Mathematics today is approaching a state of cnSIS. As the demands of science and society for mathematical literacy increase, the percentage of American college students intending to major in mathematics plummets and achievement scores of entering college students continue thelt unremit ting decline. As research in core mathematics reaches unprecedented heights of power and sophistication, the growth of diverse applied special ties threatens to fragment mathematics into distinct and frequently hostile mathematical sciences. These crises in mathematics presage difficulties for science and engineer ing, and alarms are beginning to sound in the scientific and even in the political communities. Citing a trend towards "virtual scientific and techno logical illiteracy" and a "shrinking of our national commitment to excel lence . . . in science, mathematics and technology," a recent study con ducted for the President by the U. S. National Science Foundation and Department of Education warns of serious impending shortcomings in public understanding of science. "Today people in a wide range of non scientific . . . professions must have a greater understanding of technology than at any time in our history. Yet our educational system does not now provide such understanding. " The study goes on to conclude that present trends pose great risk of manpower shortages in the mathematical and engineering sciences. "The pool from which our future scientific and engineering personnel can be drawn is . . . in danger of becoming smaller, even as the need for such personnel is increasing. " It is time to take a serious look at mathematics tomorrow.

Social constructivism is just one view of learning that places emphasis on the social aspects of learning. Other theoretical positions, such as activity theory, also emphasise the importance of social interactions. Along with social constructivism, Vygotsky's writings on children's learning have recently also undergone close scru tiny and researchers are attempting a synthesis of aspects ofVygotskian theory and social constructivism. This re-examination of Vygotsky's work is taking place in many other subject fields besides mathematics, such as language learning by young children. It is interesting to speculate why Vygotsky's writings have appealed to so many researchers in different cultures and decades later than his own times. Given the recent increased emphasis on the social nature of learning and on the interactions between student, teacher and context factors, a finer grained analysis of the nature of different theories of learning now seems to be critical, and it was considered that different views of students' learning of mathematics needed to be acknowledged in the discussions of the Working Group.

The Symposium on the Current State and Prospects of Mathematics was held in Barcelona from June 13 to June 18, 1991. Seven invited Fields medalists gavetalks on the development of their respective research fields. The contents of all lectures were collected in the volume, together witha transcription of a round table discussion held during the Symposium. All papers are expository. Some parts include precise technical statements of recent results, but the greater part consists of narrative text addressed to a very broad mathematical public. CONTENTS: R. Thom: Leaving Mathematics for Philosophy.- S. Novikov: Role of Integrable Models in the Development of Mathematics.- S.-T. Yau: The Current State and Prospects of Geometry and Nonlinear Differential Equations.- A. Connes: Noncommutative Geometry.- S. Smale: Theory of Computation.- V. Jones: Knots in Mathematics and Physics.- G. Faltings: Recent Progress in Diophantine Geometry.

With the ninth edition of the four-yearly review of mathematics education research in Australasia, the Mathematics Education Research Group of Australasia (MERGA) discusses the Australasian research in mathematics education in the four years from 2012-2015. This review aims to critically promote quality research and focus on the building of research capacity in Australasia.

This book comprises the Proceedings of the 12th International Congress on Mathematical Education (ICME-12), which was held at COEX in Seoul, Korea, from July 8th to 15th, 2012. ICME-12 brought together 3500 experts from 92 countries, working to understand all of the intellectual and attitudinal challenges in the subject of mathematics education as a multidisciplinary research and practice. This work aims to serve as a platform for deeper, more sensitive and more collaborative involvement of all major contributors towards educational improvement and in research on the nature of teaching and learning in mathematics education. It introduces the major activities of ICME-12 which have successfully contributed to the sustainable development of mathematics education across the world. The program provides food for thought and inspiration for practice for everyone with an interest in mathematics education and makes an essential reference for teacher educators, curriculum developers and researchers in mathematics education. The work includes the texts of the four plenary lectures and three plenary panels and reports of three survey groups, five National presentations, the abstracts of fifty one Regular lectures, reports of thirty seven Topic Study Groups and seventeen Discussion Groups.

Mobile technologies influence the way that we interact with the world, the way that we live. We use them for communication, entertainment, information and research. In education settings, there has been substantial investment in mobile devices, often without a concomitant investment in developing pedagogy and practices. With mobile technologies evolving rapidly, and the number of educational apps growing, there is a need for research into how they facilitate mathematics learning. Such research is of particular importance regarding how such devices may be used to open up new ways of envisaging mathematics and mathematics education, and to help develop conceptual rather than procedural or declarative knowledge. This volume draws upon international research and reports on a range of research projects that have incorporated mobile technologies for mathematics education. It presents research on the use of mobile technologies, such as iPads, iPods, iPhones, Androids, and Tablets, across a diverse range of cultures, year levels and contexts. It examines the ways in which mobile technologies, including apps, might influence students’ engagement, cognition, collaboration and attitudes, through the reshaping of the learning experience. In addition, the book presents appropriate ways to integrate mobile technologies into teaching and learning programmes. It is a significant reference book for those involved with teaching mathematics or using mobile technologies in education, while also offering insights and examples that are applicable to the use of digital technologies in education generally.