This volume traces back the history of interaction between the "computational" or "algorithmic" aspects of elementary mathematics and mathematics education throughout ages. More specifically, the examples of mathematical practices analyzed by the historians of mathematics and mathematics education who authored the chapters in the present collection show that the development (and, in some cases, decline) of counting devices and related computational practices needs to be considered within a particular context to which they arguably belonged, namely, the context of mathematics instruction; in their contributions the authors also explore the role that the instruments played in formation of didactical approaches in various mathematical traditions, stretching from Ancient Mesopotamia to the 20th century Europe and North America.

This volume provides new insights on creativity while focusing on innovative methodological approaches in research and practice of integrating technological tools and environments in mathematics teaching and learning. This work is being built on the discussions at the mini-symposium on Creativity and Technology at the International Conference on Mathematical Creativity and Giftedness (ICMCG) in Denver, USA (2014), and other contributions to the topic. The book emphasizes a diversity of views, a variety of contexts, angles and cultures of thought, as well as mathematical and educational practices. The authors of each chapter explore the potential of technology to foster creative and divergent mathematical thinking, problem solving and problem posing, creative use of dynamic, multimodal and interactive software by teachers and learners, as well as other digital media and tools while widening and enriching transdisciplinary and interdisciplinary connections in mathematics classroom. Along with ground-breaking innovative approaches, the book aims to provide researchers and practitioners with new paths for diversification of opportunities for all students to become more creative and innovative mathematics learners. A framework for dynamic learning conditions of leveraging mathematical creativity with technology is an outcome of the book as well.

Interdisciplinarity has become increasingly important for emergent professions of the 21st century yet there is a dearth of systematic studies aimed at implementing it in the school and university curricula. The Mathematics and its Connections to the Arts and Sciences (MACAS ) group places Mathematics as a vehicle through which deep and meaningful connections can be forged with the Arts and the Sciences and as a means of promoting interdisciplinary and transdisciplinary thinking traits amongst students. The Third International Symposium held by the MACAS group in Moncton, Canada in 2009 included numerous initiatives and ideas for interdisciplinarity that are implementable in both the school and university setting. The chapters in this book cover interdisciplinary links with mathematics found in the domains of culture, art, aesthetics, music, cognition, history, philosophy, engineering, technology and science with contributors from Canada, U.S, Denmark, Germany, Mexico, Iran and Poland amongst others.

This first book in the series will describe the Net Generation as visual learners who thrive when surrounded with new technologies and whose needs can be met with the technological innovations. These new learners seek novel ways of studying, such as collaborating with peers, multitasking, as well as use of multimedia, the Internet, and other Information and Communication Technologies. Here we present mathematics as a contemporary subject that is engaging, exciting and enlightening in new ways. For example, in the distributed environment of cyber space, mathematics learners play games, watch presentations on YouTube, create Java applets of mathematics simulations and exchange thoughts over the Instant Messaging tool. How should mathematics education resonate with these learners and technological novelties that excite them?

A Volume in The Montana Mathematics Enthusiast: Monograph Series in Mathematics EducationSeries Editor Bharath Sriraman, The University of MontanaInterdisciplinarity is increasingly viewed as a necessary ingredient in the training of future oriented 21st century disciplinesthat rely on both analytic and synthetic abilities across disciplines. Nearly every curricular document or vision statement ofschools and universities include a call for promoting creativity in students. Yet the construct of creativity and giftednessacross disciplines remains elusive in the sense that the prototypical examples of such work come from eminent scientists, artists and mathematicians, and little if any work has been conducted with non-eminent individuals. This monograph is anattempt to fill this gap by putting forth the view that interdisciplinarity and creativity are related constructs, and that thecultivation of domain general creativity is possible. Mathematics has historically been anchored to numerous disciplineslike theology, natural philosophy, culture and art, allowing for a flexibility of thought that is difficult to cultivate in otherdisciplines. In this monograph, the numerous chapters from Australia, U.S.A., Canada, Cyprus, Denmark and Japanprovide a compelling illustration of the intricate connection of mathematics with literature, paradoxes, history, technologyand modeling, thus serving as a conduit for interdisciplinarity, creativity and learning to occur.

This volume provides new insights on creativity while focusing on innovative methodological approaches in research and practice of integrating technological tools and environments in mathematics teaching and learning. This work is being built on the discussions at the mini-symposium on Creativity and Technology at the International Conference on Mathematical Creativity and Giftedness (ICMCG) in Denver, USA (2014), and other contributions to the topic. The book emphasizes a diversity of views, a variety of contexts, angles and cultures of thought, as well as mathematical and educational practices. The authors of each chapter explore the potential of technology to foster creative and divergent mathematical thinking, problem solving and problem posing, creative use of dynamic, multimodal and interactive software by teachers and learners, as well as other digital media and tools while widening and enriching transdisciplinary and interdisciplinary connections in mathematics classroom. Along with ground-breaking innovative approaches, the book aims to provide researchers and practitioners with new paths for diversification of opportunities for all students to become more creative and innovative mathematics learners. A framework for dynamic learning conditions of leveraging mathematical creativity with technology is an outcome of the book as well.

