Final Commentary: the Challenge Continues

Final Commentary: The Challenge Continues This edited volume started off as a practical project of the first editor to fill a self- identified void of not having a singular Canadian text that could be used as a source of relevant literature in teaching future secondary school mathematics teachers. Enter the Canadian Mathematics Education Study Group (CMESG), specifically and perhaps appropriately, a conversation during a meal at the 40th anniversary meeting of CMESG, in Kingston, Ontario, and a much bigger vision was born. By the end of a scenic boat ride, we began collaborating as editors, and the project was greatly expanded, eventually bringing together a collection of Canadian authors who work and research within Canadian secondary classrooms in some capacity. Broader vision and context would be provided by having a contributor who was foundational within the Canadian mathematics education community, begin each section with a preface. The ‘landscape’ reference was purposeful; we wanted to represent our varying culture, geography, and context as broadly as possible. As well as including Indigenous and Francophone perspectives, each section of chapters also included the voice of a current classroom teacher (“A teacher’s view”), in order to provide a practical, grassroots examination of some aspect of the section theme from a practicing teacher’s perspective. In the end, the addition of the international authors who graciously offered to read the pieces and use their own contexts to comment on the works greatly added to the depth of what could be accomplished within this single volume and allowed for us to see the possibilities for connecting our Canadian contexts to those beyond our own borders. Below we detail some final thoughts on how we put the sections together and take a look at how the commentaries in each of the six parts have challenged or supported the writings within each section. The collected volume began with a highly meaningful preface by Edward Doolittle that encompassed a fundamental vision for putting together this collection in the Canadian context. As he noted, “Indigenous culture and issues are foundational to Canada; and …continue to be a necessary part of anything Canadian” (Preface, this volume). We were deeply honored by the connections made between © Springer International Publishing AG, part of Springer Nature 2018 641 A. Kajander et al. (eds.), Teaching and Learning Secondary School Mathematics, Advances in Mathematics Education, https://doi.org/10.1007/978-3-319-92390-1 642 Final Commentary: The Challenge Continues the work of the Canadian authors that we had compiled for this volume to this fundamental part of being Canadian and working in a Canadian school context. Doolittle’s moving preface highlighted how all of the authors did in fact support this context to some degree. In this vein, he also brought the volume to an international audience in his final comments on how these are issues that all peoples face and added, “the question is what we [as Indigenous peoples] have to offer to Canada, and the world” (Doolittle, this volume). It is with this initial overview of connections to Indigeneity that situates all of the sections and chapters under one broader theme and extends the link to secondary school mathematics. We chose to begin the collection of authors’ work with a look at “The changing landscape of teaching and learning mathematics” because we have all been partici- pants and observers in how teaching in secondary schools has changed and continues to change. We were honoured that two Canada Research Chairs (Rina Zazkis and Nathalie Sinclair), as well as mathematician and long-standing mathematics education advocate Walter Whiteley, contributed prefaces to this section. In this first section, we chose to situate the volume in the historical as well as cultural landscape of our context. Beginning the contained chapters with Peter Taylor was an obvious choice because he has been pivotal in how Canadian mathematics education has been shaped over the last four decades, which he describes in his chapter. As a ‘founding father’ of CMESG, an organisation with which all of the various section preface authors have been involved, Peter has forever left a mark on teaching and learning mathematics in Canada. We also wanted to include a strong focus on the Indigenous knowledges that both inform and shape our Canadian classrooms. As a more recent aspect of our context, Canadian schools are beginning to focus on emo- tional well-being and mental health so this was also deemed a necessary aspect of this first section. Kaino’s commentary on this section looked at how the chapters were illustrative of the changing portions of school from his own context and perspective. As he noted, this section provides a chance to “re-think innovative and better ways of teaching and learning mathematics” (Kaino, Part I commentary, this volume). This need for innovative changes answers the call of many mainstream media headlines that question the effectiveness and status of mathematics education in Canada and many other areas of the world. In the end, Kaino supports the driving vision of today’s classrooms (and this volume): to “provide ways for long-term retention of mathematical knowledge” (Part I commentary, this volume). Part I provided the broad strokes of the challenges facing today’s secondary classrooms in preparing the learners to be mathematics users (and not just learners), and the remaining sections each tackle specific areas relating to classroom teaching. “Shifting to a culture of inclusion,” as introduced by David Pimm, a well-known mathematics educator in Canada, focussed attention on helping all learners to succeed in mathematics classrooms, not just those who would go on to become mathematics educators and mathematicians later in life. Our choices for the chapters examined those who are most at-risk in our classrooms including students who are coming from other parts of the world. Although most of the chapters around at-risk classrooms were Ontario based, we felt the stories were not unique to this part of the country or even the world, and the stories could highlight learners who need the Final Commentary: The Challenge Continues 643 most support in our classrooms. Through these chapters, we reiterate the fundamental idea that the information included is supportive of the quote by the Expert Panel on Student Success in Ontario (2004) as well as other learning initiatives (e.g., Ontario Ministry of Education 2013): “good for all, necessary for some” (p. 42). Beswick, in her commentary, responds to the chapters by beginning with an overview of some of the difficulties in enacting the ideas in the chapters in this section. The first challenge she brings forward is the complex issue of how a teacher’s beliefs interact (or interfere) with how pedagogy is taken up and implemented in the classroom. This idea is a theme throughout the rest of the book as many of the chapters challenge traditional ideas of what teaching mathematics at the secondary school level is and should be. Part III in the volume, introduced by Elaine Simmt, another well-known Canadian mathematics education researcher, discusses how relationships can be fostered in classroom environments. As stated by Boland and Tranter in Part I, the basis of all teaching experiences is the relationship that is formed with students and the school community. The chapters in this section critically look at different ways relationships can help foster greater student success in academics by focussing on behaviours and other characteristics. Mosvold notes, “The fostering of relationships, then, goes beyond attending to students’ mathematical thinking, and it involves getting to know their histories, the experiences they have made in and outside of school, their cultural background, and everything else that constitutes their identity” (Part III commentary, this volume). His commentary on the section notes that the connections among chapters attend to the different aspects that constitute the identities of secondary students in the classroom. As he notes, two of the chapters specifically focus on relationships within the classroom and student thinking; whereas, the other three focus on the development of the whole person through the relationships. Mosvold ends his commentary with a concern of the tendency to take theories of learning from other fields and then use them to apply to teaching by assuming them as theories of teaching. He turns his focus to how the chapter with the strongest link to teaching is also the one without an explicit theoretical foundation (Newell). The noted chapter is an interesting treatise into looking at teaching as all that a teacher does in an effort to support the learning of students. Mosvold concludes that “more conceptual work needs to be done in studies of mathematics teaching, and conceptualizations of mathematics teaching should strive towards capturing the dynamic interactions between mathematical and pedagogical aspects of the work of teaching” (Part III commentary, this volume). The commentary ends with a discussion about the complex nature of teaching and how this section has shown the need to conceptualize teaching as more than just certifications. Following the more theoretical nature of this section, the edited volume moves into specific pedagogy for teaching mathematics. The part entitled “Enhancing problem-based learning” was meant to serve as a collection of chapters that focus on specific examples of using this type of learning environment in the classroom. All of the work in the section was meant to answer the call of mandates by the Canadian Manifesto (Whiteley and Davis 2003/2016), the National Council of Teachers of Mathematics (2000), and others, to include 644 Final Commentary: The Challenge Continues more tasks and explorations in the classroom. The focus in the section is on using problems in a way that allows students to explore the mathematics, and not just use routine problems to practice previously known formulas.

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