Direct Instruction in a Problem Based Learning Environment: A Multiple-Case Study of How the Pedagogical Beliefs of Mathematics Teachers Impact Learning

The literature on mathematics pedagogy indicates a conflict between two instructional approaches which is causing a disparity among the delivery of instruction. In addition, for the past several years there has been a steady decline in the standardized numeracy scores of students in Ontario, and the United States. As a result, the problem that was investigated in this study was an examination of how the pedagogical beliefs of mathematics teachers impact learning and the phenomenon of declining scores. Fittingly, the purpose of this qualitative multi-case study was to fill a gap in knowledge around the issues of declining numeracy scores by examining the pedagogical beliefs that influence mathematics instruction through the perspectives of elementary school teachers. Data was collected through in-depth interviews, content analysis of day plans, and field notes. Thematic analysis was used to identify potential themes and subsequent cross-case analysis was used to indicate within-group similarities and inter-group differences. The units of analysis for this study were eight teachers purposely sampled from the pool of Ontario Certified Teachers (OCT) from the Greater Toronto Area (GTA) with experience teaching mathematics in grades 1-8. The results revealed that the pedagogical beliefs of the participants align with a problem based learning pedagogy, and consequently teachers are misinformed due to the faulty expectation that learners have the developmental capacity to engage in problem based learning, when in fact it is too cognitively overwhelming. It was recommended that educational systems improve training teachers to better understand how cognitive strength is developed through direct instruction and reform the current curriculum to include cognitive training instruction. It was recommended that future action research designs examine the lack of frequency that direction instruction is being applied in mathematics classrooms, and examine the relationships between direct instruction, cognition, and mathematics. In addition, it was recommended that replication of this study evaluate the instructional beliefs of teachers and their efficacy with math difficulties in other educational settings.