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Exploring Investigating and Discovering in Mathematics

Exploring  Investigating  and Discovering in Mathematics Author Vasile Berinde
ISBN-10 376437019X
Release 2003-12-17
Pages 246
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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

Discovering Mathematics Author A. Gardiner
ISBN-10 9780486452999
Release 2006-01-26
Pages 206
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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.

Exploring Mathematics

Exploring Mathematics Author Professor of Mathematics Marywood University Scranton Pennsylvania Craig Johnson
ISBN-10 9781284076226
Release 2014-08-01
Pages 755
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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"

Mathematical Investigations

Mathematical Investigations Author M. Britt
ISBN-10 0866515410
Release 1997-02-01
Pages 240
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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.

Infinite Processes

Infinite Processes Author A. Gardiner
ISBN-10 9781461256540
Release 2012-12-06
Pages 306
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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.

Exploring Mathematics

Exploring Mathematics Author John Meier
ISBN-10 9781108509282
Release 2017-08-07
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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.

Beautiful Mathematics

Beautiful Mathematics Author Martin Erickson
ISBN-10 9780883855768
Release 2011-12-22
Pages 177
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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).

Ways to Think About Mathematics

Ways to Think About Mathematics Author Steve Benson
ISBN-10 0761931058
Release 2004-10-05
Pages 242
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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.

Mindset Mathematics Visualizing and Investigating Big Ideas Grade 5

Mindset Mathematics  Visualizing and Investigating Big Ideas  Grade 5 Author Jo Boaler
ISBN-10 9781119358787
Release 2018-02-26
Pages 304
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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.

Math and Science Investigations

Math and Science Investigations Author Sally Anderson
ISBN-10 0876593880
Release 2012
Pages 191
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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!

Moving Math

Moving Math Author Mary Fiore
ISBN-10 9781551389257
Release 2017-10-17
Pages 128
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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.

Rediscovering Mathematics

Rediscovering Mathematics Author Shai Simonson
ISBN-10 9780883857700
Release 2011-04-14
Pages 207
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A guide to effective mathematical education, including a collection of topics and puzzles which aim to reignite interest in mathematics.

Teaching and Learning of mathematics

Teaching and Learning of mathematics Author
ISBN-10 9676117870
Release 2005
Pages 220
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Teaching and Learning of mathematics has been writing in one form or another for most of life. You can find so many inspiration from Teaching and Learning of mathematics also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Teaching and Learning of mathematics book for free.

Exploring Parks and Playgrounds

Exploring Parks and Playgrounds Author Catherine Twomey Fosnot
ISBN-10 0325010285
Release 2008-03
Pages 80
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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

Why Is There Philosophy of Mathematics At All

Why Is There Philosophy of Mathematics At All Author Ian Hacking
ISBN-10 9781107729827
Release 2014-01-30
Pages 212
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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.

Proofs and Refutations

Proofs and Refutations Author Imre Lakatos
ISBN-10 9781316425336
Release 2015-10-08
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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 Investigations in Early Math

Creative Investigations in Early Math Author Angela Eckhoff
ISBN-10 9780876597309
Release 2017-04-01
Pages 104
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Math crops up in everyday activities in so many ways. You can help preschoolers see math in the petals of a flower, the shape of a window, the bounce of a ball, the growth of a plant, and the repetition of a song. Instead of teaching math to preschoolers, you can be their guide as they experiment, think about problems, try solutions, gain understanding, and discuss their findings. Creative Investigations in Early Math gives teachers practical ideas for intentionally fostering young children's hands-on explorations in the following areas: Number and number sense Computation Geometry and spatial sense Measurement Data collection and statistics Patterns and relationships With your guidance, preschoolers can figure out how the world of mathematics works and how math works in their world.