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         Fractals & Chaos Activities Teach:     more detail

1. Dynamical Systems And Technology Project, TheBoston University Provides Java App
Math and Science fractals and chaos, University of the Ideas and activities, Robert Price. Ideas and activities, Using the Web to teach Mathematics, University of Colorado
Dancing Triangles
The Dynamical Systems
Technology Project
Boston University
Zooming Sierpinski This project is a National Science Foundation sponsored project designed to help secondary school and college teachers of mathematics bring contemporary topics in mathematics (chaos, fractals, dynamics) into the classroom, and to show them how to use technology effectively in this process. At this point, there are a number of Java applets available at this site for use in teaching ideas concerning chaos and fractals. There are also several interactive papers designed to help teachers and students understand the mathematics behind such topics as iteration, fractals, iterated function systems (the chaos game), and the Mandelbrot and Julia sets.
Available at this site:
    JAVA Applets for chaos and fractals
      Play the chaos game; explore iterated function systems; and make fractal movies, like the Dancing Triangles and Zooming Sierpinski above, all at your own computer. These applets are now up and running!
    The Mandelbrot Set Explorer
      This is an interactive site designed to teach the mathematics behind the Mandelbrot and Julia sets. It consists of a series of tours in which you will discover some of the incredibly interesting and beautiful mathematics behind these images. The site is designed to be used by readers of

2. Fractals
Peruse these links to information about fractals. Find out what one is and what they look like. chaos Club. Educational resources, online games and resources (instructional software, lab activities, lesson plans, student created to help teach ideas about fractals to high school
Fractals Theme Page This "Theme Page" has links to information about Fractals. Students and teachers will find curricular resources (information, content...) to help them learn about this topic. In addition, there are also links to instructional materials (lesson plans) which will help teachers provide instruction in this theme. Please read our
An Internet Fractal Lesson
To study fractals using World Wide Web and generating your own f ractal. (Grades 7-12)
Chaos Club
Educational resources, online games and message chat areas for students and teachers exploring fractals. Be sure to check out the "tutorial" for a unit by Cynthia Lanius in which elementary and middle students utilize online resources to study properties of fractals either independently or with a teacher. Lessons can be downloaded and printed.
The Explorer is a collection of information on educational resources (instructional software, lab activities, lesson plans, student created materials ...) that K-12 mathematics and science educators can download. Enter "Fractals" in the search engine and you'll see about a dozen resources.
Exploring Fractals
This site for secondary students explores several aspects of fractals. After an introduction to fractals, the author explores assigning dimensions, both non-integer and integer, and several ways of generating fractals.

3. Metastore: Books On Philosophy, Science, Technology, Fractals And Chaos, Philoso
You cannot teach a man Local activities. Our science section contains an authorativecollection of books and links to fractal geometry and chaosrelated material
"If you have anything really valuable to contribute to the world it will come through the expression of your own personality, that single spark of divinity that sets you off and makes you different from every other living creature." -Bruce Barton Book Search at bottom of page. Submit books in bottom-level categories. Home metasearch Our Mission Cyber Friends ... People that Get It metasearch Everything meta Fractal Liberty Business Drugs Skeptic Psych Spirit
Search the full contents of every website listed here.
Advanced / Help
Paperless Office Systems from Meta Enterprises The metastore shows how one can support philosophical endeavors by promoting the very ideas you wish to develop. Our books, movies, music and other products all reflect the common theme of metacultureconsilience between science, religion and freedom. Book Categories Science (46 Items)
Our science section contains an authorative collection of books and links to fractal geometry and chaos-related material. Other categories primarily contain popular science and scientific philosophy. Sites with connections to chaos theory are emphasized. Society (28 Items)
A true utopia is not fashioned to direct people towards happiness, but instead provides them the most freedom to find it themselves. When one is free from the pressures of conformity, the desire to fuck with people is greatly reduced.

