Exploring, Investigating, and Discovering in Mathematics

Author: Vasile Berinde

Publisher: Springer Science & Business Media

ISBN: 9783764370190

Category: Education

Page: 246

View: 2752


This book presents creative problem solving techniques with particular emphasis on how to develop and train inventive skills to students. It presents an array of 24 carefully selected themes from elementary mathematics: arithmetic, algebra, geometry, analysis as well as applied mathematics. The main goal of this book is to offer a systematic illustration of how to organize the natural transition from the problem solving activity towards exploring, investigating, and discovering new facts and results. The target audience are mainly students, young mathematicians, and teachers.

Discovering Mathematics

The Art of Investigation

Author: A. Gardiner

Publisher: Courier Corporation

ISBN: 0486452999

Category: Mathematics

Page: 206

View: 4518


The term "mathematics" usually suggests an array of familiar problems with solutions derived from well-known techniques. Discovering Mathematics: The Art of Investigation takes a different approach, exploring how new ideas and chance observations can be pursued, and focusing on how the process invariably leads to interesting questions that would never have otherwise arisen. With puzzles involving coins, postage stamps, and other commonplace items, students are challenged to account for the simple explanations behind perplexing mathematical phenomena. Elementary methods and solutions allow readers to concentrate on the way in which the material is explored, as well as on strategies for answers that aren't immediately obvious. The problems don't require the kind of sophistication that would put them out of reach of ordinary students, but they're sufficiently complex to capture the essential features of mathematical discovery. Complete solutions appear at the end.

Mathematical Investigations

A Series of Situational Lessons

Author: M. Britt,S. Gargiulo,P. Hughes

Publisher: Dale Seymour Publication

ISBN: 9780866515412

Category: Education

Page: 240

View: 7490


Meaningful mathematical experiences with interconnected situational lessons and real-world activities: Book One: geometry, patterns, operations research, photography, and genetic inheritance. Book Two: networks, sports math, finite-difference patterns, rates, and maps. Book Three: fundamentals of money, scaling, finance, loans, probability, and linear programming. Each investigation includes individual and whole-class activities, plus a "Check-up" that tests students' understanding.

Moving Math

How to use thinking skills to help students make sense of mathematical concepts and support numeracy development

Author: Mary Fiore,Maria Luisa Lebar

Publisher: Pembroke Publishers Limited

ISBN: 1551389258

Category: Education

Page: 128

View: 7679


Focus on “moving” the teaching and learning of mathematics by shifting instruction and assessment practices. This unique book uses critical thinking skills — inferring and interpreting, analyzing, evaluating, making connections, synthesizing, reasoning and proving, and reflecting — to help students make sense of mathematical concepts and support numeracy.

Why Is There Philosophy of Mathematics At All?

Author: Ian Hacking

Publisher: Cambridge University Press

ISBN: 1107729823

Category: Science

Page: 212

View: 2881


This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary mathematicians, it shows that proof and other forms of mathematical exploration continue to be living, evolving practices - responsive to new technologies, yet embedded in permanent (and astonishing) facts about human beings. It distinguishes several distinct types of application of mathematics, and shows how each leads to a different philosophical conundrum. Here is a remarkable body of new philosophical thinking about proofs, applications, and other mathematical activities.

Exploring Mathematics

An Engaging Introduction to Proof

Author: John Meier,Derek Smith

Publisher: Cambridge University Press

ISBN: 1107128986

Category: Mathematics

Page: 300

View: 8177


Exploring Mathematics gives students experience with doing mathematics - interrogating mathematical claims, exploring definitions, forming conjectures, attempting proofs, and presenting results - and engages them with examples, exercises, and projects that pique their interest. Written with a minimal number of pre-requisites, this text can be used by college students in their first and second years of study, and by independent readers who want an accessible introduction to theoretical mathematics. Core topics include proof techniques, sets, functions, relations, and cardinality, with selected additional topics that provide many possibilities for further exploration. With a problem-based approach to investigating the material, students develop interesting examples and theorems through numerous exercises and projects. In-text exercises, with complete solutions or robust hints included in an appendix, help students explore and master the topics being presented. The end-of-chapter exercises and projects provide students with opportunities to confirm their understanding of core material, learn new concepts, and develop mathematical creativity.

Mathematical Investigations

Concepts and Processes for the Introductory Algebra Student

Author: Phil DeMarois,Mercedes A. McGowen,Darlene Whitkanack

Publisher: Addison Wesley

ISBN: 9780321069313

Category: Mathematics

Page: 572

View: 5764


Built on AMATYC and NCTM standards, this book takes an active learning approach, focusing on collaborative for small groups. Independent learning is encouraged as problem-solving skills illustrate connections among mathematic ideas as readers discover and build on concepts explored as a group, as the book focuses on learning in a social context. Each section of a chapter opens with the investigation of a problem, in which readers gather data and collaborate on investigative activities. The book's discussion summarizes matheatic ideas gained from the investigations. At the end of each section concept maps enable readers to devise key ideas and draw connections between aspects of the concepts. For anyone interested concepts and processes or seeking an introduction to algebra.

