Authors Peitgen, Heinz-Otto; Jürgens, Hartmut; Saupe, Dietmar three of which on Strategic classroom activities in teaching fractals, Part one Introduction to fractals and chaos, and fractals for the Classroom. http://www.mathematik.uni-leipzig.de/MI/quapp/peitgen/
Extractions: This is the last volume of a series of five books on fractals, three of which on Strategic classroom activities in teaching fractals, (Springer, Volume One: 1991, and Volume Two: 1992) intended to provide companion materials for the two books Fractals for the Classroom. Part one: Introduction to Fractals and Chaos, and Fractals for the Classroom. Part 2: Complex Systems and Mandelbrot Set, written by the first three authors, and also published by Springer in 1992. These Strategic activities have been developed from a sound instructional base, stressing the connection to the contemporary curriculum for school mathematics. They may change the teaching of mathematics! The understanding of fractal objects provides a wonderful setting for students to enjoy the amazing dialogue between numeric and geometrical processes, and the fascinating interaction between mathematics and computer science. Occasionally a topic from Mathematics goes beyond the usual mathematical bondaries and captures the imagination of the public at large: fractals and chaos theory achieved such prominence. The authors of the book reviewed here contributed to this popularity. The book is very well written, and furthermore, I could not find any misprint. However, the organization of the material preceding the worksheets is a little confusing, and occasional redundant. It is easier to go back to the textbooks [op.cit.]. The first unit in this volume, unit 7 of the series, explains the Sierpinski curve and the Sierpinski gasket, connects it with Pascals's triangle via combinations, and leads over mappings and copying machines to self-similarity. The last unit discusses symmetries and compositions, algebraic mappings and fractal images, and chaos game variations. The connection between geometric genetic codes and chaos game developments is presented in what ought to be an exciting experience for the reader who walks the path suggested in this volume.
Overview.html HANDSON GROUP CLASSROOM activities HTML, video clips. fractals and chaos Simplified for the Life Sciences Hypertext version of the previous print http://www.ccs.fau.edu/~liebovitch/handout1932.html
Extractions: http://www.ccs.fau.edu/~liebovitch/larry.html If you want to speak with me please telephone, DO NOT SEND E-MAIL (I am overwhelmed with e-mail which I do not have time to read.) Overview This course emphasize WHAT mathematics is, HOW mathematicians do mathematics, and how mathematics is used in SCIENCE. Different teaching and learning styles including: LECTURE NOTES: HTML, PowerPoint slides, hypertext textbook, videotapes. HANDS-ON GROUP CLASSROOM ACTIVITIES: HTML, video clips. INDIVIDUAL SELF-DISCOVERY EXERCISES: Java applets, Excel spreadsheets.
Ethnomathematics Digital Library (EDL) Mathematics are used by all cultures in everyday activities such as weaving The use of fractals and chaos theory as a tool to study history for certain http://www.ethnomath.org/search/browseResources.asp?type=country&id=15
Ethnomathematics Digital Library (EDL) The section on Synthesis of the Teaching Material includes 6 activities with The use of fractals and chaos theory as a tool to study history for http://www.ethnomath.org/search/browseResources.asp?type=subject&id=342
CTC: Mathematics Mathematics Archives K12 Teaching Materials - An excellent list of games, activities, demonstrations and software, all related to fractals and chaos. http://www.tc.cornell.edu/CTC-Main/Services/Education/Gateways/Math_and_Science/
Extractions: General Topics Anthony Beckwith's Website - Advanced Topics in Math Course (covers topology, knot theory, chaos theory, barcodes, number theory, and other interesting topics) Ask Dr. Math - Ask Dr. Math is a question and answer service for math students and their teachers. A searchable archive is available by level and topic, as well as summaries of Frequently Asked Questions (the Dr. Math FAQ). Calculus Help - A professor in the Department of Mathematics at the University of Hawaii, authored these notes to help students learn how to use, not just understand, the concepts of calculus. A total of fifteen topics are covered and include max-min problems, exponential growth, and the derivation of Kepler's second law. Flash Cards for Kids - This is an interactive flash card site. You can choose among addition, subtraction, multiplication, and division; simple or complicated problems; and how many digits the numbers will have. While this isn't exactly high school material, it's a nice site, so we're including it anyway. Enjoy, and show it to your kid sister or brother!
