A study of adult re-entry students’ affective orientation toward mathematics and their mathematical thinking in the context of problem-solving

Abstract

This modified teaching experiment explored the perspectives of adult re-entry students enrolled in the study of mathematics at the most basic level in higher education. Specifically, it investigated characteristics of the students' affective orientation toward learning, the nature of their mathematical thinking in the context of mathematical problem-solving in contrast to procedural learning, and the possible relationship between their affective orientation toward the learning of mathematics and their mathematical thinking. Eighty-nine students enrolled in remedial level mathematics classes at a large state university completed initial questionnaires. Of the 19 re-entry students in this initial group, three participated in the entire study, which included initial and exit interviews, teaching sessions and classroom observations. Case studies of those 3 students are presented in this dissertation along with a case study of the interaction between two of them. This research yielded a rich array of results concerning re-entry students’ affective orientation toward the study of mathematics at the remedial level, and the interplay between that affective orientation and their ways and means of operating in a problem-solving setting. These results would have been difficult to derive with methodology other than an adaptation of the teaching experiment. The initial questionnaires administered to all 89 students laid the foundation, but it was within the interviews and, more significantly, the teaching sessions that the three participants’ ways of knowing were revealed and knowledge voices were heard. Indeed, the teaching sessions not only added to the results but corrected misconceptions about the participants’ ways of operating had the conclusions been based only on questionnaires and interviews. Those participants who completed the project provided strong contrasts and an abundance of findings. One of them demonstrated a particularly vivid example of differences between stated and revealed beliefs, thus alerting us to the possibilities of such differences in other individuals. The findings suggest modifications to some of the models and research methods employed in order to better investigate re-entry students’ study of mathematics in college. Moreover, they suggest modifications in the remedial mathematics courses offered to students reentering higher education that would take advantage of the experiences and world-views of such students.