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Author: Albert Cuoco
Publisher: MIT Press
ISBN: 9780262530712
Category : Computers
Languages : en
Pages : 636
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Book Description
Investigations in Algebra departs from a preoccupation with calculus as the ultimate goal of and the universal introduction to advanced mathematics by using Logo to explore combinatorics, number theory, the study of discrete functions, and other topics that are not on the traditional path to calculus. This approach encourages students to participate actively in exciting mathematics, developing in them a facility for abstraction and an appreciation for the power of mathematical methods. Most of the projects in the first two parts of the book have been worked through by students at Woburn High School, often without assistance from a teacher. In three parts, Investigations in Algebra emphasizes the treatment of functions as concrete objects modeled as Logo procedures, applies the techniques of induction and recursion to combinatorial problems, and takes up topics in number theory (including unique factorization congruence, and multiplicative functions). Integral to the presentation are numerous carefully constructed problems routine exercises, long term projects, and open ended experiments - developed in twenty years of classroom use. Investigations in Algebra is included in the series Exploring with Logo, edited by E. Paul Goldenberg.
Author: Albert Cuoco
Publisher: MIT Press
ISBN: 9780262530712
Category : Computers
Languages : en
Pages : 636
Get Book Here
Book Description
Investigations in Algebra departs from a preoccupation with calculus as the ultimate goal of and the universal introduction to advanced mathematics by using Logo to explore combinatorics, number theory, the study of discrete functions, and other topics that are not on the traditional path to calculus. This approach encourages students to participate actively in exciting mathematics, developing in them a facility for abstraction and an appreciation for the power of mathematical methods. Most of the projects in the first two parts of the book have been worked through by students at Woburn High School, often without assistance from a teacher. In three parts, Investigations in Algebra emphasizes the treatment of functions as concrete objects modeled as Logo procedures, applies the techniques of induction and recursion to combinatorial problems, and takes up topics in number theory (including unique factorization congruence, and multiplicative functions). Integral to the presentation are numerous carefully constructed problems routine exercises, long term projects, and open ended experiments - developed in twenty years of classroom use. Investigations in Algebra is included in the series Exploring with Logo, edited by E. Paul Goldenberg.
Author: Phil DeMarois
Publisher: Addison Wesley Publishing Company
ISBN: 9780321069313
Category : Mathematics
Languages : en
Pages : 596
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Book Description
Reflective of AMATYC and NCTM standards for teaching mathematics, this text (the first in a series of two texts) aims to make mathematics truly accessible to all students by taking an active approach to learning. Focused on mathematical reasoning and problem-solving strategies, Mathematical Investigations presents a series of carefully sequenced investigations where students gather data and work collaboratively to discover key concepts. The function concept is central to all topics from Chapter 3 forward and is explored through multiple representations. This text explores variables, notation, and processes explicitly rather than assuming students have mastered these concepts in previous courses. Content is explored in depth, and contextual problems are revisited throughout the text to create a spiral that gives students multiple opportunities to master important skills and concepts. Graphing calculators are integrated throughout the text to help students discover patterns and interpret data intelligently. Students construct their knowledge of a particular topic in a real-world context and then reinforce this knowledge through reflection, practice, and synthesis with other topics as they work through the text.
Author: Edward Zaccaro
Publisher:
ISBN: 9780967991580
Category : Mathematics
Languages : en
Pages : 396
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Book Description
Investigations on topics such as the dangers of short term loans, interest, and other topics of financial literacy. Explore the math behind current topics such as ethanol and hybrid cars. Learn how math mistakes in the media have had significant consequences. These and other fascinating math investigations show the ability of mathematics to cut through deception and flawed thinking.
Author: Arya ökten
Publisher: Tumblehome, Incorporated
ISBN: 9781943431625
Category : Juvenile Fiction
Languages : en
Pages : 0
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Book Description
"A playful approach to some core ideas of mathematics, this book will help lay the foundation for understanding algebra and probability. Dr. O and his young associate Arya explore and discover ideas in ciphers, triangular numbers, primes and composites, probability, and a variety of fascinating number patterns. For a parent and curious child, or for a curious child alone, these mathematical investigations will invite re-reading and further exploration."--Back cover.