Ideas And Activities chaos fractals is another good place where you can learn about fractals. You ll also find more math activities and teaching tips categorized by age http://euphrates.wpunj.edu/faculty/partnership/activities.htm
Extractions: Home Up [ Ideas and Activities ] New Jersey Mathematics Curriculum Framework Real World Data Web Resources Abacus: The Art of Calculating with Beads. The Art of Calculating with Beads is an online tutorial for learning how to use the abacus. Similar sites also for grades 5-12 are the Amazing Abacus and the Abacus AIMS Education Foundation. The Activities Integrating Mathematics and Science Education Foundation (AIMS) provides online activities and teacher resources for integrating math and science in the K-8 curriculum. Major links include an activity archive, ideas exchange, math history, puzzles, and places to visit.
Summary Investigate the history and theory of chaos and fractals, handson activities and real-life experiences and to use a variety of teaching strategies. http://home.inreach.com/kfarrell/summary.html
Extractions: Chapter 4 SUMMARY, CONCLUSION, AND RECOMMENDATIONS The Internet offers educators a new and novel medium for displaying curriculum, lesson plans, educational activities, and for collaboration. Unique features inherent in this new medium include hypertext links and a combination of visual and text media. These features allow curriculum to be redesigned to creates unique meanings for individuals. Hypertext links allow readers to make connections based on their preferences and background., and the combination of visual and text provide an opportunity to integrate learning styles and intelligences. This medium is a tool, but like all tools it changes the delivery of the message which, in turn, changes how that message is perceived. Summary Many educational sites are present on the Internet, offering educational activities, lesson plans, and text. Each of these are helpful and each has a place in the vast web of information, however, there are no sites that provide a cohesive curriculum based on one topic that pulls these many disparate sites together. The curriculum developed in this project is unique in that aspect. Also, this curriculum has been aligned with the NCTM standards and these standards have been identified so teachers know where this curriculum fits in their lesson planning. Creating this kind of curriculum posed some unique problems, primarily because there is so much information available on the Intent. Creation of a database solved some of these problems. The copy and paste feature assured accurate URL's, thereby eliminating problems with inactive links. In addition, the database made it easy to experiment with different organizational schemes until finding one that was satisfactory.
Intro To Chaos And Fractals Readings And Schedule Schedule of Readings and activities. This will change, especially toward the second All readings are from James Gleick, chaos Making a New Science, http://hornacek.coa.edu/dave/Teaching/Chaos Fractals.S05/schedule.shtml
Math Resources ways to teach fractals and chaos theory using hands on and classroom game approaches an amusement park of mathematics tessellations, fractal gallery, http://www.monroe.k12.la.us/mcs/hot_list/math.html
References fractals A Toolkit of Dynamics activities, Key Curriculum Press, 1998. Other chaos Games, in fractals, Graphics, Mathematical Education, http://ecademy.agnesscott.edu/~lriddle/ifskit/IFShelp/references.html
Extractions: Robert Devaney. Chaos, Fractals, and Dynamics: Computer Experiments in Mathematics, Pearson Learning, www.pearsonlearning.com, 1990. Robert Devaney. A First Course in Chaotic Dynamical Systems, Perseus Publishing Co. (a division of Harper/Collins), 1992. Robert Devaney, J.Choate, and A.Foster. Fractals: A Toolkit of Dynamics Activities, Key Curriculum Press, 1998. Gerald A. Edgar. Measure, Topology, and Fractal Geometry, Springer-Verlag, 1990. Sandy Fillebrown. "Other Chaos Games," in M.L.Frame and B.B.Mandelbrot, Editors, Mathematical Association of America, 2002, pages 105-109. Gary William Flake. The Computational Beauty of Nature: Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptation, MIT Press, 1998. Heinz-Otto Peitgen, Hartmut Jurgens, and Dietmar Saupe. Fractals for the Classroom, Part One: Introduction to Fractals and Chaos, Springer-Verlag, 1992. Michael F. Barnsley. Fractals Everywhere, Academic Press, 1993 (Second Edition). Richard M. Crownover. Introduction to Fractals and Chaos, Jones and Bartlett Publishers, 1995.
Ideas And Activities Other good places to learn about choas theory and fractals are chaos You ll also find more math activities and teaching tips categorized by age level in http://www.sitesforteachers.com/resources_sharp/math/math_activities.html
Extractions: About.com's Homework Help. About.com provides a searchable collection of articles that can help students with their math homework as figuring out the angles of a right triangle . The site, suitable for grades 3-12, also includes a library of useful Netlinks as well as Cathy Spalding's email service for your perplexing math questions. About Today's Date. About Today's Date, based on Richard Phillips' book Numbers: Facts, Figures , and Fiction , provides each day the history and trivia about the numbers in today's date. The site is suitable for grades 5-12. Academic Assistance Access. Academic Assistance Access offers free a tutoring service for high school students. The site, staffed by professionals in various fields, answers questions in calculus as well as in American history and the sciences. Academic Assistance Center Home Page. The Teachers and staff of AOL's Academic Assistance Center provide link access to their favorite or best information sites for grades K-12. To visit the math room, click here a teacher and a student guide to mathematics to mathematics for grades K-12.
