Based on a survey of 150 respondents and 16 timeline interviews with first-year university mathematics students in Sweden, we explore how the material resources and conditions available to them —mathematics capital— connect to their mathematical identities. We found that mathematics capital has bearing on how early in life students start to consider doing mathematics. We also found individually different trajectories among students with low mathematics capital into university mathematics. The study expands both existing theoretical and methodological ways of researching the material bearings of identity and opens up for new ways of understanding and exploring the conditions that may facilitate access to participation and success in university mathematics. It contributes to understanding on the social and cultural resources that students bring with them to start mathematics, thus complementing the insights that Simon Goodchild’s work had provided on the context of access to university mathematics.

Purpose: This study aims to distinguish the particular mathematics discourse and the teaching discourse in two countries, and explore how the differences in mathematics and teaching discourses influence what is noticed. Design/Approach/Methods: The study employs a cross-cultural case study methodology, using a mathematically rich video vignette from a Japanese classroom. Video-prompted focus-group interviews were conducted with preservice teachers (PSTs) from both countries. Findings: Indian PSTs, familiar with geometrical reasoning, notice more detailed mathematical discourses, whereas Swedish PSTs, less familiar with geometry discourse, notice broader teaching strategies. In addition, the PSTs notice unfamiliar teaching strategies and how they support mathematics learning. Both groups identify and reflect on the unfamiliar teaching practices and classroom culture observed in the Japanese video. Originality/Value: This study contributes to the research on noticing in teacher education (TE). The novelty is how the familiarity of mathematics discourse facilitates noticing details in students’ mathematical reasoning, and how an unfamiliar teaching discourse is an important learning opportunity.

This contribution seeks to understand how teacher educators, both school-based mentors and university-based teachers, take on the multiple institutional and professional tensions involved in the practicum of mathematics student teachers. We use the notion of confession and turn the gaze on narratives from our own practices in Sweden and Brazil. This shows how desires to both safeguard authority and show care and concern for student teachers are shared, whilst political and digital surveillance increase the tensions.

Le sujet de cet article est de comprendre comment des personnes qui sont professeurs et éducateurs, mentors de stagiaires de professeur d'école et professeurs d’universités, prennent en considération les tensions institutionnelles et professionnelles liées à la pratique d'étudiants en stage pour devenir professeur de mathématiques. Ici, nous utilisons la notion de confession, et plaçons notre attention sur nos propres expériences de pratiques en Suède et au Brésil. Cette analyse montre que le désir de sauvegarder l'autorité et en même temps de se montrer attentif et concerné par les stagiaires est partagé, alors même que la surveillance politique et digitale augmente les tensions.

We asked students to propose three ingredients for a magic pill to make anyone “very good at mathematics” in our Swedish context. This chapter engages both what students perceive as values in mathematics, and what they put up as characteristics for persons who know mathematics. We include a political dimension on the processes of inclusion and exclusion to understand the transforming powers in a pill for making anyone “very good at mathematics”. 735 Swedish students in grade five and eight answered the question. The results show how students put mathematical facts about numbers and calculations in their pills, together with ingredients to make you fast and intelligent, but also magic, such as unicorns. Ingredients transforming the person taking the pill were more common for girls. The suggested ingredients are reminders of the importance of reducing the emphasis on exclusionary practices, based on ability or being fast when doing mathematics. Instead, the recommendation for teachers is to include “an ounce of joy and happiness”, as one girl puts in her pill.

Practicum assessment rubrics have a backwash effect on preservice teachers' learning through the criteria they transmit. This article presents a documentary analysis of ten rubrics used across six countries: South Africa, India, England, Singapore, Canada, and Sweden. We compare the dispositions, knowledge, outcomes, and reasoning. We use Legitimation Code Theory (LCT) to show how practicum assessments are legitimated differently. Some rubrics emphasise preservice teachers’ dispositions and whether they implement protocols correctly. Others emphasise their capacity for reasoning in context. These positions call for teacher educators and policymakers to interrogate where the emphasis is in their own assessments.

In this pilot study, we examine the procedures, constructs and geometrical properties pre-service teachers (PSTs) invoke when solving a geometry problem. The aim is to develop an analytical tool to research PSTs’ mathematical discourse, assuming that the available mathematical discourse informs PSTs’ noticing of mathematics learning. As a theoretical base for mathematics discourse, we use commognition. The empirical data consists of recorded conversations of seven PSTs solving a geometry problem. The analytical tool provides a visual representation of the procedures, geometrical properties and constructs, considered as the precedent search space of the person solving the task. The analytical tool we propose visualizes the precedent search space PSTs draw on and therefore enables a culturally sensitive analysis of mathematics discourse. 

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.