Improving Mathematics Content Mastery and Enhancing Flexible Problem Solving through Team-Based Inquiry Learning

This article examines how student learning is affected by the use of team-based inquiry learning, a novel pedagogy in mathematics that uses team-based learning to implement inquiry-based learning. We conducted quasi-experimental and observational studies in intermediate level mathematics courses, finding that team-based inquiry learning led to increased content mastery and that students took a more flexible approach to solving problems. We also found that in the courses using this pedagogy, women (but not men) had a reduction in communication apprehension over the course of a semester. We conclude that team-based inquiry learning effectively enhances student learning and problem solving, preparing students for future academic success and fostering career readiness

Scientific Representational Fluency:Defining, Diagnosing, and Developing

This thesis advocates the importance of representational fluency in physics education. Multiple representations in science (e.g. graphs, words, equations, and diagrams) has been an area of much interest in physics education research in recent years. Representational fluency, however, is a somewhat novel idea. The thesis argues that this little-used term, representational fluency, is a way to draw together various ideas on how and why the use of multiple representations is important for physics students, educators, and education researchers alike. Representational fluency is investigated by considering three questions: what is representational fluency; what role does representational fluency play in physics learning; and how can students’ development of representational fluency be facilitated? This thesis explores these questions through the format of an introduction, five journal articles, and a general discussion combining the conclusions of each paper. The first paper presents the development, use, and publication of a survey to measure representational fluency, the Representational Fluency Survey (RFS), which is the first of such surveys in the literature. The RFS is a seven item survey which involves the participant solving problems that are difficult due to the representations in the question, rather than the level of physics content knowledge. A second paper illustrates how the RFS is used to further develop our understanding of representational fluency. The RFS allowed diagnosis of significant differences in the levels of representational fluency of different cohorts of students at the University of Sydney and identification of various features of students with a high level of representational fluency. It was found that the representational fluency of students with a higher level of physics learning experience was significantly greater than that of students with a lower level of physics learning experience and the difference was evident even within the first year cohort. Due to the apparent disparity of levels of representational fluency amongst different cohorts of students at the university, the subsequent three papers relate to research into effective pedagogies that facilitate the development of representational fluency. A format of presenting direct instruction on a particular physics representation through worksheets and consolidating this knowledge with applied questions was trialled as a possible method of instruction. It was found to alter the way that students use representations in following questions. This was done in the context of students in their final year of high school. The format was adapted to suit a university physics course in the structure of a semester-long set of weekly online learning modules designed to introduce students to representations relevant to the upcoming week’s lectures. The uptake and effectiveness of online learning modules was investigated first: it was found that university students were willing to participate in the modules and that the modules were of benefit to student engagement as intended in their design. Therefore, an experiment was conducted with the first year physics students at the University of Sydney. The students were randomly separated into two streams. One stream participated in weekly online learning modules focussed on relevant physics representations, the other stream participated in similar modules which more conventionally focussed on relevant physics concepts. Using the RFS as a pre-post test, it was found that students participating in the modules on physics representations had the largest learning gains in representational fluency. This demonstrates an effective pedagogical tool to support students in developing their representational fluency. Using an established test of conceptual physics understanding, it was also found that the students from each stream of online learning modules developed conceptual physics knowledge by comparative amounts across the semester. In these ways, this thesis advocates the importance of representational fluency, through defining, diagnosing, and developing representational fluency of university students

Prospective Mathematics Teachers‘ Knowledge for Teaching Algebra in China and the U.S

This study examined teachers‘ knowledge for teaching algebra, with a particular focus on teaching the concept of function and quadratic relations in China and the United States. An embedded mixed methods design was adapted, a design in which the main data set consists of written answers to a questionnaire, while the supportive data set is comprised of the written answers to open-ended questions and follow-up interviews. A structural equation model was adopted to analyze the status and structure of teacher knowledge for teaching algebra in China and the U.S. A qualitative analysis of the answers to the open-ended questions and follow-up interviews is aimed to further illustrate and interpret the quantitative findings. Three hundred and seventy six Chinese and 115 U.S. prospective middle and high school mathematics teachers participated in this survey. Based on an extensively quantitative and qualitative data analysis, the following conclusions were made. First, the Chinese participants demonstrated a stronger knowledge for teaching algebra when compared with their U.S. counterparts. Second, the structure of knowledge for teaching algebra of the Chinese participants is much more interconnected than that of their U.S. counterparts. Third, the Chinese participants showed flexibility in choosing appropriate perspectives of function concept and in selecting multiple representations in contrast to their U.S. counterparts. Fourth, this flexibility is found to be closely related to school math and teaching math. Finally, the number of college math and math education courses taken impacts teachers‘ knowledge for teaching algebra. The findings of this study hold several implications for mathematics teacher preparation in general and studies on mathematics teachers‘ knowledge in particular. Theoretically, the complexity of understanding and measuring mathematics teachers‘ knowledge for teaching was examined and discussed. This study also enriches the understanding of mathematics teachers‘ knowledge for teaching at middle and high schools in China and the United States. Specifically, the Chinese practice of developing teachers‘ basic knowledge, skills, and flexibility provides an alternative for U.S. mathematics teacher educators to reflect on their practice. Practically, what we can learn from this study to improve mathematics teacher preparation in China and the U.S. is discussed. Finally, the limitations of this study are discussed and further studies are suggested

Engaging multiple representations in grade eight: exploring mathematics teachers' perspectives and instructional practices in Canada and Nigeria

This study was inspired by and utilises representations, one of the mathematical learning processes (NCTM, 2000), which is currently acclaimed as one of the reform-based instructional approaches to teaching and learning algebra. This concurrent mixed methods research project explored elementary in-service teachers’ goals for, beliefs about and knowledge of representations, both in Ontario and Lagos. Data were collected through an online survey completed by 91 middle school in-service teachers concurrently with interviews with ten of them. Findings from the survey indicated that teachers from the Lagos subsample had weaker understandings about representations compared with their counterparts from Ontario. In the interviews, participants described to varying degrees their goals for and use of representations as opportunities for students to show connections, relationships, and reasoning, supporting students’ confidence in problem-solving, and facilitation and opportunities for questioning and discussion. This research suggests that teachers generally, but particularly in Lagos, need a deeper understanding of representations and need to further develop the specialized mathematics content knowledge related to patterning and algebra. Other findings showed that: planning and sequencing instruction, use of contextual learning tasks, opportunities for students to generate their own representations, linking students’ prior knowledge to new situations, and translation among multiple representations were reported as critical to teachers’ use of representations. Recommendations are made to create more awareness among teachers, of the value, use and knowledge about representations. These findings would be relevant to school boards, teacher educators, researchers, and professional development providers wishing to improve teachers’ use of representations, via enhanced beliefs, and knowledge