We continue with the series of Selected Mathematics Topics, designed for high school students. In this text we introduce the mathematical group concept, one of the most important mathematical theories of recent centuries. To achieve this, we begin in the first chapter by reviewing the concept of function between sets. In the second, third and fourth chapters we intuitively study the group concept, using examples of so-called permutation games, such as the Rubik's cube. Even, we see how the groups serve to solve some of these games, like the solitaire game. In the last chapters we introduce some musical terms that help us to see a group example in music.
In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illustrations.
Make math matter to students in grades 5 and up using Math Projects! This 64-page book provides exciting individual, partner, and small-group projects that promote creative problem solving. Students compute, read, write, and utilize social and artistic skills with the more than 50 projects! The book supports NCTM standards and aligns with state, national, and Canadian provincial standards.
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.
This new book is an exciting follow-up to the authors bestsellers on differentiated math instruction, Good Questions and More Good Questions. Eyes on Math is a unique teaching resource that provides engaging, full-color graphics and pictures with text showing teachers how to use each image to stimulate mathematical teaching conversations around key K–8 concepts. Teachers using the book can download the images for projection onto classroom white boards or screens. The questions and answers will help both students and teachers look more deeply and see the math behind the math!
"The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them."--Kevin Hartnett, Quanta Magazine" This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart."--James Tanton, Global Math Project For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires--such as for play, beauty, freedom, justice, and love--and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can--and must--be open to all.
The Daily 5, Second Edition retains the core literacy components that made the first edition one of the most widely read books in education and enhances these practices based on years of further experience in classrooms and compelling new brain research. The Daily 5 provides a way for any teacher to structure literacy (and now math) time to increase student independence and allow for individualized attention in small groups and one-on-one. Teachers and schools implementing the Daily 5 will do the following: Spend less time on classroom management and more time teaching Help students develop independence, stamina, and accountability Provide students with abundant time for practicing reading, writing, and math Increase the time teachers spend with students one-on-one and in small groups Improve schoolwide achievement and success in literacy and math. The Daily 5, Second Edition gives teachers everything they need to launch and sustain the Daily 5, including materials and setup, model behaviors, detailed lesson plans, specific tips for implementing each component, and solutions to common challenges. By following this simple and proven structure, teachers can move from a harried classroom toward one that hums with productive and engaged learners. What's new in the second edition: Detailed launch plans for the first three weeks Full color photos, figures, and charts Increased flexibility regarding when and how to introduce each Daily 5 choice New chapter on differentiating instruction by age and stamina Ideas about how to integrate the Daily 5 with the CAFE assessment system New chapter on the Math Daily 3 structure
