Exploring, Investigating, and Discovering in Mathematics

Author: Vasile Berinde

Publisher: Springer Science & Business Media

ISBN: 9783764370190

Category: Education

Page: 246

View: 3642

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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: 4715

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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.

Ways to Think About Mathematics

Activities and Investigations for Grade 6-12 Teachers

Author: Steve Benson,Susan Addington

Publisher: Corwin Press

ISBN: 9780761931058

Category: Education

Page: 242

View: 5382

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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.

Exploring Mathematics

Author: Professor of Mathematics Marywood University Scranton Pennsylvania Craig Johnson

Publisher: Jones & Bartlett Publishers

ISBN: 1284076229

Category:

Page: 755

View: 7326

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Includes Access to Student Companion Website! Exploring Mathematics: Investigations with Functions is designed for one- or two- term mathematics courses for humanities and liberal arts majors. This unique ten-chapter text covers modern applications of mathematics in the liberal arts and situates the discipline within its rich and varied history. Exploring Mathematics draws on examples from the humanities, including how math is used in music and astronomy, and features perforated pages for easy study and review. The student-friendly writing style and informal approach demystifies the subject matter and offers an engaging and informative overview that will pique students curiosity and desire to explore mathematics further. Organized around the use of algebraic functions, this text builds conceptual bridges between each chapter so that students develop advanced mathematical skills within a larger context. Unlike other texts that present mathematical topics as a disconnected set of rules and equations, Exploring Mathematics flows seamlessly from one subject to the next, situating each within its historical and cultural context. This text provides a unique opportunity to showcase the richness of mathematics as a foundation upon which to build understanding of many different phenomena. Students will come away with a solid knowledge base of the unifying ideas of mathematics and the ability to explain how mathematics helps us to better our society and understand the world around us. The Text's Objectives: The author chose the topics based on meeting the specific NCTM curriculum standards to: 1. Strengthen estimation and computational skills. 2. Utilize algebraic concepts. 3. Emphasize problem-solving and reasoning. 4. Emphasize pattern and relationship recognition. 5. Highlight importance of units in measurement. 6. Highlight importance of the notion of a mathematical function. 7. Display mathematical connections to other disciplines. Key Features: A full color, interactive design provides students with a safe environment to graph solutions, check off chapter objectives, and answer questions directly in their textbook Piques student interest in math by relating it to areas such as astronomy and music, found in Chapter 4, Astronomy and the Methods of Science and Chapter 9, Mathematics in Music and Cryptology Utilizes the concept of a function as a central theme, providing a common thread through chapters Presents an engaging, student-friendly style with problem sets that incorporate real-world applications and data An abundance of examples illustrating important applications are presented in each section, while four-color pictures and diagrams reinforce key concepts and increase student comprehension Every new, printed copy includes access to a student companion website, featuring a lab manual and student solutions manual"

Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 5

Author: Jo Boaler,Jen Munson,Cathy Williams

Publisher: John Wiley & Sons

ISBN: 1119358787

Category: Education

Page: 304

View: 5027

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Engage students in mathematics using growth mindset techniques The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the fifth-grade level through visualization, play, and investigation. During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message—that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual mathematics tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that: There is no such thing as a math person - anyone can learn mathematics to high levels. Mistakes, struggle and challenge are the most important times for brain growth. Speed is unimportant in mathematics. Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics. With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum.

Rediscovering Mathematics

You Do the Math

Author: Shai Simonson

Publisher: MAA

ISBN: 0883857707

Category: Mathematics

Page: 207

View: 2749

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A guide to effective mathematical education, including a collection of topics and puzzles which aim to reignite interest in mathematics.

Beautiful Mathematics

Author: Martin Erickson

Publisher: MAA

ISBN: 0883855763

Category: Mathematics

Page: 177

View: 1227

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This book is about beautiful mathematical concepts and creations. Mathematical ideas have an aesthetic appeal that can be appreciated by those who have the time and dedication to investigate. Mathematical topics are presented in the categories of words, images, formulas, theorems, proofs, solutions, and unsolved problems. Readers will investigate exciting mathematical topics ranging from complex numbers to arithmetic progressions, from Alcuin's sequence to the zeta function, and from hypercubes to infinity squared.Do you know that a lemniscate curve is the circular inversion of a hyperbola? That Sierpinski's triangle has fractal dimension 1.585….? That a regular septagon can be constructed with straightedge, compass, and an angle trisector? Do you know how to prove Lagrange's theorem that every positive integer is the sum of four squares? Can you find the first three digits of the millionth Fibonacci number? Discover the keys to these and many other mathematical problems. In each case, the mathematics is compelling, elegant, simple, and beautiful.Who should read this book? There is something new for any mathematically-minded person. High school and college students will find motivation for their mathematical studies. Professional mathematicians will find fresh examples of mathematical beauty to pass along to others. Within each chapter, the topics require progressively more prerequisite knowledge. An appendix gives background definitions and theorems, while another gives challenging exercises (with solutions).

