exploring investigating and discovering in mathematics

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Exploring Investigating And Discovering In Mathematics

Author : Vasile Berinde
ISBN : 376437019X
Genre : Education
File Size : 60. 44 MB
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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

Author : A. Gardiner
ISBN : 9780486452999
Genre : Mathematics
File Size : 47. 27 MB
Format : PDF, ePub
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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

Author : Professor of Mathematics Marywood University Scranton Pennsylvania Craig Johnson
ISBN : 9781284076226
Genre :
File Size : 59. 45 MB
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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"

Ways To Think About Mathematics

Author : Steve Benson
ISBN : 0761931058
Genre : Education
File Size : 27. 7 MB
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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 : John Meier
ISBN : 9781107128989
Genre : Mathematics
File Size : 67. 10 MB
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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.

Mindset Mathematics Visualizing And Investigating Big Ideas Grade 5

Author : Jo Boaler
ISBN : 9781119358763
Genre : Education
File Size : 39. 33 MB
Format : PDF, Kindle
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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.

Mathematical Investigations

Author : M. Britt
ISBN : 0866515410
Genre : Education
File Size : 44. 5 MB
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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.

Exploring Parks And Playgrounds

Author : Catherine Twomey Fosnot
ISBN : 0325010285
Genre : Education
File Size : 85. 62 MB
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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

Moving Math

Author : Mary Fiore
ISBN : 9781551389257
Genre : Education
File Size : 73. 6 MB
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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

Author : Shai Simonson
ISBN : 9780883857700
Genre : Mathematics
File Size : 32. 84 MB
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A guide to effective mathematical education, including a collection of topics and puzzles which aim to reignite interest in mathematics.

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