‘Good teaching’ remains disputed, but few studies have empirically studied variations in views of good teaching as reflected in teacher education. This study performed a content analysis of criteria for student teacher lesson observations stated in protocols from universities in six countries. Similarities across the protocols were the absence of images of the charismatic and the technical-professional teacher, and the dearth of teleological aspects. The degree to which protocols reflected a knowledge base, had clear implementation requirements, valued reasoned judgement, and valued transformation of content varied. On the basis of this range of images of the desired teacher, we suggest four categories of teacher images: the knowledgeable teacher, the knowledge-transforming teacher, the efficient teacher, and the constantly improving teacher, and further discuss the possibility of an inspired teacher.

Det finns många bilder av vad som är en bra matematiklärare. Det här bokkapitlet belyser de bilder som målas upp i den senaste lärarutbildningsutredningen. Genom en textanalys av de stycken som handlar om matematik framträder fyra bilder som begär olika saker av matematikläraren och lärarutbildningen: läraren ska vara ämneskunnig, undervisningsskicklig, intresseutvecklande och dessutom vara född med rätt biologisk, social och kulturell bakgrund. I utredningen framträder en bild av matematikämnet som en rad användbara fakta och beräkningsstrategier, och det målas upp som något förgivettaget gott att matematikelever behöver bli intresserade av och lära sig använda matematik. Att elever ibland inte lär sig matematik kommer därför att reflekteras i bilden av matematikläraren, där både matematikläraren och matematiklärarutbildningen målas upp som bristfälliga. Genom att bilden synliggör en viss typ av matematiklärarstudent, medan andra blir osynliga, har bilden makten att både inkludera och exkludera studenter.

The present study adds to an ongoing debate about third spaces in teacher education, spaces where theory and practice come together. One third space is constituted by the written tasks from practicum. Yet research has shown only modest emphasis on theory in such tasks. Tasks from two versions of a programme are used to represent two different positions on linking theory and practice. The tasks were therefore analysed with respect to the demarcation of conceptual objects as well as practice-based contexts. The findings indicate a difference with respect to the demarcation of conceptual objects, especially concepts relating to mathematics and mathematics education. This is seen as indicative of the reduced encouragement of linking theory and practice. 

Post-lesson conversations between student teachers and their mentor teachers is an opportunity for learning to teach mathematics. However, there is a plethora of perspectives on how mathematics should be taught, and therefore the question posed addresses what de-ritualising routines mentor teachers privilege in their mentoring of mathematics student teachers. The data consisted of post-lesson mentor conversations from six pairs of mentors and mentees. From the conversations, the parts where the use of time was discussed were selected for an analysis of privileged teaching approaches. The analytic approach for teaching was based on de-ritualising prompts, developed in commognitive theory for learning mathematics. The main finding was that mentor teachers privilege learner agentivity in mathematics teaching. Mentors foregrounded how such agentivity relates to both contextual restraints in the classroom and to other de-ritualising steps. One contribution of this study was de-ritualising processes as a unifying conceptualisation of teaching activities and mathematics learning. A second contribution was the unique opportunity mentors provide for student teachers learning, where de-ritualising prompts in mathematics teaching are related to a classroom context with constraints of time and learners needs.