Mind Bugs: The Origins of Procedural Misconceptions

(Learning, Development, and Conceptual Change)
Kurt VanLehn

The MIT Press | 1990 | 266 páginas | epub | 830 Kb

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Descrição: As children acquire arithmetic skills, they often develop "bugs" - small, local misconceptions that cause systematic errors. Mind Bugs combines a novel cognitive simulation process with careful hypothesis testing to explore how mathematics students acquire procedural skills in instructional settings, focusing in particular on these procedural misconceptions and what they reveal about the learning process. VanLehn develops a theory of learning that explains how students develop procedural misconceptions that cause systematic errors. He describes a computer program, "Sierra," that simulates learning processes and predicts exactly what types of procedural errors should occur. These predictions are tested with error data from several thousand subjects from schools all over the world. Moreover, each hypothesis of the theory is tested individually by determining how the predictions would change if it were removed from the theory. Integrating ideas from research in machine learning, artificial intelligence, cognitive psychology, and linguistics, Mind Bugs specifically addresses error patterns on subtraction tests, showing, for example, why some students have an imperfect understanding of the rules for borrowing. Alternative explanatory hypotheses are explored by incorporating them in Sierra in place of the primary hypotheses, and seeing if the program still explains all the subtraction bugs that it explained before. Kurt VanLehn is Assistant Professor in the Department of Psychology at Carnegie Mellon University. Mind Bugs is included in the series Learning, Development, and Conceptual Change, edited by Lila Gleitman, Susan Carey, Elissa Newport, and Elizabeth Spelke.

Mathematics Education: The Singapore Journey

(Series on Mathematics Education)
Wong Khoon Yoong

World Scientific Publishing | 2009 | 564 páginas | pdf | 5 Mb

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Descrição: This comprehensive book is a state-of-the-art review of research and practices of mathematics education in Singapore. It traces the fascinating journey from the original development of the Singapore mathematics curriculum in the 1950s to the present day, and reports on diverse findings about the Singapore experience that are not readily available in print. All of the authors are active mathematics educators or senior mathematics teachers in Singapore, thus adding authenticity and distinctiveness to the stories covered in this book. The issues they so earnestly explore in this book will undoubtedly be of interest to graduate students, mathematics educators, and the international mathematics education community.

Early Childhood Mathematics

Susan Sperry Smith
3.ª Edição

Allyn & Bacon | 2005|  | 288 páginas | pdf | 16 Mb

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Descrição: This NCTM Standards-based book encourages the teacher or future teacher to create an active learning environment that fosters curiosity, confidence, and persistence in children as they learn math. Because the knowledge of important mathematical relationships, number sense, and the ability to solve problems are three key ingredients to the successful acquisition of math in the early years, this book pays special attention to helping teachers foster those skills and ways of thinking.

Table of Contents1 Foundations, myths, and standards 12 The language of math 193 Early math concepts : matching, classification, comparing, and ordering or seriation 364 Space and shape 545 Pattern, function, and early algebra 756 Graphing 917 Developing number sense 1068 Problem solving : addition and subtraction 1309 Understanding our place value system 15210 Measurement 16911 Problem solving : multiplication and division 19112 Assessment 20913 Planning for success : a good beginning 22614 Thematic units 240App. A The more or less game 267App. B Algebraic solution 267App. C Glyph clowns 268App. D Ten strips 269App. E Dot cards 269App. F Five and ten frames 270App. G Bear pond 270App. H First-grade mathematics informal assessment 271App. I Bingo card 273App. J One hundred chart 273App. K A curriculum web 274

Elementary and Middle School Mathematics: Teaching Developmentally

6th Edition
John A. Van de Walle

Allyn & Bacon | 2006 | 576 páginas | pdf | 50 Mb

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Descrição: This leading K-8 math methods text has the most coverage of the NCTM standards, the strongest coverage of middle school mathematics, and the highest student approval of any text currently available. Elementary and Middle School Mathematics provides an unparalleled depth of ideas and discussion to help students develop a real understanding of the mathematics they will teach. John Van de Walle, one of the foremost experts on how children learn mathematics, finds that 80 percent of the students who purchase this book keep it for reference when they begin their professional teaching careers. This text reflects the NCTM Principles and Standards and the benefits of constructivist-or student-centered-mathematics instruction. Moreover, it is structured for maximum flexibility, offering 24 brief, compartmentalized chapters that may be mixed and matched to fit any course or teaching approach.

Language for Learning Mathematics: Assessment for Learning in Practice

Clare Lee

Open University Press | 2006 | 136 páginas | pdf

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Descrição: Make math easier to comprehend for your students
For many of your middle-school and high-school students, expressing mathematical ideas isn't easy. The language of math is often abstract and hard to get a handle on. Now Assessment for Learning in the Mathematics Classroom helps you help your students to express what they already know and increase their understanding. Providing practical strategies for bringing more discourse into lesson plans, this book gives you a powerful way to raise standards in the classroom.

Head First Statistics

Dawn Griffiths

O'Reilly Media, Inc. | 2008 | 716 páginas | pdf | 17 Mb

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Descrição: Wouldn't it be great if there were a statistics book that made histograms, probability distributions, and chi square analysis more enjoyable than going to the dentist? Head First Statistics brings this typically dry subject to life, teaching you everything you want and need to know about statistics through engaging, interactive, and thought-provoking material, full of puzzles, stories, quizzes, visual aids, and real-world examples.

Whether you're a student, a professional, or just curious about statistical analysis, Head First's brain-friendly formula helps you get a firm grasp of statistics so you can understand key points and actually use them. Learn to present data visually with charts and plots; discover the difference between taking the average with mean, median, and mode, and why it's important; learn how to calculate probability and expectation; and much more.

Head First Statistics is ideal for high school and college students taking statistics and satisfies the requirements for passing the College Board's Advanced Placement (AP) Statistics Exam. With this book, you'll:

Study the full range of topics covered in first-year statisticsTackle tough statistical concepts using Head First's dynamic, visually rich format proven to stimulate learning and help you retain knowledge Explore real-world scenarios, ranging from casino gambling to prescription drug testing, to bring statistical principles to lifeDiscover how to measure spread, calculate odds through probability, and understand the normal, binomial, geometric, and Poisson distributionsConduct sampling, use correlation and regression, do hypothesis testing, perform chi square analysis, and moreBefore you know it, you'll not only have mastered statistics, you'll also see how they work in the real world. Head First Statistics will help you pass your statistics course, and give you a firm understanding of the subject so you can apply the knowledge throughout your life.

La geometria non-euclidea

Roberto Bonola
(versão em italiano)

liberliber | PDF | 1 Mb

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