Jana Visnovska

Mathematics Teachers as Instructional Designers: What Does it Take?

In this chapter, we draw on a 5-year interventionist professional development study that we conducted with a group of middle-school mathematics teachers in the United States. The fifth and final year of the study involved a performance assessment in which the teachers collectively designed an instructional unit on statistics that aimed both to build on what they learned in the professional development group and to address the objectives for middle-school statistics prescribed by the standards and objectives for mathematics in their states. This performance assessment provided a window into the teachers’ documentation work, especially on the resources they needed to engage in this type of design work effectively. We draw on this case to problematize the rhetoric of teachers as instructional designers. In doing so, we question the common assumption that groups of teachers are capable of designing coherent instructional sequences from provided materials immediately and without ongoing support. We illustrate that teachers becoming effective instructional designers and the associated professionalization of teaching are significant accomplishments.

On comparing mathematical models and pedagogical learning

Comparing and contrasting different mathematical models of realistic situations is one way in which the relative strengths and weaknesses of these models, and the mathematics that underpins them, can become the focus of discussion in a mathematics classroom. This chapter reports on one episode from a research and development project where teachers were learning to orchestrate such classroom discussions with a view to providing opportunities for their students to apply mathematical understanding and skills in context. While the teachers did discuss a range of models they also experienced difficulty in reconciling the conflicting ideas represented in these models.

Present Research on Mathematics Textbooks and Teachers’ Resources in ICME-13: Conclusion and Perspectives

This chapter summarizes and discusses the state of the art of research on mathematics textbooks and other resources and their use as depicted in this volume. The discussion focuses on three questions: First, what are the theoretical and methodological tools used in order to conceptualize and investigate textbook and resource use? Second, what can we learn about the use of textbooks and resources by teachers from the chapters in this volume? Third, what do we learn from comparing teachers-resources interactions across different countries? Based on the discussion, conclusions are drawn regarding perspectives of future research on mathematics textbooks and resources and their use.

Developing Statistical Numeracy: The Model Must Make Sense

Teaching statistical numeracy in middle school classrooms requires high quality instruction that promotes opportunities to use mathematics in modelling problem situations. In this chapter we report on a professional development session that involved nine teachers from six rural and remote high schools in Queensland, Australia. Results indicate that some teachers focused on the mathematics they would teach, limiting numeracy opportunities, while others focussed on making sense of the problem by modelling, thereby promoting statistical numeracy. This research suggests that ongoing learning opportunities where such differences become the point of professional discussions are needed to support teachers’ understanding and appreciation of the role of modelling in promoting statistical numeracy.

Research on Mathematics Textbooks and Teachers’ Resources

This book focuses on issues related to mathematics teaching and learning resources, including mathematics textbooks, teacher guides, student learning and assessment materials, and online resources. The book highlights various theoretical and methodological approaches used to study teaching and learning resources, and addresses the areas of resources, teachers, and students at an international level. As for the resources, the book examines the role textbooks and other curricular or learning resources play in mathematics teaching, learning, and assessment. It asks questions such as: Could we consider different types of textbooks and roles they play in teaching and learning? How does the digitalization of information and communication affect these roles? What are defining features of e-textbooks, and how could we characterize the differences between the traditional textbooks and e-textbooks? As for the teachers, the book discusses the relationships between teachers’ individual and collective resources, and the way in which we could model such relationships. Specific questions addressed are: What is the role of teachers in developing textbooks and other teaching and learning materials? What are the relationships between resource designers and users? What are the consequences of these changing roles and relationships for the teaching of mathematics, and for teacher knowledge and professional development? As for the students, the book explores how students, as well as their teachers, interact through resources. It raises and addresses questions such as: What are the effects of modern ICT (particularly internet) on students’ use and the design of resources? How do changing patterns of use and design affect student behaviour, learning, and relationships to the subject of mathematics?This introduction aims to situate this monograph as a result of the work of the Topic Study Group (TSG) 38 at the 13th International Congress on Mathematical Education, held in Hamburg in July 2016. Beyond this goal, it aims to evidence the fact that, far from being an isolated work, the contributions received to this TSG, their number as well as their content, witness the emergence, at an international level, of a new field of research, dedicated to the teachers’ resources. After having set this scene, this introduction shortly overviews the chapters of this monograph, structured in four sections.

Resourcing teachers in transition to plan for interactions with students’ ideas

We explore how resources support teachers’ work broadly, and their preparation for interactions with students’ ideas specifically. We draw on data from two professional development design experiments aimed at supporting teachers in making students’ mathematical reasoning central to their instructional decisions. The forms of support that traditional resources and expectations provided were no longer present when teachers transitioned to proactively planning for classroom interactions. We identify new forms of support that designed instructional sequences can provide for teachers by (a) specifying simple initial goals for students’ reasoning, (b) supporting teachers’ design for classroom interactions, and (c) increasing the likelihood that these designs would do useful work in classrooms.

Research on mathematics textbooks and teachers’ resources: advances and issues

This book focuses on issues related to mathematics teaching and learning resources, including mathematics textbooks, teacher guides, student learning and assessment materials, and online resources. The book highlights various theoretical and methodological approaches used to study teaching and learning resources, and addresses the areas of resources, teachers, and students at an international level. As for the resources, the book examines the role textbooks and other curricular or learning resources play in mathematics teaching, learning, and assessment. It asks questions such as: Could we consider different types of textbooks and roles they play in teaching and learning? How does the digitalization of information and communication affect these roles? What are defining features of e-textbooks, and how could we characterize the differences between the traditional textbooks and e-textbooks? As for the teachers, the book discusses the relationships between teachers’ individual and collective resources, and the way in which we could model such relationships. Specific questions addressed are: What is the role of teachers in developing textbooks and other teaching and learning materials? What are the relationships between resource designers and users? What are the consequences of these changing roles and relationships for the teaching of mathematics, and for teacher knowledge and professional development? As for the students, the book explores how students, as well as their teachers, interact through resources. It raises and addresses questions such as: What are the effects of modern ICT (particularly internet) on students’ use and the design of resources? How do changing patterns of use and design affect student behaviour, learning, and relationships to the subject of mathematics?This introduction aims to situate this monograph as a result of the work of the Topic Study Group (TSG) 38 at the 13th International Congress on Mathematical Education, held in Hamburg in July 2016. Beyond this goal, it aims to evidence the fact that, far from being an isolated work, the contributions received to this TSG, their number as well as their content, witness the emergence, at an international level, of a new field of research, dedicated to the teachers’ resources. After having set this scene, this introduction shortly overviews the chapters of this monograph, structured in four sections.

Introduction: Research in Mathematics Education in Australasia 2012–2015

This chapter presents an overview of the most recent volume in a series of reviews entitled Research in Mathematics Education in Australasia. Each of MERGA’s four-yearly reviews proudly highlights and critiques the research in mathematics education in Australasia over the previous 4 years. In this chapter, we provide an overview of the history of the four-yearly review and explain the processes of how this review was brought together. Each chapter is briefly introduced within four key themes: Issues and contexts for mathematics education; learning and teaching; teacher preparation and development; and the future.