4. Math Activities Self Directed Learning 8-14
Select and discuss activities with help from parents or teacher. (chaos, fractals, dynamics) bar graphs and pie charts. These activities will teach the ability to apply math skills
Click here to review learning and management tools. Math Skills/ Advanced Studies SECTION 1
Learning Objectives

Your Work Bench


Practice Quizzes
Learning Activities
Complete the Stock Market Activity

Master three activities
and report completion to parents and teacher.
Go Learn!
Your Work Bench Take online notes, develop reports, submit questions. For longer assignments use Develop a Report . For other activities, you may copy and paste your work to EMail Assignment to submit to parents and teacher, or copy and paste your online work to a Word file and save. Use this feature to draft short reports, ask questions, or request assistance. Your teacher will suggest additional activities in areas of interest and strength. They will also suggest activities and projects to develop skills in areas that need improvements. Your progress is based upon knowledge and understanding. Go learn! Extra Help. Use define word You may also use Resources Learning Objectives: They will demonstrate communication skills of reading, writing, listening, speaking, viewing and presenting from the core of language and literacy skills. The ultimate purpose of the following learning activities is to ensure that all learners are offered the opportunities, the encouragement and the support to develop the basic math skills they need to pursue lifelong goals, meet business objectives and participate as an informed member of society. These skills will be accomplished by successful completion of selected resources, assessment activities and tutorials to the satisfaction of parents and/or teacher.

5. Law And Disorder: The New Science Of Chaos
and Exploring fractals. fractals are chaos and order, math and This web site will teach you about the programming Fractal Explorer, and interactive activities, our goal is to
    Volume 3
    Law and Disorder
    The New Science of Chaos
    By R.C.L

    Chapter Six of Laws of Wisdom
      For more on Fractals and Chaos visit the School of Wisdom's Fractal Webs.

      The outer world can often seem as chaotic as our inner world - our stream of consciousness. Coherence can all too easily elude us. We usually experience a convoluted flow of happenings and events. The fragmented, fractal nature of everyday reality, and people, is one of our basic problems. To use thinking to sort things out - to start making sense of it all - we must first find the basic structure to reality. The structure reveals the order underneath the chaos.
        The Four Attractors
      We have seen the fourfold nature of consciousness; the laws concerning the four functions and four brain waves. An equivalent fourfold law applies in the material world. This was recently discovered by scientists working in the new field of Chaos. They found that seemingly-chaotic, lawless actions in the outer world actually followed a hidden order. The order they discovered was fourfold. They found that all outer phenomena are governed by what they call the four "attractors". The attractors are forces which bring order out of disorder. They are called the point attractor, the cycle or circuit attractor, the torus attractor and the strange attractor. The attractors are in accord with the four functions: torus-sensing; cycle-thinking; point-feeling and strange-willing. They form a basic Constitutional Law of the outer world of nature.

6. Classroom Activities
Classroom activities. As mentioned in the introduction, most of mathematical phenomena such as chaos, fractals, and bifurcations. ideas you are probably trying to teach anyway.
Classroom Activities
As mentioned in the introduction, most of the ideas discussed here have been presented to high school students in mathematics clubs, in summer workshops, and in the classroom itself. The experiences have been quite positive. Iteration is the key to many ideas in dynamical systems, and students are able to grasp the concept quite easily. Working only with x + c for real and complex values of c , students can be exposed to contemporary mathematical phenomena such as chaos, fractals, and bifurcations. If you are reluctant to deal with complex numbers and prefer to work only with real numbers, students can still understand and compute orbits and draw time-series plots and histograms. They can also do something we didn't have time to covernamely, orbit and bifurcation diagrams. Those ideas are covered in the programs Lab 2 - Plot and Analyze and Lab 3 - Orbit Diagram . We can look at them, if you're interested. Also, the ideas in last summer's workshop using the program Lab 4 - Fractals are accessible to students at all levels. This material can occupy students for several weeks.

