Mathematics and the Search for Knowledge

Mathematics and the Search for Knowledge

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  • Author: Morris Kline
  • Publisher: Oxford University Press, USA
  • ISBN: 0198020619
  • Category : Mathematics
  • Languages : en
  • Pages : 270

Requires a minimum of technical knowledge and gives an illuminating oversight of the historical developments...with many interesting observations along the way.--Proceedings of the Edinburgh Mathematical Society The lively writing makes this suitable supplementary reading for advanced undergraduates from many disciplines. An extensive and often technical bibliography is included for those who want to go further.


Mathematical Knowledge in Teaching

Mathematical Knowledge in Teaching

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  • Author: Tim Rowland
  • Publisher: Springer Science & Business Media
  • ISBN: 904819766X
  • Category : Education
  • Languages : en
  • Pages : 304

The quality of primary and secondary school mathematics teaching is generally agreed to depend crucially on the subject-related knowledge of the teacher. However, there is increasing recognition that effective teaching calls for distinctive forms of subject-related knowledge and thinking. Thus, established ways of conceptualizing, developing and assessing mathematical knowledge for teaching may be less than adequate. These are important issues for policy and practice because of longstanding difficulties in recruiting teachers who are confident and conventionally well-qualified in mathematics, and because of rising concern that teaching of the subject has not adapted sufficiently. The issues to be examined in Mathematical Knowledge in Teaching are of considerable significance in addressing global aspirations to raise standards of teaching and learning in mathematics by developing more effective approaches to characterizing, assessing and developing mathematical knowledge for teaching.


The Nature of Mathematical Knowledge

The Nature of Mathematical Knowledge

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  • Author: Philip Kitcher
  • Publisher: Oxford University Press, USA
  • ISBN: 0195035410
  • Category : Electronic books
  • Languages : en
  • Pages : 300

This book argues against the view that mathematical knowledge is a priori, contending that mathematics is an empirical science and develops historically, just as natural sciences do. Kitcher presents a complete, systematic, and richly detailed account of the nature of mathematical knowledge and its historical development, focusing on such neglected issues as how and why mathematical language changes, why certain questions assume overriding importance, and how standards of proof are modified.


Mathematics, the Loss of Certainty

Mathematics, the Loss of Certainty

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  • Author: Morris Kline
  • Publisher:
  • ISBN: 9781435108479
  • Category : Mathematics
  • Languages : en
  • Pages : 0


Mathematics in Western Culture

Mathematics in Western Culture

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  • Author: Morris Kline
  • Publisher: Oxford University Press
  • ISBN: 0195345452
  • Category : Mathematics
  • Languages : en
  • Pages : 513

This book gives a remarkably fine account of the influences mathematics has exerted on the development of philosophy, the physical sciences, religion, and the arts in Western life.


Mathematics and the Physical World

Mathematics and the Physical World

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  • Author: Morris Kline
  • Publisher: Courier Corporation
  • ISBN: 0486136310
  • Category : Mathematics
  • Languages : en
  • Pages : 514

Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.


How Not to Be Wrong

How Not to Be Wrong

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  • Author: Jordan Ellenberg
  • Publisher: Penguin
  • ISBN: 0143127535
  • Category : Mathematics
  • Languages : en
  • Pages : 482

“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.


Mathematics for the Nonmathematician

Mathematics for the Nonmathematician

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  • Author: Morris Kline
  • Publisher: Courier Corporation
  • ISBN: 0486316130
  • Category : Mathematics
  • Languages : en
  • Pages : 672

Erudite and entertaining overview follows development of mathematics from ancient Greeks to present. Topics include logic and mathematics, the fundamental concept, differential calculus, probability theory, much more. Exercises and problems.


Primary Mathematics: Knowledge and Understanding

Primary Mathematics: Knowledge and Understanding

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  • Author: Claire Mooney
  • Publisher: Learning Matters
  • ISBN: 1473907055
  • Category : Education
  • Languages : en
  • Pages : 280

The essential subject knowledge text for primary mathematics. Secure subject knowledge and understanding is the foundation of confident, creative and effective teaching. This comprehensive text includes interactive tasks, a self assessment section to allow trainees to better understand their level of knowledge and M level extension boxes to provide further challenge in all chapters. This 7th edition is updated in line with the new National Curriculum and includes updated research summaries reflecting the latest thinking. This highly recommended text helps trainee primary teachers develop and consolidate their knowledge of mathematics.


Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8

Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8

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  • Author: Jennifer M. Bay-Williams
  • Publisher: Corwin
  • ISBN: 1071818430
  • Category : Education
  • Languages : en
  • Pages : 265

Because fluency practice is not a worksheet. Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand. Figuring Out Fluency in Mathematics Teaching and Learning offers educators the inspiration to develop a deeper understanding of procedural fluency, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. In a friendly and accessible style, this hands-on guide empowers educators to support students in acquiring the repertoire of reasoning strategies necessary to becoming versatile and nimble mathematical thinkers. It includes: "Seven Significant Strategies" to teach to students as they work toward procedural fluency. Activities, fluency routines, and games that encourage learning the efficiency, flexibility, and accuracy essential to real fluency. Reflection questions, connections to mathematical standards, and techniques for assessing all components of fluency. Suggestions for engaging families in understanding and supporting fluency. Fluency is more than a toolbox of strategies to choose from; it’s also a matter of equity and access for all learners. Give your students the knowledge and power to become confident mathematical thinkers.