Mathematics Made Visual
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Author | : Claudi Alsina |
Publisher | : MAA |
Total Pages | : 202 |
Release | : 2006-07-06 |
Genre | : Education |
ISBN | : 9780883857465 |
The object of this book is to show how visualization techniques may be employed to produce pictures that have interest for the creation, communication and teaching of mathematics. Mathematical drawings related to proofs have been produced since antiquity in China, Arabia, Greece and India but only in the last thirty years has there been a growing interest in so-called 'proofs without words.' In this book the authors show that behind most of the pictures 'proving' mathematical relations are some well-understood methods. The first part of the book consists of twenty short chapters, each one describing a method to visualize some mathematical idea (a proof, a concept, an operation,...) and several applications to concrete cases. Following this the book examines general pedagogical considerations concerning the development of visual thinking, practical approaches for making visualizations in the classroom and a discussion of the role that hands-on material plays in this process.
Author | : John Hattie |
Publisher | : Corwin Press |
Total Pages | : 209 |
Release | : 2016-09-15 |
Genre | : Education |
ISBN | : 1506362958 |
Selected as the Michigan Council of Teachers of Mathematics winter book club book! Rich tasks, collaborative work, number talks, problem-based learning, direct instruction...with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school. That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in "visible" learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings. Deep learning phase: When—through the solving of rich high-cognitive tasks and rigorous discussion—students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency. Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K-12 through intentionally designed guided, collaborative, and independent learning.
Author | : Guillermo Mendieta |
Publisher | : Meaningful Learning |
Total Pages | : 402 |
Release | : 2006-02 |
Genre | : Mathematics |
ISBN | : 0977321282 |
Pictorial Mathematics is a comprehensive and engaging resource for teaching and learning second through algebra level mathematics. It uses multiple representations and effective visuals to help learners with a wide variety of learning styles to develop a strong conceptual understanding of each concept. Pictorial Mathematics provides the perfect bridge between the abstract and the concrete. Its 400 pages are packed with invaluable tools to help teachers, parents and the learner develop meaning, connections and a deeper conceptual understanding of key mathematical concepts. Inside, you?ll find such resources as:More than 1,000 engaging visual exercises, Powerful and engaging models for the development of conceptual understanding of place value, fractions, ratios, geometry, the four operations and algebra concepts, Energizing tasks -- for small groups, large classrooms, or individuals alike, Master guides to create personalized pictorial problems, Tools to differentiate instruction, A complete set of 38 pictorial templates: from printable manipulatives to graphing paper with suggested activities for these. For previews of the book go to www.pictorialmath.com.
Author | : DK |
Publisher | : National Geographic Books |
Total Pages | : 0 |
Release | : 2014-06-16 |
Genre | : Juvenile Nonfiction |
ISBN | : 1465420177 |
Covering the essential math concepts learned in the first years of school, Amazing Visual Math brings a whole new dimension to learning. Amazing Visual Math is an interactive hands-on experience that makes math fun. Key curriculum subjects including shapes, patterns, telling time, lines of symmetry, addition, subtraction, measurement and more are explained through over 50 interactive elements throughout the book including pop-ups, flaps, and pull the tab elements, making an otherwise tedious subject entertaining. Ideal for developing manual dexterity skills and sharpening visual learning skills, Amazing Visual Math is a hands-on experience kids won't want to put down. Supports the Common Core State Standards.
Author | : Anthony Ashton |
Publisher | : Bloomsbury Publishing USA |
Total Pages | : 68 |
Release | : 2003-04-01 |
Genre | : Science |
ISBN | : 0802714099 |
Ashton presents a short, illustrated introduction to the evolution of simple harmonic theory. Illustrations.
Author | : DK |
Publisher | : Penguin |
Total Pages | : 128 |
Release | : 2018-08-07 |
Genre | : Juvenile Nonfiction |
ISBN | : 1465482288 |
Key math vocabulary and concepts for young children explained simply in this friendly and informative reference book. Clear, accessible pictures and diagrams support this first introduction to numbers, calculating, measuring, geometry, and data-collecting, making basic maths skills easier to understand. Packed with key terms and useful tips to help remember as well as practical examples of math in daily life, Visual Guide to Math is ideal even for reluctant kids. Place value, number bonds, multiplication tables, and fractions are just a few of the math concepts explained and reinforced in a variety of ways for children with different learning styles. Covering everything a young child needs to know, this unique reference book follows the curriculum and provides a strong foundation for math skills through the rest of the school years. A perfect homework help to support children as they take their first steps in math and build confidence.
Author | : Claudi Alsina |
Publisher | : MAA |
Total Pages | : 348 |
Release | : 2011-08-04 |
Genre | : Mathematics |
ISBN | : 0883853523 |
An exploration of the mathematics of twenty geometric diagrams that play a crucial role in visualizing mathematical proofs. Those teaching undergraduate mathematics will find material here for problem solving sessions, as well as enrichment material for courses on proofs and mathematical reasoning.
Author | : David C. Ullrich |
Publisher | : American Mathematical Soc. |
Total Pages | : 506 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0821844792 |
Presents the Dirichlet problem for harmonic functions twice: once using the Poisson integral for the unit disk and again in an informal section on Brownian motion, where the reader can understand intuitively how the Dirichlet problem works for general domains. This book is suitable for a first-year course in complex analysis
Author | : Tristan Needham |
Publisher | : Princeton University Press |
Total Pages | : 530 |
Release | : 2021-07-13 |
Genre | : Mathematics |
ISBN | : 0691203709 |
An inviting, intuitive, and visual exploration of differential geometry and forms Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss’s famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein’s field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell’s equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book. Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.
Author | : Tristan Needham |
Publisher | : Oxford University Press |
Total Pages | : 620 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : 9780198534464 |
This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.