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Mathematics teaching routinely traumatizes students. Why, and what changes can we make so this is not so? Lipari (2009) argues that the ethical call of conscience is not a speaking, but a listening. We draw on her conceptions of listening otherwise and listening being to see and intervene in dynamics of potential harm in mathematics teaching. We analyse six cases for three features: attention to difference, prioritizing of compassion, and openness to self-transcendence. Our analysis reveals that teaching in these short episodes is uniformly listening oriented or speaking oriented, with speaking- oriented teaching common even when teaching engages students actively in discussion. Further, our analysis suggests mechanisms for routinely disrupting patterns of harm in mathematics teaching. 

Teaching is everywhere, yet much of what is involved in teaching remains hidden, with comprehensive theories lacking. These challenges serve as the backdrop for research on mathematics teaching and the work of Thematic Working Group 19. To make progress, the group has used four domains to organize and consider research on teaching. This paper reviews the contributions and issues that arose in the group at CERME13. We elaborate on how the domains stimulated discussions of the meaning of teaching across papers, and we provide reflections and implications for future work. 

Stakeholders agree that the mathematical education of teachers needs to focus on mathematical knowledge for teaching, but the practice-based nature of this knowledge poses challenges for mathematics teacher educators — for understanding it, developing tasks that maintain its integrity in practice, and teaching it to teachers in ways that meaningfully support their learning to teach. We know little, however, about how mathematics teacher educators conceptualize the teaching that knowledge is to support. Our analysis reveals that thinking develops from a view of teaching as straightforward, where aspects can be treated in isolation, to a view of it as requiring focused attention while maintaining mutual regard for the whole. This difference has implications for how mathematics teacher educators understand specialized mathematical knowledge and for how to support their understanding and teaching of it. 

This introduction for TWG19 offers a brief history of the group and describes past challenges the group has experienced when discussing papers — seeing papers as related and as contributing to a common effort. These challenges led us as TWG19 team leaders to develop three initiatives to support communication among researchers who work in different contexts with different purposes. The initiatives are presented and used to discuss the papers. We conclude with implications for the future. 

I argue that we are morally obliged to consider the significant privilege of our lives and the whiteness of mathematics education institutions. Further, to determine implications for our work will require: (i) questioning things we’ve long taken for granted; (ii) developing means for stepping outside our training and standards; and (iii) learning to work together and in communities of those who are not like us but with whom we find alignment. Failing to take up this imperative confirms that we are the problem and existing injustice is our choice, not a reality imposed on us. I mean to argue this with both fervour and humility, using my own personal and professional journey to raise possibilities for us to consider, as a community, in charting the future of mathematics education research. 

Professional fields face persistent challenges in connecting practice and theory. In particular, tensions exist as to how theory and knowledge are developed, as well as what constitutes authority for practice. Together the articles in this issue explore three elements of the turn toward ”practice-based” research and professional education in mathematics education: designing teaching and learning in and for practice, learning mathematics teaching as a practice, and collaborating across professional roles and identities. In this commentary, we interrogate meanings of practice-based research on teaching and discuss themes across this collection of articles. We then argue for three imperatives for future efforts: (i) working on shared understandings of what the term ”practice-based” might mean; (ii) developing more nuanced conceptualizations of ”teaching”; and (iii) attending explicitly to justice in practice. 

Mathematics teaching produces and reproduces social injustice. It also has the potential to disrupt patterns of inequity and advance just communities of practice. Drawing from literature on equitable mathematics teaching, we analyze the work of leading a discussion of student solutions in ways that nurture healthy identities, relationships and societies. From a conceptual analysis of a Norwegian mathematics lesson, we first identify dynamics of race and gender at play, then identify three key aspects of mathematics teaching that can serve to disrupt these dynamics while creating opportunities for alternative identities, relationships and futures: (i) having regard for property and its use; (ii) taking up student thinking as participatory citizenship; and (iii) orchestrating collective mathematical work. We discuss nuances of this work and implications for research on teaching. 

Researchers conceptualize mathematical knowledge for teaching in different ways, but a coherent approach to the mathematical education of teachers requires teacher educators’ understanding to be robust and shared. At present, we know little about how teacher educators interpret and operationalize this important domain. Our analysis of interview data indicates two sites of divergence in teacher educators’ understanding. Some view this knowledge as a resource for the mathematical work of teaching, treating it as distant from actual practice, whereas others view it as a slice of the dynamic and situational work. Also, some view the mathematical work of teaching, and its knowledge demands, as detached from particulars of students and schooling, while others view this work as inseparable from student identities and the larger environments within which instruction occurs, thus integrating regard for equity. Implications are discussed.