Exploratory Problems in Mathematics

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Publisher : National Council of Teachers of
ISBN 13 : 9780873533386
Total Pages : 168 pages
Book Rating : 4.5/5 (333 download)

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Book Synopsis Exploratory Problems in Mathematics by : Frederick W. Stevenson

Download or read book Exploratory Problems in Mathematics written by Frederick W. Stevenson and published by National Council of Teachers of. This book was released on 1992 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book attempts to introduce students to the creative aspects of mathematics through exploratory problems. The introduction presents the criteria for the selection of the problems in the book. Criteria indicate that problems should: be immediately attractive, require data to be generated or gathered, appeal to students from junior high school to graduate school, involve fundamental mathematics concepts, have satisfying solutions, and suggest several other problems. Chapter 1 describes the exploratory process that includes an inductive phase, a deductive phase, and a creative phase. Chapter 2 illustrates this process in a problem incorporating the calculator in the exploration. All the problems in the book follow the same format. The format includes a paragraph about the problem, questions to be explored, and a suggested beginning for the exploration. Chapters 3, 4, and 5 describe three mathematical excursions that illustrate the format while demonstrating the power of calculators and computers in the process. Chapters 6, 7, and 8 present 60 problems in chapters entitled "Twenty Mathematical Excursions,""Twenty Mathematical Expeditions," and "Twenty Computer-assisted Explorations." The excursions are generally shorter and perhaps easier; the expeditions are more extensive and open ended; and the computer explorations need a programmable hand calculator or a computer. Explorations involve topics such as prime numbers, Fibonacci sequences, Pascal's triangle, continued fractions and chaos. A list of suggested readings has 22 entries. (MDH)

Exploratory problems in mathematics

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Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (256 download)

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Book Synopsis Exploratory problems in mathematics by : Fred Stevenson

Download or read book Exploratory problems in mathematics written by Fred Stevenson and published by . This book was released on 1980 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Empowering Mathematics Learners: Yearbook 2017, Association Of Mathematics Educators

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Publisher : World Scientific
ISBN 13 : 9813224231
Total Pages : 395 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Empowering Mathematics Learners: Yearbook 2017, Association Of Mathematics Educators by : Berinderjeet Kaur

Download or read book Empowering Mathematics Learners: Yearbook 2017, Association Of Mathematics Educators written by Berinderjeet Kaur and published by World Scientific. This book was released on 2017-04-12 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contributes towards the literature in the field of mathematics education, specifically on aspects of empowering learners of mathematics. The book, comprising eighteen chapters, written by renowned researchers in mathematics education, provides readers with approaches and applicable classroom strategies to empower learners of mathematics.The chapters in the book can be classified into four sections. The four sections focus on how learners could be empowered in their learning, cognitive and affective processes, through mathematical content, purposefully designed mathematical tasks, whilst developing 21st century competencies.

Icons of Mathematics: An Exploration of Twenty Key Images

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Publisher : American Mathematical Soc.
ISBN 13 : 1470456168
Total Pages : 327 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Icons of Mathematics: An Exploration of Twenty Key Images by : Claudi Alsina

Download or read book Icons of Mathematics: An Exploration of Twenty Key Images written by Claudi Alsina and published by American Mathematical Soc.. This book was released on 2020-06-01 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present twenty icons of mathematics, that is, geometrical shapes such as the right triangle, the Venn diagram, and the yang and yin symbol and explore mathematical results associated with them. As with their previous books (Charming Proofs, When Less is More, Math Made Visual) proofs are visual whenever possible. The results require no more than high-school mathematics to appreciate and many of them will be new even to experienced readers. Besides theorems and proofs, the book contains many illustrations and it gives connections of the icons to the world outside of mathematics. There are also problems at the end of each chapter, with solutions provided in an appendix. The book could be used by students in courses in problem solving, mathematical reasoning, or mathematics for the liberal arts. It could also be read with pleasure by professional mathematicians, as it was by the members of the Dolciani editorial board, who unanimously recommend its publication.

