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Mollie MacGregor and Kaye Stacey

Research studies have found that the majority of students up to age 15 seem unable to interpret algebraic letters as generalised numbers or even as specific unknowns. Instead, they ignore the letters, replace them with numerical values, or regard them as shorthand names. The principal explanation given in the literature has been a general link to levels of cognitive development. In this paper we present evidence for specific origins of misinterpretation that have been overlooked in the literature, and which may or may not be associated with cognitive level. These origins are: intuitive assumptions and pragmatic reasoning about a new notation, analogies with familiar symbol systems, interference from new learning in mathematics, and the effects of misleading teaching materials. Recognition of these origins of misunderstanding is necessary for improving the teaching of algebra.

Edited by Helle Alrø, Ole Ravn and Paulo Valero

Critical mathematics education brings together a series of concerns related to mathematics and its role in society, the practices of teaching and learning of mathematics in educational settings, and the practices of researching mathematics education. The work of Ole Skovsmose has provided a seminal contribution to the shaping of those concerns in the international community of mathematics educators and mathematics education researchers. This book gathers contributions of researchers from five continents, for whom critical mathematics education has been an inspiration to think about many different topics such as the dialogical and political dimensions of teacher education, mathematical modeling, the philosophy of mathematics from social and political perspectives, teaching practices in classrooms, the connection between mathematics and society, the scope and limits of critical thinking in relation to mathematics and mathematics education, and the political dimension of researching mathematics education.
The book is not only a tribute to Ole Skovsmose’s long academic career; it is also a way of providing an overview of the roots of the critical mathematics education concerns, their current developments in different parts of the world, and their future directions. With a diversity of styles and forms of texts, this book is addressed to all those teachers and researchers who would like to be introduced or would like to go deeper into the types of insights that critical mathematics education offers.

David A. Reid and Christine Knipping

Edited by Christopher Andersen, Nora Scheurer, María del Puy Leonor Pérez Echeverría and Eva Teubal

Learning and teaching complex cultural knowledge calls for meaningful participation in different kinds of symbolic practices, which in turn are supported by a wide range of external representations, as gestures, oral language, graphic representations, writing and many other systems designed to account for properties and relations on some 2- or 3-dimensional objects. Children start their apprenticeship of these symbolic practices very early in life. But being able to understand and use them in fluid and flexible ways poses serious challenges for learners and teachers across educational levels, from kindergarten to university.
This book is intended as a step in the path towards a better understanding of the dynamic relations between different symbolic practices and the acquisition of knowledge in various learning domains, settings and levels. Researchers from almost twenty institutions in three different continents present first hand research in this emerging area of study and reflect on the particular ways and processes whereby participation in symbolic practices based on a diversity of external representations promotes learning in specific fields of knowledge.
The book will be useful for persons interested in education, as well as cognitive psychologists, linguists and those concerned by the generation, appropriation, transmission and communication of knowledge.

Edited by Gerald Kulm

This book presents a coherent collection of research studies on teacher knowledge and its relation to instruction and learning in middle-grades mathematics. The authors provide comprehensive literature reviews on specific components of mathematics knowledge for teaching that have been found to be important for effective instruction. Based on the analysis of video data collected over a six-year project, the chapters present new and accessible research on the learning of fractions, early concepts of algebra, and basic statistics and probability.

The three sections of the book contain chapters that address research on the development of mathematics knowledge for teaching at the undergraduate level, instructional practices of middle-grades teachers, and the implications of teacher knowledge of mathematics for student learning. The chapters are written by members of a research team led by the Editor that has been working for the past six years to develop practical and useful theories and findings on variables that affect teaching and learning of middle grades mathematics.

Mathematics knowledge for teaching is a topic of great current interest. This book is a valuable resource for mathematics education researchers, graduate students, and teacher educators. In addition, professional developers and school district supervisor and curriculum leaders will find the concrete examples of effective teaching strategies useful for teacher workshops.

Marcelo C. Borba, Ana Paula dos Santos Malheiros and Rúbia Barcelos Amaral Zulatto

This book will address the discussion on online distance education, teacher education, and how the mathematics is transformed with the Internet, based on examples that illustrate the possibilities of different course models and on the theoretical construct humans-with-media. We will attempt to give the reader the sensation of experiencing one of the various distance courses in which we have participated, or a virtual community that does not have the structure of a course. And if the reader has not yet participated in any of these possibilities, we believe that the book may help, but not substitute, the experience of participating in a discussion list, a course, or a virtual community constituted by a specific interest.
This book is part of a collection of books called Trends in Mathematics Education, originally published in Brazil. This collection began being published in 2001 and currently has 21 titles published by more than 30 different authors. It is designed to present research to a broader audience that extends beyond academia. The books have been widely used in graduate courses, research groups and in some undergraduate classes. About 60, 000 copies of the Portuguese edition have been sold. Some titles have been translated into Spanish and English.


Judy Anderson, Janette Bobis and Jenni Way

In the past ten years, research surrounding teacher professional learning and development in mathematics education has increased rapidly in both volume and focus. An examination of recent studies emanating from large-scale professional development projects has enabled the identification of key features associated with effective professional development. Similarly, trends from a large number of smaller-scale studies have emerged and helped raise important questions for future research into teacher professional development and learning. The review shows that there is still a great deal to learn about what makes professional development more effective. Recommendations for future research are presented.


Colleen Vale and Hannah Bartholomew

The meaning of gender equity, the degree and nature of gender equity in mathematical outcomes and pedagogical practices, and the theoretical position of researchers of gender and mathematics are the concerns of the review of literature presented in this chapter. Findings generally reveal few significant gender differences in mean scores for achievement in Australia and New Zealand for the period under review, but gender differences favouring males in a range of affective factors, and in senior secondary participation, persist. Feminist and post-modern theories influenced some research into pedagogical practices, however most of the Australasian research conducted in the current period drew upon difference or deficit theory.


Allan L. White

This chapter focuses on Australasian research into the mathematical understandings of students in the middle years of school (years 4-9), a key stage in students’ mathematical development in terms of engagement with mathematics and future study choices. Research focusing on student thinking across a range of content areas including rational number, space, algebra, and chance and data is reviewed. Studies on related issues including primary to secondary transition and teacher professional learning are also discussed. A range of areas for further research is presented.