Tertiary mathematics and content connections in the development of mathematical knowledge for teaching

Emphasis on the importance of subject matter expertise in teaching secondary mathematics is found in the research literature and in policy. In the United States, for instance, the No Child Left Behind Act, calls for secondary teachers to be certified in a subject specialization. In Canada, admission to secondary teacher education programs requires extensive subject-specific university coursework. However, it is unclear if or how extensive subject matter expertise impacts the practices of teachers in a secondary classroom. This study aims to explore how advanced coursework in mathematics, beyond the scope of the high school curriculum, impacts the ways prospective teachers understand and teach secondary content. Using a qualitative case study methodology, five prospective secondary mathematics teachers participated, with data obtained through document analysis and semi-structured task-based interviews. Participants engaged with classroom-relevant tasks and were explicitly asked how they could draw upon advanced mathematics to inform their teaching. Participants also detailed their perceptions of the role advanced mathematics plays in their development as teachers. Results from this study reveal that participants saw little value in the content of advanced mathematics to their teaching, but expressed value towards the beliefs and values gained through advanced mathematics, such as problem solving and rigour. Some participants demonstrated misconceptions at the secondary level, which had direct connections to content from their post-secondary mathematics coursework. For example, all participants made the false claim that a real-valued polynomial can be factored if and only if it has a root. Results extend the literature through rich empirical data which illuminates how prospective secondary mathematics teachers perceive and use advanced mathematics in understanding the secondary curriculum. While participants held content knowledge beyond the secondary curriculum, this knowledge was not integrated in a way that impacted their understanding of secondary mathematics. An understanding of post-secondary mathematics has the potential to be of value to secondary teachers in the classroom, but this potential needs a space to be unlocked. I argue that mathematicians and teacher educators need to work together to build opportunities for prospective teachers to build connections between the mathematics they know and the mathematics they need to teach.Education, Faculty ofCurriculum and Pedagogy (EDCP), Department ofGraduat

Navigating the landscape of pedagogical training: The journeys of three mathematics graduate students

This article describes the landscape of teaching assistantships (TAships) in the Mathematics Department of a large, public, research institution. First, we present visualized data describing the terrain for all mathematics graduate students. Second, we focus on three specific journeys in that terrain. We employ an autoethnographical research methodology to analyze the pedagogical paths of three recent graduates through written reflection. We highlight some surprising themes that emerge, identify key moments in each reflection, and make three proposals, applicable in broader contexts, to capture and confer their benefits.   Dans notre article, nous traçons le portrait de l’assistanat d’enseignement dans le département de Mathématique d’un grand établissement public de recherche. Tout d’abord, nous présentons des données sous forme visuelle de manière à décrire la réalité sur le terrain des étudiants en mathématique des cycles supérieurs. Ensuite, nous portons notre attention sur trois parcours particuliers. Au moyen de réflexions menées par écrit, nous utilisons une méthodologie de recherche autoethnographique afin d’analyser le parcours pédagogique de trois nouveaux diplômés. Nous soulignons certains thèmes surprenants, nous dégageons les moments clés de chaque réflexion, puis nous énonçons trois propositions – lesquelles peuvent être utilisées dans un contexte plus large – et nous en présentons les avantages