Visualization In Teaching And Learning Mathematics

The twenty papers in the book give an overview of research analysis, practical experience, and informed opinion about the role of visualization in teaching and learning mathematics, especially at the undergraduate level. Visualization, in its broadest level. Visualization, in its broadest sense, is as old as mathematics, but progress in computer graphics has generated a renaissance of interest in visual representations and visual thinking in mathematics.

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.

This unique volume surveys recent research on spatial visualization in mathematics in the fields of cognitive psychology and mathematics education. The general topic of spatial skill and mathematics has a long research tradition, but has been gaining attention in recent years, although much of this research happens in disconnected subfields. This volume aims to promote interaction between researchers, not only to provide a more comprehensive view of spatial visualization and mathematics, but also to stimulate innovative new directions in research based on a more coordinated effort. It features ten chapters authored by leading researchers in cognitive psychology and mathematics education, as well as includes dynamic commentaries by mathematics education researchers on cognitive psychology chapters, and by cognitive psychologists on mathematics education chapters. Among the topics included: From intuitive spatial measurement to understanding of units. Spatial reasoning: a critical problem-solving tool in children’s mathematics strategy tool-kit. What processes underlie the relation between spatial skill and mathematics? Learning with and from drawing in early years geometry. Communication of visual information and complexity of reasoning by mathematically talented students. Visualizing Mathematics makes substantial progress in understanding the role of spatial reasoning in mathematical thought and in connecting various subfields of research. It promises to make an impact among psychologists, education scholars, and mathematics educators in the convergence of psychology and education.

What does it mean to have a visual representation of a mathematical object, concept, or process? What visualization strategies support growth in mathematical thinking, reasoning, generalization, and knowledge? Is mathematical seeing culture-free? How can information drawn from studies in blind subjects help us understand the significance of a multimodal approach to learning mathematics? Toward a Visually-Oriented School Mathematics Curriculum explores a unified theory of visualization in school mathematical learning via the notion of progressive modeling. Based on the author’s longitudinal research investigations in elementary and middle school classrooms, the book provides a compelling empirical account of ways in which instruction can effectively orchestrate the transition from personally-constructed visuals, both externally-drawn and internally-derived, into more structured visual representations within the context of a socioculturally grounded mathematical activity. Both for teachers and researchers, a discussion of this topic is relevant in the history of the present. The ubiquity of technological tools and virtual spaces for learning and doing mathematics has aroused interest among concerned stakeholders about the role of mathematics in these contexts. The book begins with a prolegomenon on the author’s reflections on past and present visual studies in mathematics education. In the remaining seven chapters, visualization is pursued in terms of its role in bringing about progressions in mathematical symbolization, abduction, pattern generalization, and diagrammatization. Toward a Visually-Oriented School Mathematics Curriculum views issues surrounding visualization through the eyes of a classroom teacher-researcher; it draws on findings within and outside of mathematics education that help practitioners and scholars gain a better understanding of what it means to pleasurably experience the symmetric visual/symbolic reversal phenomenon – that is, seeing the visual in the symbolic and the symbolic in the visual."

Mathematics is, by its very nature, an abstract discipline. However, many students learn best by thinking in terms of tangible constructs. Enhancing Mathematics Understanding through Visualization: The Role of Dynamical Software brings these conflicting viewpoints together by offering visual representations as a method of mathematics instruction. The book explores the role of technology in providing access to multiple representations of concepts, using software applications to create a rich environment in which a student’s understanding of mathematical concepts can flourish. Both students and instructors of mathematics at the university level will use this book to implement various novel techniques for the delivery of mathematical concepts in their classrooms. This book is part of the Research Essential collection.

CRYSTAL—Alberta was established to research ways to improve students’ understanding and reasoning in science and mathematics. To accomplish this goal, faculty members in Education, Science, and Engineering, as well as school teachers joined forces to produce a resource bank of innovative and tested instructional materials that are transforming teaching in the K-12 classroom. Many of the instructional materials cross traditional disciplinary boundaries and explore contemporary topics such as global climate change and the spread of the West Nile virus. Combined with an emphasis on the use of visualizations, the instructional materials improve students’ engagement with science and mathematics. Participation in the CRYSTAL—Alberta project has changed the way I think about the connection between what I do as a researcher and what I do as a teacher: I have learned how to better translate scientific knowledge into language and activities appropriate for students, thereby transforming my own teaching. I also have learned to make better connections between what students are learning and what is happening in their lives and the world, thereby increasing students’ interest in the subject and enriching their learning experience.

Engage students in mathematics using growth mindset techniques The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the first-grade level through visualization, play, and investigation. During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message—that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that: There is no such thing as a math person - anyone can learn mathematics to high levels. Mistakes, struggle and challenge are the most important times for brain growth. Speed is unimportant in mathematics. Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics. With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum.

Semiotics as a Tool for Learning Mathematics is a collection of ten theoretical and empirical chapters, from researchers all over the world, who are interested in semiotic notions and their practical uses in mathematics classrooms. Collectively, they present a semiotic contribution to enhance pedagogical aspects both for the teaching of school mathematics and for the preparation of pre-service teachers. This enhancement involves the use of diagrams to visualize implicit or explicit mathematical relations and the use of mathematical discourse to facilitate the emergence of inferential reasoning in the process of argumentation. It will also facilitate the construction of proofs and solutions of mathematical problems as well as the progressive construction of mathematical conceptions that, eventually, will approximate the concept(s) encoded in mathematical symbols. These symbols hinge not only of mental operations but also on indexical and iconic aspects; aspects which often are not taken into account when working on the meaning of mathematical symbols. For such an enhancement to happen, it is necessary to transform basic notions of semiotic theories to make them usable for mathematics education. In addition, it is also necessary to back theoretical claims with empirical data. This anthology attempts to deal with such a conjunction. Overall, this book can be used as a theoretical basis for further semiotic considerations as well as for the design of different ways of teaching mathematical concepts.