University Teachers’ Practices in Teaching Algebra: Students’ Engagement in Constructing Multiple Representations

Abstract

Engaging students in constructing multiple representations and translating between them help students to become proficient in learning mathematics. The fact may also apply to abstract courses such as algebra at the university level. However, to what extent and in what ways teachers are engaging their students in constructing multiple representations while teaching algebra at the undergraduate and graduate levels, particularly in Nepal, was not explored. In this regard, the study aimed to explore university teachers’ practices of applying multiple representations in facilitating algebra. It is qualitative research under an interpretive research paradigm. I purposively selected five teachers who had been teaching algebra at the undergraduate or graduate level for at least five years. I prepared interview guidelines, including points concerning the way of teaching definitions, theorems, and proving theorems. I conducted interviews with all five participants. Then, I transcribed the interview data, coded the data, and generated four themes: Dominance of algebraic/verbal representations; variation among teachers in selection of representations; nature of content and students’ academic level provide a basis for selecting representations; and graphical representation as most helpful and challenging. I interpreted themes with the theories concerned with representations in mathematics. The conclusion was that although there was variation among teachers regarding the selection of a particular type of representation, the common practice was that verbal/symbolic representations were highly used and graphical representation was rarely used by teachers, depending upon the nature of the content. Moreover, low engagement of students in making connections among four representations indicates the need of searching optimal strategy of addressing this issue to ensure conceptual understanding. The results of this study may be helpful for teachers to use different representations appropriately in teaching, students to improve their meaningful learning, and textbook writers to make books multiple representation friendly.