Exploratory Examples for Real Analysis

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Publisher : American Mathematical Soc.
ISBN 13 : 1470458357
Total Pages : 160 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Exploratory Examples for Real Analysis by : Joanne E. Snow

Download or read book Exploratory Examples for Real Analysis written by Joanne E. Snow and published by American Mathematical Soc.. This book was released on 2003-12-31 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text supplement contains 12 exploratory exercises designed to facilitate students' understanding of the most elemental concepts encountered in a first real analysis course: notions of boundedness, supremum/infimum, sequences, continuity and limits, limit suprema/infima, and pointwise and uniform convergence. In designing the exercises, the [Author];s ask students to formulate definitions, make connections between different concepts, derive conjectures, or complete a sequence of guided tasks designed to facilitate concept acquisition. Each exercise has three basic components: making observations and generating ideas from hands-on work with examples, thinking critically about the examples, and answering additional questions for reflection. The exercises can be used in a variety of ways: to motivate a lecture, to serve as a basis for in-class activities, or to be used for lab sessions, where students work in small groups and submit reports of their investigations. While the exercises have been useful for real analysis students of all ability levels, the [Author];s believe this resource might prove most beneficial in the following scenarios: A two-semester sequence in which the following topics are covered: properties of the real numbers, sequences, continuity, sequences and series of functions, differentiation, and integration. A class of students for whom analysis is their first upper division course. A group of students with a wide range of abilities for whom a cooperative approach focusing upon fundamental concepts could help to close the gap in skill development and concept acquisition. An independent study or private tutorial in which the student receives a minimal level of instruction. A resource for an instructor developing a cooperative, interactive course that does not involve the use of a standard text. Ancillary materials, including Visual Guide Sheets for those exercises that involve the use of technology and Report Guides for a lab session approach are provided online at: http:www.saintmarys.edu/~jsnow. In designing the exercise, the [Author];s were inspired by Ellen Parker's book, Laboratory Experiences in Group Theory, also published by the MAA.

Analysing the Solution of Word Problems in Mathematics: an Exploratory Study

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Publisher :
ISBN 13 :
Total Pages : 374 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Analysing the Solution of Word Problems in Mathematics: an Exploratory Study by : Jeremy Kilpatrick

Download or read book Analysing the Solution of Word Problems in Mathematics: an Exploratory Study written by Jeremy Kilpatrick and published by . This book was released on 1967 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Analyzing the Solution of World Problems in Mathematics: and Exploratory Study

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Publisher :
ISBN 13 :
Total Pages : 179 pages
Book Rating : 4.:/5 (87 download)

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Book Synopsis Analyzing the Solution of World Problems in Mathematics: and Exploratory Study by : Jeremy Kilpatrick

Download or read book Analyzing the Solution of World Problems in Mathematics: and Exploratory Study written by Jeremy Kilpatrick and published by . This book was released on 1967 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Worked Problems in Applied Mathematics

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Publisher :
ISBN 13 :
Total Pages : 429 pages
Book Rating : 4.:/5 (848 download)

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Book Synopsis Worked Problems in Applied Mathematics by : Nikolaĭ Nikolaevich Lebedev

Download or read book Worked Problems in Applied Mathematics written by Nikolaĭ Nikolaevich Lebedev and published by . This book was released on 1979 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematics Explorations for Ages 10 to 100

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Publisher :
ISBN 13 : 9781494235796
Total Pages : 374 pages
Book Rating : 4.2/5 (357 download)

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Book Synopsis Mathematics Explorations for Ages 10 to 100 by : Fred Stevenson

