedagogical practices take into account the environment in which learning occurs as well as the background of the student body. Mathematics educators should be aware that what count as the finest practices are institution dependent. This paper reports on three such pedagogical practices, with cooperative learning at their core, that have worked with remarkable success and could be adopted at different institutions. Formatted Interactive Lecture Leaves highlight the need for active learning by creating an interactive learning environment. Student Projects showcase the relevancy of mathematics by making connections to the diverse majors prevalent in our classrooms. The Program for Excellence in Mathematics, based on collaborative learning, challenges motivated students to strive for excellence. Details of these pedagogical practices as well as appropriate evidence of success are presented.

KEYWORDS: Cooperative learning, experiential learner, student projects, excellence program.

INTRODUCTION

During the 1998 International Congress of Mathematicians, Mathematics Education took center stage during a debate on the subject of calculus reform. Under consideration was the comparison between traditional methods of instruction and reform initiatives. While the pros and cons were hashed out, there was a clear consensus on one item: the word reform was perhaps inappropriate for describing the new pedagogical strategies called for in mathematics education. It was clear from the discussions [1, 16] that the word renewal is a far better descriptor of the rising currents propagating throughout undergraduate mathematics education.

The mathematics renewal movement has been successful in reshaping the undergraduate mathematics curriculum to reflect the connections mathematics has to other disciplines. In many cases this movement has opened up partnerships with other departments. As a result, many mathematics departments have made a transition from their role as an instructional filter to that of an instructional pump. The major implication of this change is that calculus has now become a valuable tool for our students and not a barrier that they need to overcome. In the United States, the National Science Foundation (NSF) has had a major impact on the renewal movement since 1987. Table 1 briefly shows the percentage increase in institutional participation. Detailed assessments of the renewal movement in undergraduate mathematics can be found in [18] and [5].

Although the genesis of calculus reform was centered on content, in time many educators began considering questions of pedagogy. As the renewal movement spreads its influence into courses above and below the calculus level, coupled with a growing national interest in undergraduate education [10], it is necessary to consider pedagogy along with content. Pedagogy will facilitate pervasive implementation of mathematics renewal across the undergraduate mathematics curriculum. It is then reasonable to raise the question, "Is there a single pedagogical technique that is appropriate for all types of higher education institutions, which can effectively be implemented in the mathematics classroom?" We believe the answer is affirmative. Cooperative learning stands out as the primary candidate for several reasons [6, 4].

In this article, we will identify two reasons why cooperative learning should be an integral component in undergraduate mathematics education. We will first view cooperative learning as a process embedded in sound pedagogical practices. Then we will proceed to demonstrate the connections of cooperative learning to the Kolb Learning Cycle. In the second part of the article, we describe a combination of three pedagogical practices that have been helpful in creating a cooperative learning environment in the classroom.

EXPERIENTIAL LEARNER

In 1987, Chickering and Gamson [3] put forth seven principles of "Good Practice" in undergraduate education:

1. Encourages student-faculty contact.

2. Encourages cooperation among students.

3. Encourages active learning.

4. Gives prompt feedback.

5. Emphasizes time on task.

6. Communicates high expectations.

7. Respects diverse talents and ways of learning.

A quick glance at these seven principles should convince the reader that cooperative learning, when properly implemented, will relate closely to each of the seven principles. Let us understand these relations carefully. In trying to communicate ideas to each group, the faculty member necessarily initiates more contact with the students compared to traditional teaching methods. This is the essence of Principle # 1. Cooperative learning groups are expected to have esprit de corps among each member of the group [6]. Furthermore, mutual responsibility, sense of belonging, and substantial group work creates an environment which lends itself to the practices identified in Principles # 2, 3, and 5. Because evaluation of group work is done consistently in cooperative learning, the students receive feedback (Principle # 4) about their work. Moreover, group members get prompt feedback from their peers as they share ideas in their search for optimal answers. Respect for diverse talents and ways of learning (Principle #7) occurs as a result of students often having to acknowledge and sometimes even reconcile with different viewpoints and levels of understanding. With all these components in place, well-implemented cooperative learning in a classroom will always communicate high expectations (Principle #6).