This open access Topical Survey offers a brief overview of the current state of research on and activities for mathematically gifted students around the world. This is of interest to a broad readership, including educational researchers, research mathematicians, mathematics teachers, teacher educators, curriculum designers, doctoral students, and other stakeholders. It first discusses research concerning the nature of mathematical giftedness, including theoretical frameworks and methodologies that are helpful in identifying and/or creating mathematically gifted students, which is described in this section. It also focuses on research on and the development of mathematical talent and innovation in students, including connections between cognitive, social and affective aspects of mathematically gifted students. Exemplary teaching and learning practices, curricula and a variety of programs that contribute to the development of mathematical talent, gifts, and passion are described as well as the pedagogy and mathematics content suitable for educating pre-service and in-service teachers of mathematically gifted students. The final section provides a brief summary of the paper along with suggestions for the research, activities, and resources that should be available to support mathematically gifted students and their teachers, parents, and other stakeholders.

This first book in the series will describe the Net Generation as visual learners who thrive when surrounded with new technologies and whose needs can be met with the technological innovations. These new learners seek novel ways of studying, such as collaborating with peers, multitasking, as well as use of multimedia, the Internet, and other Information and Communication Technologies. Here we present mathematics as a contemporary subject that is engaging, exciting and enlightening in new ways. For example, in the distributed environment of cyber space, mathematics learners play games, watch presentations on YouTube, create Java applets of mathematics simulations and exchange thoughts over the Instant Messaging tool. How should mathematics education resonate with these learners and technological novelties that excite them?

This book celebrates the 15th anniversary of the bi-annual symposium series Mathematics and its Connections to the Arts and Sciences (MACAS), which was first held in 2005 following the continued collaboration of an international group of researchers from ICME Topic Study Group 21. The MACAS-conferences bring together scientists and educators who are interested in the connection between mathematics, arts and science in educational curriculum, while emphasizing on, as well as researching about, the role of mathematics. By pooling together these different approaches and viewpoints between mathematics, arts and sciences, this book reveals possible synergies and paths for collaborations. In view of the challenges of the 21st century, a modern approach to education with a focus on multi- and interdisciplinarity is more important than ever. The role of mathematics assumes a key role in this approach as it is connected to all other disciplines, such as STEM education, physics, chemistry, biology, aesthetics and language, and can serve as a bridge between them. This book discusses, amongst others, the curricular approaches to integrate mathematics and other disciplines, the importance of mathematical modelling and the interdisciplinarity ways for learning and studying of mathematics, as well as the intercultural dimensions of mathematics and mathematics in the digital era. All topics will be presented from very different perspectives and regarding very different contexts, including digitization, culture and sustainability. This unique collection will serve as a very valuable and compact source for all above mentioned scientists and educators, as well as for use in advanced teacher education courses.

Interdisciplinarity has become increasingly important for emergent professions of the 21st century yet there is a dearth of systematic studies aimed at implementing it in the school and university curricula. The Mathematics and its Connections to the Arts and Sciences (MACAS ) group places Mathematics as a vehicle through which deep and meaningful connections can be forged with the Arts and the Sciences and as a means of promoting interdisciplinary and transdisciplinary thinking traits amongst students. The Third International Symposium held by the MACAS group in Moncton, Canada in 2009 included numerous initiatives and ideas for interdisciplinarity that are implementable in both the school and university setting. The chapters in this book cover interdisciplinary links with mathematics found in the domains of culture, art, aesthetics, music, cognition, history, philosophy, engineering, technology and science with contributors from Canada, U.S, Denmark, Germany, Mexico, Iran and Poland amongst others.

Our study aims to develop an operational model for the identification and fostering of mathematically gifted students at the regular elementary classroom. It reflects seven years of experience in teaching of challenging mathematics curriculum to Kindergarten through Grade 6 children having various levels of abilities. In our analysis of lessons, we discussed two questions: How to interpret young children's mathematical work in terms of mathematical giftedness? and What kind of didactical situations are favourable in order to foster mathematical abilities? In the search for efficient inclusive teaching strategies, we developed a theoretical framework based on the model of the 'challenging situations approach'. On the basis of classroom observations and examples of students' solutions of challenging mathematical tasks, we identified several characteristics of mathematical giftedness, such as mathematical precocity, thinking in concepts and relationships, high motivation and perseverance, systemic and reflective mind, as well as seeing the world with 'mathematical eyes'. Recommendations for research and practice are also given.

A Volume in The Montana Mathematics Enthusiast: Monograph Series in Mathematics EducationSeries Editor Bharath Sriraman, The University of MontanaInterdisciplinarity is increasingly viewed as a necessary ingredient in the training of future oriented 21st century disciplinesthat rely on both analytic and synthetic abilities across disciplines. Nearly every curricular document or vision statement ofschools and universities include a call for promoting creativity in students. Yet the construct of creativity and giftednessacross disciplines remains elusive in the sense that the prototypical examples of such work come from eminent scientists, artists and mathematicians, and little if any work has been conducted with non-eminent individuals. This monograph is anattempt to fill this gap by putting forth the view that interdisciplinarity and creativity are related constructs, and that thecultivation of domain general creativity is possible. Mathematics has historically been anchored to numerous disciplineslike theology, natural philosophy, culture and art, allowing for a flexibility of thought that is difficult to cultivate in otherdisciplines. In this monograph, the numerous chapters from Australia, U.S.A., Canada, Cyprus, Denmark and Japanprovide a compelling illustration of the intricate connection of mathematics with literature, paradoxes, history, technologyand modeling, thus serving as a conduit for interdisciplinarity, creativity and learning to occur.