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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., TRACE VR 017-03614

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.

This presentation draws on the methodological pilot from a new research project focused on in/exclusion in higher education physics and mathematics (PI: last author), illustrating the reciprocal process of theoretical and methodological fine-tuning as the project literally takes its first empirical steps during walking ethnographies in higher education settings. The project explores the paths of students from under-represented groups into the fields of physics and mathematics, and the identities that they build as they engage with these disciplinary areas. We are inspired by socio-material perspectives that consider humans and nonhumans as constantly performed and enacted (de Freitas & Curinga, 2015). In their engagement with the disciplines of physics and mathematics, the students link into socio-historic practices and virtues, learning those through participation (Daston & Gallison 2007). From such a perspective, scientific knowledge can not be separated from the knower. More specifically, Mol (2002) argues that objects and subjects need to be understood as enacted inseparably in the multiple materialized relations of scientific practice. As such, human actors, scientific practices, materialities are all entangled in distributed networks of materialization of practice. Identity can be studied by tracing the assemblages of practice in which bodies, spaces and materials - objects, instruments, artefacts, matter - as well as language as materialities come to be connected (Acton 2017). In order to trace the reciprocity of student identities and scientific materialities we use walking ethnographies to identify configurations of identity that promote students’ successful engagement. In the walking ethnographies students are invited to take the researcher around places of importance to them as physics or mathematics students (e.g. laboratories, lecture halls, social areas, study spaces), focusing on the use of materials in the places (e.g. which objects, material, Immpact

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.

To trace and represent changes in mathematics teaching over time is a challenge for research. This methodological paper proposes a framework for visually representing teacher moves in mathematics lessons. Based on commognitive theory, a framework of de-ritualising moves towards explorative teaching is developed. Two lessons of mathematics student teachers ‘teaching-as-usual’ in their final practicum are used for the development of a coding-scheme. The analysis enables to represent several de-ritualising moves, and the visual and fine-grained analysis is a promising result for longitudinal research on de-ritualisations in teaching-as-usual., TRACE

As part of practicum, student teachers are often asked to provide written reflections on their teaching, sometimes in the form ofself-inquiry confessions. Confessional practices in teacher education havebeen critiqued in earlier research, andthis article provide an empirically-based discussion from four student teachers’ reflectivelogbooks. The findings show and how confessional reflections are entangled with five discourses aboutgood teachers:they interactwithlearners, follow curriculum, legitimise mathematics, use educational theory, andhold particular attributes of body and soul. The first move in confessions, the self-examination, was part of all four logbooks. However, it was rarely used for the second move of self-improvement. From this, the purposefulness of confessional reflections can be questioned, and hence the ethical considerations of intruding student teachers’ integrity by assessing their inner feelings and beliefs.

As with any programs in teacher education, Swedish mathematics teacher education is influenced by changing political winds, developments in Information and Communication Technology (ICT), culture, history, PISA results, research-based program designs, and a fair amount of passion. Content and outcomes are nationally determined and include the requirement of a strong research foundation, but this is often not how practcing techers work, which exerts its own pull on teacher education. The specific implementations of programs take different forms at the universities that offer mathematics teacher education. In order to provide a comprehensive yet meaningful ntroduction to both the current system and current practices, we describe the overall organization of Swedish mathematics teacher education, and then offer short cases of implemented programs. To ensure inclusivity, the various parts are written by mathematics educators from the respective institutions. In this way, both variation across mathematicas teacher education for diffrent grade levels and variation across different institutions working with the same national directives can be distinguished. Issues such as the academization of teacher education are problematized, as are other forces that constitute the crosscurrents in Swedish mathematics teacher education.

‘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., TRACE

As with any programs in teacher education, Swedish mathematics teacher education is influenced by changing political winds, developments in Information and Communication Technology (ICT), culture, history, PISA results, research-based program designs, and a fair amount of passion. Content and outcomes are nationally determined and include the requirement of a strong research foundation, but this is often not how practcing techers work, which exerts its own pull on teacher education. The specific implementations of programs take different forms at the universities that offer mathematics teacher education. In order to provide a comprehensive yet meaningful ntroduction to both the current system and current practices, we describe the overall organization of Swedish mathematics teacher education, and then offer short cases of implemented programs. To ensure inclusivity, the various parts are written by mathematics educators from the respective institutions. In this way, both variation across mathematicas teacher education for diffrent grade levels and variation across different institutions working with the same national directives can be distinguished. Issues such as the academization of teacher education are problematized, as are other forces that constitute the crosscurrents in Swedish mathematics teacher education.