Author: Stuart A. Kauffman
Publisher: Oxford University Press
ISBN: 0190283858
Category : Science
Languages : en
Pages : 469
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Book Description
"It may be that I have stumbled upon an adequate description of life itself." These modest yet profound words trumpet an imminent paradigm shift in scientific, economic, and technological thinking. In the tradition of Schrödinger's classic What Is Life?, Kauffman's Investigations is a tour-de-force exploration of the very essence of life itself, with conclusions that radically undermine the scientific approaches on which modern science rests--the approaches of Newton, Boltzman, Bohr, and Einstein. Building on his pivotal ideas about order and evolution in complex life systems, Kauffman finds that classical science does not take into account that physical systems--such as people in a biosphere--effect their dynamic environments in addition to being affected by them. These systems act on their own behalf as autonomous agents, but what defines them as such? In other words, what is life? Kauffman supplies a novel answer that goes beyond traditional scientific thinking by defining and explaining autonomous agents and work in the contexts of thermodynamics and of information theory. Much of Investigations unpacks the progressively surprising implications of his definition. Significantly, he sets the stages for a technological revolution in the coming decades. Scientists and engineers may soon seek to create autonomous agents--both organic and mechanical--that can not only construct things and work, but also reproduce themselves! Kauffman also lays out a foundation for a new concept of organization, and explores the requirements for the emergence of a general biology that will transcend terrestrial biology to seek laws governing biospheres anywhere in the cosmos. Moreover, he presents four candidate laws to explain how autonomous agents co-create their biosphere and the startling idea of a "co-creating" cosmos. A showcase of Kauffman's most fundamental and significant ideas, Investigations presents a new way of thinking about the fundamentals of general biology that will change the way we understand life itself--on this planet and anywhere else in the cosmos.
Author: James J. Kaput
Publisher: Routledge
ISBN: 1351577093
Category : Education
Languages : en
Pages : 552
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Book Description
This volume is the first to offer a comprehensive, research-based, multi-faceted look at issues in early algebra. In recent years, the National Council for Teachers of Mathematics has recommended that algebra become a strand flowing throughout the K-12 curriculum, and the 2003 RAND Mathematics Study Panel has recommended that algebra be “the initial topical choice for focused and coordinated research and development [in K-12 mathematics].” This book provides a rationale for a stronger and more sustained approach to algebra in school, as well as concrete examples of how algebraic reasoning may be developed in the early grades. It is organized around three themes: The Nature of Early Algebra Students’ Capacity for Algebraic Thinking Issues of Implementation: Taking Early Algebra to the Classrooms. The contributors to this landmark volume have been at the forefront of an effort to integrate algebra into the existing early grades mathematics curriculum. They include scholars who have been developing the conceptual foundations for such changes as well as researchers and developers who have led empirical investigations in school settings. Algebra in the Early Grades aims to bridge the worlds of research, practice, design, and theory for educators, researchers, students, policy makers, and curriculum developers in mathematics education.
Author: Phil DeMarois
Publisher:
ISBN: 9780065023824
Category : Mathematics
Languages : en
Pages : 244
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Book Description
Author: Phil DeMarois
Publisher:
ISBN: 9780065012880
Category : Algebra
Languages : en
Pages : 434
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Book Description
Author: Steve Benson
Publisher: Corwin Press
ISBN: 9780761931058
Category : Education
Languages : en
Pages : 266
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Book Description
Funded by the National Science Foundation and successfully field-tested in a variety of settings, the materials presented give teachers the opportunity to grow as learners for the classes they teach.
Author: Phil DeMarois
Publisher:
ISBN: 9780757559150
Category : Mathematics
Languages : en
Pages : 574
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Book Description