Exploring Mathematics

An Engaging Introduction to Proof

Author: John Meier,Derek Smith

Publisher: Cambridge University Press

ISBN: 1107128986

Category: Mathematics

Page: 300

View: 5396

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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.

Investigating Mathematics Teaching

A Constructivist Enquiry

Author: Barbara Jaworski

Publisher: Routledge

ISBN: 1135716110

Category: Education

Page: 252

View: 9126

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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.

Exploring Parks and Playgrounds

Multiplication and Division of Fractions

Author: Catherine Twomey Fosnot,Fosnot,Lynn D. Tarlow

Publisher: Firsthand

ISBN: 9780325010281

Category: Education

Page: 80

View: 1711

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Exploring Parks and Playgrounds: Multiplication and Division of Fractions is one of five units in the Contexts for Learning Mathematics' Investigating Fractions, Decimals, and Percents (4 - 6) The focus of this unit is the development of students' understanding of multiplication with rational numbers. The context of parks and playgrounds is used to introduce the double number line and the array models as helpful tools. Initially students are asked to explore the situation of two cousins running on a 26-mile course that winds through a park. They each ran half the course the previous year, and this year they complete 7/12 and 5/8 of the course, respectively. They know the exact portions they ran because of the course markers and water stations along the course. Students work to determine the number of miles that the cousins completed this year. In this first investigation, the distributive property and the use of landmark fractions (such as 1/2) provide a focus. Next students work with the training data of a running club whose members train on a three-mile track in the park. This context is used to engage students in exploring the relationship between the operations of multiplication and division with rational numbers. Many students confuse these operations when working with fractions, so they are deliberately juxtaposed at the beginning of the unit as a way to prevent misconceptions from developing. As the unit progresses into the second week, the context of designing a playground is used to support the development of specific mathematical ideas about the commutative property of multiplication with rational numbers, about the use of the word "of " to denote multiplication, and about fractional parts in relation to a changing whole. Students explore the story of two different empty lots: a section of each lot will be used as a playground, and then part of each playground will be covered with blacktop to be used for games like basketball and kickball. Both lots are the same size, but the part allocated to be a playground and the part to be blacktopped differ for each. The students investigate the problem of determining whether one lot has more blacktop, exploring equivalent, but not necessarily, congruent areas. The playground context supports students' use of an array model for multiplication, and the focus shifts to the commutative and associative properties. Several minilessons for multiplication of rational numbers are also included in the unit. These are structured using strings of related problems as a way to explicitly guide learners toward computational fluency. To learn more visit http://www.contextsforlearning.com

Proofs and Refutations

The Logic of Mathematical Discovery

Author: Imre Lakatos

Publisher: Cambridge University Press

ISBN: 1316425339

Category: Science

Page: N.A

View: 4516

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Imre Lakatos's Proofs and Refutations is an enduring classic, which has never lost its relevance. Taking the form of a dialogue between a teacher and some students, the book considers various solutions to mathematical problems and, in the process, raises important questions about the nature of mathematical discovery and methodology. Lakatos shows that mathematics grows through a process of improvement by attempts at proofs and critiques of these attempts, and his work continues to inspire mathematicians and philosophers aspiring to develop a philosophy of mathematics that accounts for both the static and the dynamic complexity of mathematical practice. With a specially commissioned Preface written by Paolo Mancosu, this book has been revived for a new generation of readers.

Creative Activities in Mathematics

Lower and Middle Primary

Author: Derek Holton,Cath Pearn

Publisher: N.A

ISBN: 9781742862583

Category: Education

Page: 128

View: 914

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Problem-based learning is a powerful alternative to drill-and-practice or skills-based learning, especially within mathematics, but it can be difficult to source rich materials that engage an entire class. The Creative Activities in Mathematics series provides a wealth of investigations and open-ended active learning activities, designed to engage students with mathematics and develop their problem-solving, collaboration and mathematical skills. Book One provides twelve different class activities suitable for students from Foundation to Year 4, along with teaching notes and staged lesson plans. Each activity is a whole-class investigation with open-ended answers that takes a particular scenario and develops it over three levels. This enables it to be used both at different year levels and with students of differing ability in the same class. All activities are firmly rooted in the Australian Curriculum: Mathematics and linked to the content descriptors of the Number & Algebra, Measurement & Geometry and Statistics & Probability strands. The companion website provides links to additional information and problem-based activities from around the Web, as well as student-friendly activity worksheets for teachers to download and print for their classes.