Books On Special Topics activities that are very useful for teaching Escherstyle tessellation techniques chaos, fractals, and Dynamics Computer Experiments in Mathematics http://dimacs.rutgers.edu/Volumes/schools/paper82/node16.html
Extractions: Marcia Ascher; Chapman and Hall, 1991; $42. This is a fascinating book, which will give you a new perspective on mathematical ideas that one often takes for granted, such as the words used for counting. Of special interest is a chapter exploring Eulerian paths, a standard topic in discrete mathematics (e.g., see [ ]), as an artistic aid to story-telling in the South Pacific islands. This is the source of some of the material in the module Drawing Pictures with One Line , described on page . The following is an excerpt from a review by Susan Picker LP `90. But Ethnomathematics explores more than the topic of graph theory as it presents the mathematical ideas of number, kin relations, games of chance and strategy, and symmetric strip decorations. ...It provides a comprehensive look at the meaning and use of similar mathematical ideas in different cultures, illuminating both the mathematics and the culture in which it appears, and through this showing the value of the study of mathematics in a multicultural setting.
Math Ideas And Activities M-Z The site contains activities, teaching strategies, new curriculum developments, and a listing of fractals, chaos is another good tutorial by the author. http://www.nuatc.org/resources/weblinks/math/mathideasM_Z.html
Extractions: Return to Resources Ideas and Activities M - Z MacTutor History of Mathematics Archive. The MacTutor History of Mathematics Archive, provided by University of St Andrews in Scotland features a collection of more than 1,500 biographies of mathematicians, with snapshots arranged in alphabetical and chronological lists. This site, suitable for grades 6-12, also includes birthplace maps, history topics, an index to female mathematicians, and related Web resources. Harvey Heinz 's Magic Squares, Magic Stars & Other Patterns contains an extensive collection of `magic' number patterns, from the simple 3x3 square to the intricate five-in-one star for grades 7-12. The site includes other interesting patterns, such as narcissistic numbers and prime patterns. All the presentations are clearly illustrated and well explained. To find additional magic square resources, scroll to "Links to similar Web sites". Magic Squares.
Extractions: Skip Navigation You Are Here ENC Home ENC Features ENC Focus By Year ... New Directions in Curriculum: Chaos and Fractals Search the Site More Options Don't lose access to ENC's web site! Beginning in August, goENC.com will showcase the best of ENC Online combined with useful new tools to save you time. Take action todaypurchase a school subscription through goENC.com Classroom Calendar Digital Dozen ENC Focus ... Ask ENC Explore online lesson plans, student activities, and teacher learning tools. Find detailed information about thousands of materials for K-12 math and science. Read articles about inquiry, equity, and other key topics for educators and parents. Create your learning plan, read the standards, and find tips for getting grants. Fractals : exploring its simplicity, beauty, and mathematics This World Wide Web (WWW) site, maintained by Jacobo Bulaevsky, an electrical engineer and math hobbyist, contains information and interactive Java Applets on eleven types of fractals and the mathematics behind them. The site demonstrates through graphics how each type of fractal is generated, then employs Applets to help students visualize the iteration rules by allowing them to perform each iteration at the touch of a button.
Extractions: Skip Navigation You Are Here ENC Home Curriculum Resources Browse Search the Site More Options Don't lose access to ENC's web site! Beginning in August, goENC.com will showcase the best of ENC Online combined with useful new tools to save you time. Take action todaypurchase a school subscription through goENC.com Classroom Calendar Digital Dozen ENC Focus ... Ask ENC Explore online lesson plans, student activities, and teacher learning tools. Search Browse Frequently Asked Questions Resource of the Day ... About Curriculum Resources Read articles about inquiry, equity, and other key topics for educators and parents. Create your learning plan, read the standards, and find tips for getting grants. 34 Records Sorted by Date Use these menus to limit browse results using specific criteria Grade: All Grade Levels Pre-K to 2 3 to 5 6 to 8 9 to 12 Post Sec. Media Type: All Media Types Only Web Sites Excluding Web Sites Cost: All Costs Low Cost (Less than $50) Free Return to Subject Tree Modify using Advanced Search Fire!!