Download or read book Mathematics Explorations for Ages 10 to 100 written by Fred Stevenson and published by . This book was released on 2013-11-20 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: (356 pages, 152 illustrations)This book is entitled “Exploratory Problems from ages 10 – 100, A Travel Guide to Mathematics”. It includes 26 exploratory problems complete with questions and answers to the problems as well as a detailed explanation of the mathematics involved. In fact, 80% of each problem is devoted to a discussion of the mathematics. This feature will ensure that the teacher, even of very bright students, will have an advantage in that they will know the answers and be able to talk about them in detail. The book is an outgrowth of my 45 years of teaching. I am a Professor of Mathematics so I have taught primarily University undergraduate and graduate students, but I have also taught secondary school students, secondary teachers, and I have conducted junior high math camps in the summer-time for 25 years. Through all of this I have found that, at every level, there are students who can handle mathematical concepts far beyond what the general public would guess.This is an especially good time to introduce these problems. There is a need for students and teachers to address mathematical problems for their own sake. You can label these problems as “problems of the week”, “exploratory problems”, or just plain “fun problems” and you'd be surprised how many students will light up when an out-of-curriculum challenge is presented. And there are plenty of non-students who love challenges as well.Finally we should not undersell the subject of mathematics, it is a serious field of study. It assumes a natural place as a subject in elementary, middle, high school, college, and graduate school, but it is more. It is as important to the history of humanity as thought itself.

Exploratory Examples for Real Analysis

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Publisher : Cambridge University Press
ISBN 13 : 9780883857342
Total Pages : 164 pages
Book Rating : 4.8/5 (573 download)

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Book Synopsis Exploratory Examples for Real Analysis by : Joanne E. Snow

Download or read book Exploratory Examples for Real Analysis written by Joanne E. Snow and published by Cambridge University Press. This book was released on 2003 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every mathematician must make the transition from the calculations of high school to the structural and theoretical approaches of graduate school. Essentials of Mathematics provides the knowledge needed to move onto advanced mathematical work, and a glimpse of what being a mathematician might be like. No other book takes this particular holistic approach to the task. The content is of two types. There is material for a ""transitions"" course at the sophomore level; introductions to logic and set theory, discussions of proof writing and proof discovery, and introductions to the number systems (natural, rational, real, and complex). The material is presented in a fashion suitable for a Moore Method course, although such an approach is not necessary. An accompanying Instructor's Manual provides support for all flavors of teaching styles. In addition to presenting the important results for student proof, each area provides warm-up and follow-up exercises to help students internalize the material. The second type of content is an introduction to the professional culture of mathematics. There are many things that mathematicians know but weren't exactly taught. To give college students a sense of the mathematical universe, the book includes narratives on this kind of information. There are sections on pure and applied mathematics, the philosophy of mathematics, ethics in mathematical work, professional (including student) organizations, famous theorems, famous unsolved problems, famous mathematicians, discussions of the nature of mathematics research, and more. The prerequisites for a course based on this book include the content of high school mathematics and a certain level of mathematical maturity. The student must be willing to think on an abstract level. Two semesters of calculus indicates a readiness for this material.

Mathematical Problem Solving

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Publisher : Elsevier
ISBN 13 : 1483295486
Total Pages : 426 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Mathematical Problem Solving by : ALAN H. SCHOENFELD

Download or read book Mathematical Problem Solving written by ALAN H. SCHOENFELD and published by Elsevier. This book was released on 2014-06-28 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is addressed to people with research interests in the nature of mathematical thinking at any level, topeople with an interest in "higher-order thinking skills" in any domain, and to all mathematics teachers. The focal point of the book is a framework for the analysis of complex problem-solving behavior. That framework is presented in Part One, which consists of Chapters 1 through 5. It describes four qualitatively different aspects of complex intellectual activity: cognitive resources, the body of facts and procedures at one's disposal; heuristics, "rules of thumb" for making progress in difficult situations; control, having to do with the efficiency with which individuals utilize the knowledge at their disposal; and belief systems, one's perspectives regarding the nature of a discipline and how one goes about working in it. Part Two of the book, consisting of Chapters 6 through 10, presents a series of empirical studies that flesh out the analytical framework. These studies document the ways that competent problem solvers make the most of the knowledge at their disposal. They include observations of students, indicating some typical roadblocks to success. Data taken from students before and after a series of intensive problem-solving courses document the kinds of learning that can result from carefully designed instruction. Finally, observations made in typical high school classrooms serve to indicate some of the sources of students' (often counterproductive) mathematical behavior.