Trepartssamtalet, dvs ett samtal mellan kurslärare, student och VFU-handledare, är en central del i den verksamhetsförlagda utbildningen (VFU), och dessutom ett av få tillfällen i hela lärarutbildningen där campus, student och skola möts. Studenterna lyfter fram trepartssamtalet i kursutvärderingar som ett av de viktigaste inslagen under utbildningen. Men trepartssamtalet är också kostsamt på olika sätt. Det kostar i tid att resa ut till skolorna och det behövs också många lärare att bemanna dem. Det är därför viktigt att utveckla och utforska olika former för samtal i VFU som inte är en ren minskning av kvalitet, utan kan vara en form som gynnar studenternas lärande. Projektet omfattar två delstudier där I) studerar digitala trepartssamtal och II) studerar trepartssamtal i grupp. Delprojekt I) är en erfarenhetsbaserad studie där vi jämför våra resultat med till exempel Karlstads universitet som har lärarutbildning (och därmed trepartssamtal) på distans (Johansson och Johansson, 2018). Delprojekt II) innebär trepartssamtal med studentpar, och genomförs som en möjlig aktivitet inom klustren i den nya VFU-organisationen. Studier har visat att studenter som gör VFU i par eller grupp har möjlighet att genom gemensam planering och gemensamma reflektioner hitta kopplingar mellan den egna undervisningen och innehållet i de lästa kurserna (Cavanagh & McMaster, 2015; Manuchechrie, 2002). Delprojekt II sker också i samverkan med VFU-kursansvariga vid institutionerna HSD och ISD. Under paneldiskussionen kommer vi presentera resultaten i de olika delprojekten, vad vi har lärt oss och vilka utmaningar som vi kan ställas inför, till exempel: •Tekniska krav och hantering av GDPR •Krav på stödstrukturer, till exempel digitala verktyg, gott samarbete med VFU-sekretariatet för placeringar och med lärare i övriga kurser •Pedagogiska anpassningar av kursuppgifter och rutiner för samtalet •Studenters och lärares engagemang och medverkan i projektet •Att både få komma tillbaka till e

This chapter reports and problematizes relationships between the expected democratic actions as part of the politically expected democratically inclusion of students’ wishes and concerns; and students’ valuing of mathematical activities in mathematics classrooms, departing from the Swedish results from a large-scale quantitative cross-cultural survey. We asked what are the conflicts between most valued activities by Swedish students and the valuing of democratic actions. The quantitative study showed that students value “knowing the times tables” and “teachers’ explanations” and “correctness” over explorative, communicational and collaborative activities. We discuss the cultural and historical reasons behind these results and argue that we must understand the valuing of times tables or teachers’ explanations as an expression of enculturated and therefore culturally valued actions in mathematics classrooms, where this enculturation takes place not only in school, but in conversations with parents, grandparents, in media and in children’s books. We also argue that the conflict between the political expectations of democratic participation and actions, and the invitation to students to influence teaching on the one hand, and on the other hand students use of this influence through valuing teacher explaining, mastering times tables and understanding why the answer is incorrect, rather conserve a mathematics teaching organised around values as objectism and control than through openness and rationalism., We are grateful for critical conversations with Prof. Em. Alan Bishop, Prof. Em. Philip Clarkson and Assoc. Prof. W. T. Seah and with dear colleagues at Stockholm University: Anette de Ron and Elisabeth Hector.

Starting from questions about what is privileged in mathematics teacher education, we conducted a systematic review of research on practicum. One element was to in-terrogate the notion of the desired mathematics (student) teacher reflected in existing research. Selecting peer reviewed, empirically based articles for 2001-2017 resulted in the inclusion of 51 articles. Our findings suggest the desired teacher implied in papers to have content knowledge, MKT/PCK, positive beliefs and attitudes, and the ability to reflect on teaching. Teachers who can exercise reasoned judgement were more frequently valued than teachers who can implement specific practices., TRACE

Teacher education generally has both a contextual component of observing and teaching in schools, and decontextualized elements in university courses (cf. Tatto et al., 2012). University courses may be content courses, general pedagogical courses, or mathematics education courses. The assessment criteria of each component or course transmit, both explicitly and implicitly, notions of the desired teacher. Our key concept is the desired teacher. This recognises the teacher as both a subject and as subjected to discourses of power which constitute categories such as ‘teacher’ and ‘good teacher’ (cf. Montecino & Valero, 2015). Notions or images of the desired teacher produce ‘regimes of truth’ which normalise reflection - or not, normalise transformation of content as part of teaching - or not, etc. The notion of what the good teacher is, has varied over time and place. Images of the charismatic teacher with the disposition to teach, have been around for a long time, and still prevail in popular culture (Connell, 2009). Connell also identified a technical-professional model, which prevails in descriptions of teachers’ “technical know-how”. But what are current, competing, contrasting or co-existing images of the desired teacher? This gives rise to this question guiding the work in the group: What are the images of the desired teacher reflected in references to desired knowledge and valued application practices, in institutional materials etc.?, TRACE

Starting from questions about what is privileged in mathematics teacher education, we conducted a systematic review of research on practicum. One element was to in-terrogate the notion of the desired mathematics (student) teacher reflected in existing research. Selecting peer reviewed, empirically based articles for 2001-2017 resulted in the inclusion of 51 articles. Our findings suggest the desired teacher implied in papers to have content knowledge, MKT/PCK, positive beliefs and attitudes, and the ability to reflect on teaching. Teachers who can exercise reasoned judgement were more frequently valued than teachers who can implement specific practices., TRACE

The Third Wave Project

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., TRACE