UOB MathsLinks: Mathematics Education Sites On WWW Taking Maths Further, Teachers Teaching with Technology, Conferences, Local activities, Written for anyone with an interest in chaos, fractals, http://www.edu.bham.ac.uk/maths/links/
Extractions: D D'Ambrosio, Beatriz S., Implementing the Standards: Highlighting the Humanistic Dimensions of Mathematics Activity through Classroom Discourse, Dec 1995, 770-772 D'Augustine, Charles H., What Our Collegiate Business Students Need to Learn from Secondary Schools, Mar 1989, 163-165 Dajani-Brown, Samar, Upward Bound Regional Mathematics-Science Center, Oct 1998, 640 Dale Seymour Publications, Graph Paper Masters, Dec 1989, 736 . Line Design Poster Sets, Apr 1993, 350-351 . Math and Music: Harmonious Connections.; Symmetry in Fractals; Symmetry in Wheels, Feb 1995, 152-154 Daniels, David S., Applications: Fast Brakes!, Feb 1989, 104-107, 111 . Gary O's Fence Question, Mar 1993, 252-254 . Mathematical Modeling: Lemonade from Lemons, Oct 1989, 516-519 Dauben, Joseph W., The Art of Renaissance Science: Galileo and Perspective, Sep 1992, 496 Daughtry, Doyle; et al, Calculus: Understanding Change, Dec 1994, 724 Davis, Donald M., The Nature and Power of Mathematics, Oct 1994, 573
Mathematics Resources For Educators Frisbie Middle School activities for teaching 7th grade math. fractals/Chaotic Behavior in Systems. chaos in the Classroom The chaos Game; http://falcon.jmu.edu/~ramseyil/math.htm
Extractions: Mathematics Resources K-12 Welcome to the Internet School Library Media Center mathematics page. You will find mathematics history, organizations, puzzles and games, tutorials, lesson plans, math education and more on this page. Separate pages are devoted to geometry algebra calculus statistics . Be sure to preview all categories to find information you need since content will be distributed across different categories. You can search this site, use an index or sitemap
Mandelbrot On Fractals, Academia, And Industry TT It seems that science now is obsessed with fractals and chaos. I mean some activities simply must be replaced by other activities. http://www-tech.mit.edu/V121/N63/Mandelbrot.63f.html
Extractions: By Akshay Patil staff writer The Tech had an opportunity to talk to math and physics legend Benoit B. Mandelbrot during his short visit to MIT. One of the fathers of fractal science, Mandelbrot discovered a mathematical set of numbers whose graphical representation is so stunning that it is often considered the face of fractals and chaos today. The Tech: Do you have any personal heroes and inspirations that have driven you over the years? Benoit Mandelbrot: For a long time my hero was John von Neumann, who was, among other things, one of the pioneers of computers. I was a post-doc with von Neumann when Dr. von Neumann died and he was my hero because he succeeded during his life in doing work in mathematics and application based technologies; all without compromising his perfectly rigorous manner of doing things. In time, more heroes appeared. One that is not so widely known I think, a pity, is a Spaniard who lived a hundred years ago, his name was Santiago Ramon y Cajal. Do you know his name? Ramon y Cajal was a doctor in Spain who described the structures of the nervous system, which is made of molecules, if you wish, which are the neurons, and atoms, which are parts of neurons, and how they interact. He then drew pictures of all these neurons. It was so perfect, so early, that in the early 1950s when neuron anatomy awoke again, because of new progress here at MIT, my friends at MIT were using as the reference for the nervous system, a book, first published in Spanish 60 years before. They were using the French translation from 1903 .
Astronomy Bibliography Fractals And Astronomy fractals for the Classroom, Strategic activities, Volume 1. New York SpringerVerlag. fractals, chaos, Power Laws Minutes from an Infinite Paradise. http://www.umich.edu/~lowbrows/biblio/fractals.html
Extractions: Fractals and Astronomy by Dave Snyder Fractals are a mathematical subject, so a full understanding of fractals requires mathematics. A person can look at a rainbow, a waterfall or a cloud and enjoy the beauty of these objects without understanding the physics behind any of them. And fractals are the same way. However, in my view fractals become even more enjoyable as one understands the mathematics behind them. This is hardly an exhaustive list of reference materials on the subject. A complete literature search for the author Mandelbrot will produce a couple hundred works on a variety of subjects (Mandelbrot was a prolific author). A complete subject search and/or citation search would produce even more. This is an attempt to list a few representative examples of works to show what fractals are and how they apply to specific areas in astronomy, however I have included references on physics as well. Science News, (April 5), p. 217. Aharony, A. and Feder, J., editors. 1989. Fractals in Physics: Essays in Honour of Benoit B. Mandelbrot
