Braille readers use a braille display and text-to-speech synthesizer while reading and comprehending mathematical expressions and equations. Teachers need to have technological, pedagogical and content (TPACK) knowledge and skills for exploiting the potential of these devices in mathematics education. They have to understand how the use of…

This paper presents the "Mathematics Teacher's Specialised Knowledge" (MTSK) model. It acknowledges earlier contributions to understanding and structuring teachers' knowledge, in particular, the special debt owed to Shulman's notion of "pedagogical content knowledge" and to Ball and collaborators' "Mathematical Knowledge…

This qualitative research presents how a mathematics teacher educator's feedbacks to two lower secondary school mathematics teachers affects their design of hypothetical learning trajectories regarding teaching patterns and their teaching practice. The data comes from a web portal, which was designed as a professional development tool for…

Teachers' personal understanding of knowledge and how it is acquired has important implications for their approaches to teaching and engaging pupils in learning. This article extends learning about emergent teachers' professional knowledge by critiquing and theorising survey responses detailing student teachers' experience of teaching during their…

This article examines the shared experiences and understandings teachers draw on to teach children with an awareness of linguistic diversity. To do so, we analyzed interviews from Turkey and the United States and drew on philosophical hermeneutics as a way to develop a disruptive understanding of teachers' views regarding the role of languages in…

Teachers are increasingly being called upon to teach in ways that develop 21st century learning skills in their students. Various frameworks for 21st century learning have been proposed and while they differ, all agree on four components for development--creativity, collaboration, communication and critical thinking. Both individually and…

Over the past few decades there has been increased interest in how students and teachers think and learn about negative numbers from a variety of perspectives. In particular, there has been debate about when integers should be taught and how to teach them to best support students' learning. This book brings together recent work from researchers to…

The nature of mathematics teachers' knowledge specific to teaching mathematics [MTK] is of ongoing concern in mathematics education research. This article contributes to our under-standing of this knowledge with particular focus on reflective awareness. It discusses MTK based on ways it has been used in research. It highlights reflective awareness…

Although the importance of mathematical problem solving is now widely recognised, relatively little attention has been given to the conceptualisation of mathematical processes such as representing, analysing, interpreting and communicating. The construct of Mathematical Knowledge for Teaching (Hill, Ball & Schilling, 2008) is generally…

In this paper, we present an emerging set of learning conjectures and design principles to be used in the development of professional learning tasks that support elementary teachers' learning of mathematics learning trajectories. We outline our theoretical perspective on teacher knowledge of learning trajectories, review the literature concerning…

These Proceedings are a written record of the research presented at the 35th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA 2013) held in Chicago, Illinois, November 14-17, 2013. The theme of the conference is Broadening Perspectives on Mathematics Thinking and Learning.…

Ambitious teaching is a form of teaching that requires a high level of teacher responsiveness to what students do as they actively engage with the subject matter. Thus, a teacher enacting ambitious teaching is often confronted with uncertainties about how to advance students' learning while also building on students' contributions. In…

This paper offers for discussion and critique a conceptual framework that applies a situative perspective on learning to the study of learning to teach mathematics. From this perspective, such learning occurs in many different situations--mathematics and teacher preparation courses, pre-service field experiences, and schools of employment. By…

This brochure highlights key concepts of the American Federation of Teachers (AFT) "Thinking Mathematics" courses. Citing adherence to No Child left Behind Act (NCLB) mandates, these courses are: (1) based on scientific research about how children learn mathematics; (2) designed to increase teacher mathematical knowledge; (3) provide a…

This document contains the third volume of the proceedings of the 28th Annual Conference of the International Group for the Psychology of Mathematics. Conference presentations are centered around the theme "Inclusion and Diversity". A total of 65 research reports are presented here: (1) A Teacher's Model of Students Algebraic Thinking…