Visualizing Mathematics
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Visualizing Mathematics with 3D Printing
The first book to explain mathematics using 3D printed models. Winner of the Technical Text of the Washington Publishers Wouldn’t it be great to experience three-dimensional ideas in three dimensions? In this book—the first of its kind—mathematician and mathematical artist Henry Segerman takes readers on a fascinating tour of two-, three-, and four-dimensional mathematics, exploring Euclidean and non-Euclidean geometries, symmetry, knots, tilings, and soap films. Visualizing Mathematics with 3D Printing includes more than 100 color photographs of 3D printed models. Readers can take the book’s insights to a new level by visiting its sister website, 3dprintmath.com, which features virtual three-dimensional versions of the models for readers to explore. These models can also be ordered online or downloaded to print on a 3D printer. Combining the strengths of book and website, this volume pulls higher geometry and topology out of the realm of the abstract and puts it into the hands of anyone fascinated by mathematical relationships of shape. With the book in one hand and a 3D printed model in the other, readers can find deeper meaning while holding a hyperbolic honeycomb, touching the twists of a torus knot, or caressing the curves of a Klein quartic.
Visualizing Mathematics
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.
Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 6
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 sixth-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.