Mathematics Elsewhere

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Publisher : Princeton University Press
ISBN 13 : 0691187649
Total Pages : 220 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Mathematics Elsewhere by : Marcia Ascher

Download or read book Mathematics Elsewhere written by Marcia Ascher and published by Princeton University Press. This book was released on 2018-06-05 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics Elsewhere is a fascinating and important contribution to a global view of mathematics. Presenting mathematical ideas of peoples from a variety of small-scale and traditional cultures, it humanizes our view of mathematics and expands our conception of what is mathematical. Through engaging examples of how particular societies structure time, reach decisions about the future, make models and maps, systematize relationships, and create intriguing figures, Marcia Ascher demonstrates that traditional cultures have mathematical ideas that are far more substantial and sophisticated than is generally acknowledged. Malagasy divination rituals, for example, rely on complex algebraic algorithms. And some cultures use calendars far more abstract and elegant than our own. Ascher also shows that certain concepts assumed to be universal--that time is a single progression, for instance, or that equality is a static relationship--are not. The Basque notion of equivalence, for example, is a dynamic and temporal one not adequately captured by the familiar equal sign. Other ideas taken to be the exclusive province of professionally trained Western mathematicians are, in fact, shared by people in many societies. The ideas discussed come from geographically varied cultures, including the Borana and Malagasy of Africa, the Tongans and Marshall Islanders of Oceania, the Tamil of South India, the Basques of Western Europe, and the Balinese and Kodi of Indonesia. This book belongs on the shelves of mathematicians, math students, and math educators, and in the hands of anyone interested in traditional societies or how people think. Illustrating how mathematical ideas play a vital role in diverse human endeavors from navigation to social interaction to religion, it offers--through the vehicle of mathematics--unique cultural encounters to any reader.

Analyzing the Solution of Word Problems in Mathematics

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Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (819 download)

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Book Synopsis Analyzing the Solution of Word Problems in Mathematics by : Jeremy Kilpatrick

Download or read book Analyzing the Solution of Word Problems in Mathematics written by Jeremy Kilpatrick and published by . This book was released on 1971 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Hand-on Math

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Publisher :
ISBN 13 :
Total Pages : 188 pages
Book Rating : 4.:/5 (321 download)

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Book Synopsis Hand-on Math by : William Dennis Hogan

Download or read book Hand-on Math written by William Dennis Hogan and published by . This book was released on 1987 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Posing and Solving Mathematical Problems

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Publisher : Springer
ISBN 13 : 3319280236
Total Pages : 400 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Posing and Solving Mathematical Problems by : Patricio Felmer

Download or read book Posing and Solving Mathematical Problems written by Patricio Felmer and published by Springer. This book was released on 2016-04-29 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects recent research on posing and solving mathematical problems. Rather than treating these two crucial aspects of school mathematics as separate areas of study, the authors approach them as a unit where both areas are measured on equal grounds in relation to each other. The contributors are from a vast variety of countries and with a wide range of experience; it includes the work from many of the leading researchers in the area and an important number of young researchers. The book is divided in three parts, one directed to new research perspectives and the other two directed to teachers and students, respectively.

Mathematics for Human Flourishing

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Publisher : Yale University Press
ISBN 13 : 0300237138
Total Pages : 287 pages
Book Rating : 4.3/5 (2 download)

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Book Synopsis Mathematics for Human Flourishing by : Francis Su

Download or read book Mathematics for Human Flourishing written by Francis Su and published by Yale University Press. This book was released on 2020-01-07 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them."--Kevin Hartnett, Quanta Magazine" This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart."--James Tanton, Global Math Project For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires--such as for play, beauty, freedom, justice, and love--and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can--and must--be open to all.

The Effects of Feedback During Exploratory Mathematics Problem Solving

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Publisher :
ISBN 13 :
Total Pages : 51 pages
Book Rating : 4.:/5 (781 download)

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Book Synopsis The Effects of Feedback During Exploratory Mathematics Problem Solving by : Emily Ruth Fyfe

Download or read book The Effects of Feedback During Exploratory Mathematics Problem Solving written by Emily Ruth Fyfe and published by . This book was released on 2012 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt: