Preservice Teachers\u27 Procedural and Conceptual Understanding of Fractions and the Effects of Inquiry-Based Learning on this Understanding

ABSTRACT Non-negative rational numbers play a major role in the K-8 curriculum and continue to permeate mathematics content through high school and college in all strands of mathematics. The difficulty that both students and teachers encounter with these concepts is well documented in the literature. This study looked at preservice teacher knowledge and how an alternative means of instruction might improve their conceptual understanding of fractions. To accomplish this task, the study took place in two stages over the course of two semesters. During the first stage, preservice teachers\u27 conceptual and procedural knowledge of fractions and their associated algorithms were examined through a two-part written assessment and through individual interviews. The results indicate that these participants posses not only weak conceptual knowledge, but weak procedural knowledge as well. Also, when dealing with division, some of the participants\u27 misunderstandings were due in part to a lack of understanding regarding division of whole numbers. During the second stage of the study, skills and knowledge of preservice teachers who had completed an inquiry-based fraction unit were compared with the skills and knowledge of preservice teachers exposed to a lecture-based unit to determine if one group possesses a better conceptual understanding of fractions and the standard algorithms associated with addition and division. The results indicated that students in an inquiry-based approach to teaching fractions possessed a deeper understanding of fractions and their associated algorithms. Further, the skills of those in the inquiry-based groups were as good as those from the lecture groups, even though skills were not emphasized during the unit. Another important result was the indication that knowledge retention was greater with the preservice teachers in the inquiry-based section. This study also investigated the impact that inquiry-based lessons have on teacher attitudes as they relate to mathematics and beliefs about mathematics instruction