Infinite Processes

Background to Analysis

Author: A. Gardiner

Publisher: Springer Science & Business Media

ISBN: 1461256542

Category: Mathematics

Page: 306

View: 1508

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What shall we say of this metamorphosis in passing from finite to infinite? Galileo, Two New Sciences As its title suggests, this book was conceived as a prologue to the study of "Why the calculus works"--otherwise known as analysis. It is in fact a critical reexamination of the infinite processes arising in elementary math ematics: Part II reexamines rational and irrational numbers, and their representation as infinite decimals; Part III examines our ideas of length, area, and volume; and Part IV examines the evolution of the modern function-concept. The book may be used in a number of ways: firstly, as a genuine pro logue to analysis; secondly, as a supplementary text within an analysis course, providing a source of elementary motivation, background and ex amples; thirdly, as a kind of postscript to elementary analysis-as in a senior undergraduate course designed to reinforce students' understanding of elementary analysis and of elementary mathematics by considering the mathematical and historical connections between them. But the contents of the book should be of interest to a much wider audience than this including teachers, teachers in training, students in their last year at school, and others interested in mathematics.

HP-48G/GX Investigations in Mathematics

Author: Don R. LaTorre,Donald L. Kreider,T. G. Proctor

Publisher: N.A

ISBN: 9781886801233

Category: Computers

Page: 636

View: 9076

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The computer disk contains a collection of special-purpose HP-48G/GX calculator programs contained in the book. "To be used in conjunction with the HP F1201A Serial Interface Kit (DOS/Windows), which contains the connector and necessary software to download these programs"--Disk label.

Real Life Math Investigations

30 Activities That Apply Mathematical Thinking to Real-Life Situation

Author: Martin Lee,Marcia Miller

Publisher: Scholastic

ISBN: 9780590963848

Category: Educational games

Page: 96

View: 2547

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Math and Science Across Cultures

Activities and Investigations from the Exploratorium

Author: Maurice Bazin,Modesto Tamez,Exploratorium Teacher Institute (San Francisco, Calif.)

Publisher: N.A

ISBN: 9781565845411

Category: Mathematics

Page: 176

View: 612

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From the creators of the bestselling "The Explorabook" come innovative, hands-on math and science activities of many cultures. With instructions in this book, one can construct a Brazilian carnival instrument, play a peg solitaire game from Madagascar, or count like an Egyptian. Illustrations throughout.

On the Shoulders of Giants:

New Approaches to Numeracy

Author: Mathematical Sciences Education Board,National Research Council

Publisher: National Academies Press

ISBN: 0309042348

Category: Education

Page: 240

View: 7488

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What mathematics should be learned by today's young people as well as tomorrow's workforce? On the Shoulders of Giants is a vision of richness of mathematics expressed in essays on change, dimension, quantity, shape, and uncertainty, each of which illustrate fundamental strands for school mathematics. These essays expand on the idea of mathematics as the language and science of patterns, allowing us to realize the importance of providing hands-on experience and the development of a curriculum that will enable students to apply their knowledge to diverse numerical problems.

25 Real Life Math Investigations

That Will Astound Teachers and Students

Author: Edward Zaccaro,Luke Zaccaro

Publisher: N.A

ISBN: 9780967991580

Category: Mathematics

Page: 396

View: 5283

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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.

Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 3

Author: Jo Boaler,Jen Munson,Cathy Williams

Publisher: John Wiley & Sons

ISBN: 1119358795

Category: Education

Page: 256

View: 3688

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Engage students in mathematics using growth mindset techniques The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the third-grade level through visualization, play, and investigation. During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message—that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that: There is no such thing as a math person - anyone can learn mathematics to high levels. Mistakes, struggle and challenge are the most important times for brain growth. Speed is unimportant in mathematics. Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics. With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum.

Math and Science Investigations

Helping Young Learners Make Big Discoveries

Author: Sally Anderson

Publisher: Gryphon House

ISBN: 9780876593882

Category: Education

Page: 191

View: 3922

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A unique teaching resource that uses children's books and hands-on investigations to bring math and science concepts to life!