Discovering Mathematics With Maple

An Interactive Exploration for Mathematicians Engineers and Econometricians

Author: R.J. Stroeker,J.F. Kaashoek

Publisher: Springer Science & Business Media

ISBN: 9783764360917

Category: Computers

Page: 227

View: 4686


This book introduces Maple in a rather special way; namely, it shows how a computer algebra system most naturally fits into a mathematically oriented work environment. The intended audience is the mixed group of mathematicians, econometricians, engineers and other scientists, principally those who in their chosen discipline need to work with mathematical ideas and techniques. The book distinguishes itself from existing ones in the following ways: - It instructs the reader about the use of Maple by posing problems of a strictly mathematical nature. - It is intended not as a mere introduction to Maple, but also to show how Maple - and other computer algebra systems - may enrich our knowledge and deepen our understanding of mathematics. In that respect it focusses on mathematics rather than on Maple. In doing this it tries to convince scientists who are not naturally inclined to incorporate the computer into their daily work routine that a computer algebra system may very well enhance their theoretical work.

Investigating Mathematics Teaching

A Constructivist Enquiry

Author: Barbara Jaworski

Publisher: Routledge

ISBN: 1135716110

Category: Education

Page: 252

View: 7617


Barbara Jaworski addresses a number of questions that are central to research on reform in mathematics education today. In this volume she attempts to chart critically yet honestly her own developing ideas as she undertakes a several-year-long enquiry into mathematics teaching and gives a very personal account of her developing conceptions, conjectures, thoughts and reflections. The author accounts for her research both genetically and biographically, simultaneously restructuring the development of her ideas and giving a rigorous, critical and reflective account.

Der Zahlenteufel

Ein Kopfkissenbuch für alle, die Angst vor der Mathematik haben

Author: Hans Magnus Enzensberger

Publisher: N.A

ISBN: 9783423625937


Page: 264

View: 610


Panning for Gold

15 Investigations to Enrich Middle School Mathematics

Author: Daniel J. Brahier

Publisher: Heinemann Educational Books

ISBN: 9780325010458

Category: Education

Page: 214

View: 9563


Presents fifteen extended math investigations designed to provide middle school students with experience in solving real-life problems in algebra, geometry, data analysis and probability, number and operations, and measurement.

Discovering Higher Mathematics

Four Habits of Highly Effective Mathematicians

Author: Alan Levine,Alan L. Levine

Publisher: Academic Press

ISBN: 9780124454606

Category: Mathematics

Page: 174

View: 8238


Funded by a National Science Foundation grant, Discovering Higher Mathematics emphasizes four main themes that are essential components of higher mathematics: experimentation, conjecture, proof, and generalization. The text is intended for use in bridge or transition courses designed to prepare students for the abstraction of higher mathematics. Students in these courses have normally completed the calculus sequence and are planning to take advanced mathematics courses such as algebra, analysis and topology. The transition course is taken to prepare students for these courses by introducing them to the processes of conjecture and proof concepts which are typically not emphasized in calculus, but are critical components of advanced courses. * Constructed around four key themes: Experimentation, Conjecture, Proof, and Generalization * Guidelines for effective mathematical thinking, covering a variety of interrelated topics * Numerous problems and exercises designed to reinforce the key themes

Exploring Mathematics and Science Teachers’ Knowledge

Windows into teacher thinking

Author: Hamsa Venkat,Marissa Rollnick,John Loughran,Mike Askew

Publisher: Routledge

ISBN: 1134683715

Category: Education

Page: 236

View: 628


Globally, mathematics and science education faces three crucial challenges: an increasing need for mathematics and science graduates; a declining enrolment of school graduates into university studies in these disciplines; and the varying quality of school teaching in these areas. Alongside these challenges, internationally more and more non-specialists are teaching mathematics and science at both primary and secondary levels, and research evidence has revealed how gaps and limitations in teachers’ content understandings can lead to classroom practices that present barriers to students’ learning. This book addresses these issues by investigating how teachers’ content knowledge interacts with their pedagogies across diverse contexts and perspectives. This knowledge-practice nexus is examined across mathematics and science teaching, traversing schooling phases and countries, with an emphasis on contexts of disadvantage. These features push the boundaries of research into teachers’ content knowledge. The book’s combination of mathematics and science enriches each discipline for the reader, and contributes to our understandings of student attainment by examining the nature of specialised content knowledge needed for competent teaching within and across the two domains. Exploring Mathematics and Science Teachers’ Knowledge will be key reading for researchers, doctoral students and postgraduates with a focus on Mathematics, Science and teacher knowledge research.


Author: Brendan Kelly

Publisher: Brendan Kelly Publishing Inc.

ISBN: 9781895997187

Category: Mathematics

Page: 96

View: 861