Thinking about Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Thinking about Mathematics write by Stewart Shapiro. This book was released on 2000-07-13. Thinking about Mathematics available in PDF, EPUB and Kindle. Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout history and covers historical figures such as Plato, Aristotle, Kant, and Mill. It also presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines.
Building Thinking Classrooms in Mathematics, Grades K-12
Building Thinking Classrooms in Mathematics, Grades K-12 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Building Thinking Classrooms in Mathematics, Grades K-12 write by Peter Liljedahl. This book was released on 2020-09-28. Building Thinking Classrooms in Mathematics, Grades K-12 available in PDF, EPUB and Kindle. A thinking student is an engaged student Teachers often find it difficult to implement lessons that help students go beyond rote memorization and repetitive calculations. In fact, institutional norms and habits that permeate all classrooms can actually be enabling "non-thinking" student behavior. Sparked by observing teachers struggle to implement rich mathematics tasks to engage students in deep thinking, Peter Liljedahl has translated his 15 years of research into this practical guide on how to move toward a thinking classroom. Building Thinking Classrooms in Mathematics, Grades K–12 helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur. This guide Provides the what, why, and how of each practice and answers teachers’ most frequently asked questions Includes firsthand accounts of how these practices foster thinking through teacher and student interviews and student work samples Offers a plethora of macro moves, micro moves, and rich tasks to get started Organizes the 14 practices into four toolkits that can be implemented in order and built on throughout the year When combined, these unique research-based practices create the optimal conditions for learner-centered, student-owned deep mathematical thinking and learning, and have the power to transform mathematics classrooms like never before.
How Not to Be Wrong
How Not to Be Wrong - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook How Not to Be Wrong write by Jordan Ellenberg. This book was released on 2015-05-26. How Not to Be Wrong available in PDF, EPUB and Kindle. “Witty, compelling, and just plain fun to read . . ." —Evelyn Lamb, Scientific American The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it. Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer? How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God. Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.
Introduction to Mathematical Thinking
Introduction to Mathematical Thinking - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Mathematical Thinking write by Keith J. Devlin. This book was released on 2012. Introduction to Mathematical Thinking available in PDF, EPUB and Kindle. "Mathematical thinking is not the same as 'doing math'--unless you are a professional mathematician. For most people, 'doing math' means the application of procedures and symbolic manipulations. Mathematical thinking, in contrast, is what the name reflects, a way of thinking about things in the world that humans have developed over three thousand years. It does not have to be about mathematics at all, which means that many people can benefit from learning this powerful way of thinking, not just mathematicians and scientists."--Back cover.
The Oxford Handbook of Philosophy of Mathematics and Logic
The Oxford Handbook of Philosophy of Mathematics and Logic - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Oxford Handbook of Philosophy of Mathematics and Logic write by Stewart Shapiro. This book was released on 2005-02-10. The Oxford Handbook of Philosophy of Mathematics and Logic available in PDF, EPUB and Kindle. Covers the state of the art in the philosophy of maths and logic, giving the reader an overview of the major problems, positions, and battle lines. The chapters in this book contain both exposition and criticism as well as substantial development of their own positions. It also includes a bibliography.
