Catering for the mathematical needs of disabled learners equitably and productively requires the anti-ableist preparation and professional development of teachers. In CAPTeaM (Challenging Ableist Perspectives on the Teaching of Mathematics), we design tasks that emulate inclusion-related challenges from the mathematics classroom, and we engage teachers with these tasks in workshop settings. In this paper, we focus on evidence from one type of task in which participants engage in small groups with solving a mathematical problem while at least one of them is temporarily and artificially deprived of access to a sensory field or familiar channel of communication. In this paper, we focus on evidence of emerging resignification – discursive and affective shifts in the participating teachers’ sense-making about what makes the construction of mathematical meaning possible and valuably different – as they work on the tasks. By linking Vygotsky’s vision about the educational changes required to empower and include disabled learners with more contemporary ideas from embodied cognition and disability studies, our analyses show how engagement with the tasks affects participants’ realisation and appreciation of interdependencies between learners, teacher, resources, and emotions, highlights alternative forms of mathematical agency and gives opportunities to turn initial sense of impasse and despair into joy.

In this chapter, I draw on my experiences as mathematics education researcher collaborating with research mathematicians in order to tell a story of paths crossing at four points: in research, teaching, professional development and public engagement. I discuss these four tiers of examples to propose a re-imagining of this story, not merely as a story of paths crossing – but as a story of paths “meeting” at a vanishing point, a point where the boundaries between the two communities fade into insignificance, recede and may even be replaced by a strong sense of joint and multi-faceted enterprise. I conclude with indicating how this joint enterprise may look like in the near future.KeywordsUniversity mathematics educationMathematicians’ teaching practicesCollaboration between mathematics education mathematics researchers

Mathematics education courses in mathematics undergraduate programs often aim to introduce students to the field of mathematics education research (RME) or/and to prepare them for the profession of mathematics teaching. This aim requires a balance of attention to mathematical content together with attention to RME findings. Such balance is the focus of this chapter in which we propose course activities and an assessment frame for undergraduates’ engagement with both mathematical and pedagogical discourses. We draw on the MathTASK program (https://www.uea.ac.uk/groups-and-centres/a-z/mathtask) to present the design principles of activities that contextualize the use of mathematics education theory and mathematical content to specific learning situations that may emerge in the classroom. Such activities pose mathematical and pedagogical challenges (MC and PC) to often long-held views about mathematics and its pedagogy. Participants were eight final-year undergraduate mathematics students who attended a mathematics education course, in which the aforementioned activities were part of their formative and summative assessment. Analysis of student responses through a commognitive lens examined the students’ reification of mathematical and pedagogical discourse (RMD and RPD) in response to MC and PC by the end of the course. Here, we sample evidence of how students responded to MC (e.g., in terms of mathematical accuracy) and PC (e.g., in terms of routines, narratives and word use in their engagement with RME) and we explore the relation between RMD and RPD in their responses. Our findings highlight the capacity of MathTASK activities to challenge, and potentially shift, students’ often deeply rooted mathematical and pedagogical narratives.KeywordsMathematical discourseMathematics education discourseMathTASKUndergraduate mathematicsMathematical challengePedagogical challengeFormative and summative assessment

Mathematics Education courses are increasingly present in university programmes in Mathematics and in Education. In this chapter, we propose approaches to teaching and assessment which consider and address some of the challenges that university teachers face as they welcome students from diverse communities to Mathematics Education as an academic discipline. To this aim, we draw on our experiences of design, delivery and assessment of two introductory, optional courses in Research in Mathematics Education (RME), one to final-year BA Education students in an Education Department and one to final-year BSc Mathematics students in a Mathematics Department. We aim to discuss how such courses can facilitate students’ cross-disciplinary transition (from Mathematics or Education to Mathematics Education). First, we outline the literature and the theoretical underpinnings that ground the design of the two courses and their assessment frame. This frame consists of a typology of four characteristics of engagement with RME discourses which is informed by the Theory of Commognition and has emerged from our prior research with secondary mathematics teachers and university mathematics lecturers: consistency, specificity, reification of RME discourse, reification of mathematical discourse. Subsequently, we outline the two courses and sample one activity and student work from each course to demonstrate the use of our assessment frame and highlight insights emerging from its use (for example, in tracing narratives about mathematics and its pedagogy as students engage with the courses). We conclude with a brief discussion of the pedagogical potential of such activities – and of the two courses more broadly – for undergraduate students’ introduction to RME.KeywordsMathematics Education courses (for Mathematics or Education undergraduates)Transition (from Mathematics or Education to Mathematics Education)MathTASKFormative and summative assessmentTheory of CommognitionDiscursive shifts

MathTASK é um programa de pesquisa e desenvolvimento que engaja professores de matemática em situações de sala de aula desafiadoras e altamente contextualizadas na forma de tarefas (chamadas de mathtasks). As respostas de professores às tarefas revelam seus discursos matemáticos e pedagógicos e abrem oportunidades para articular, considerar e reconstruir tais discursos. As tarefas foram usadas como instrumento de pesquisa e também de formação de professores e desenvolvimento profissional no Reino Unido, na Grécia e no Brasil. Neste artigo, apresentamos o programa MathTASK e um exemplo de mathtask. Em seguida, apresentamos um resumo dos construtos teóricos que emergiram na análise dos dados do programa MathTASK. Então, indicamos os princípios gerais do uso de mathtasks na pesquisa e formação de professores e damos quatro exemplos dos princípios, cada um dirigido a diferentes aspectos do ensino e da aprendizagem de matemática, e cada um desenvolvido tendo em mente níveis educacionais e contextos. Concluímos com observações sobre os benefícios de usar mathtasks como uma forma de estimular e facilitar reflexões de professores de matemática sobre suas práticas.