7. Math Resources
chaos in the Classroom ways to teach fractals and chaos theory using hands on of educationalresources (instructional software, lab activities, lesson plans

A+ Math

Visit the game room and play exciting games like Matho and Concentration. Test your math skills with flashcards. A homework helper, too. The Abacus
requires Java to operate the online abacus, but has links and information useful to students and teachers Algebra On-Line
Free service designed to allow students, teachers, and parents throughout the world to communicate. Also offers free private tutoring to any and all students... Algebra Story and Word Problems
problems and stories by grade level with illustrated solutions Ask Dr. Math
elementary - college archives of questions already asked and answered or email Dr. Math with a question of your own Blue Dog Can Count!
key in a problem and Blue Dog will bark the answer Brain Teasers
Both entertaining and mentally challenging. Each Wednesday evening three new Brain Teasers, one at each of three grade ranges (3-4, 5-6, 7+), are provided. Solutions are posted on the following Wednesday. ChangeMaker: The Cash Register Game
Never get short-changed. All you do is figure out how many of each bill or coin that you expect to get back when you pay for something.

8. Brief Vita: Robert L. Devaney
students who have taken calculus; and chaos, fractals, and Dynamics A Tool Kit ofDynamics activities, all aimed on all continents so if you teach at South
Robert L. Devaney
A native of Methuen, Massachusetts, Professor Robert L. Devaney is currently Professor of Mathematics at Boston University. He received his BA from Holy Cross College in Worcester, MA in 1969 and his PhD from the University of California at Berkeley in 1973 under the direction of Stephen Smale. (Click here for his complete "mathematical" genealogy.) He taught at Northwestern University, Tufts University, and the University of Maryland before coming to BU in 1980. His main area of research is dynamical systems, primarily complex analytic dynamics, but also including Hamiltonian systems, planar mappings, and computer experiments in dynamics. Lately, he has become intrigued with the incredibly rich topological aspects of dynamics, including such things as indecomposable continua and Cantor bouquets. He is the author of over seventy research papers in these fields. He is also the author or editor of ten books on various aspects of dynamical systems theory. These include " An Introduction to Chaotic Dynamical Systems ," a text for advanced undergraduate and graduate students in Mathematics and researchers in other fields; "

9. Briefme: Jan_24_2000_vol_061_No_13.htm
The notions of determinative chaos, fractals, and nonlinear is a hypertextbook of chaos theory, a Other activities teach various physical concepts and use
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10. Cbbkgd
Handheld fractals-activities for the Using Discrete Mathematics to teach 'Regular'Math Cellular Automata and Natural fractals , chaos and Computers Workshop
Educational and Professional Background
L. Charles (Chuck) Biehl
    Professional Activities
    (Most recent listed first) Publications
    • "Forest Fires, Oil Spills, and Fractal Geometry: An Investigation in Two Parts."; "Part 1: Cellular Automata and Modeling Natural Phenomena"; The Mathematics Teacher ;Volume 91 Number 8; November, 1998; pp.682-7.
        "Forest Fires, Oil Spills, and Fractal Geometry: An Investigation in Two Parts"; "Part 2: Natural Phenomena and Fractal Complexity"; The Mathematics Teacher ; Volume 92 Number 2; February, 1999; pp.128-39.
          "Discrete Mathematics in the Classroom: A Fresh Start for Secondary Students"; Discrete Mathematics: Impact in the K - 12 Curriculum; The Mathematical Association of America; 1997; pp.317-22.
            "Goodwill Tours" classroom activity; Mathematics of the States ; CoMAP; Lexington, MA; 1996; pp.131-8.
              "Fractal Programs for the TI-8X"; Precalculus: A Graphing Approach (contributing author); R. Larson et al; D.C. Heath; 1993-5.
                "Fractal Programs for the TI-8X; College Algebra: A Graphing Approach (contributing author); R. Larson et al; D.C. Heath; 1993-5.

11. Greater Hartford Academy Of Math & Science Curriculum
6, Mathematics Field Day “chaos fractals” an Interactive kits, elementaryteachers conduct fun and challenging hands-on science activities that teach



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CREC Programs A-Z Academy of the Arts Administrative Services BEST Birth to Three Capitol Region Partnership Capitol Region Choice Program Center for Creative Youth Children's Therapy Specialists Choice Programs Cisco Networking Computer Services Conference Facilities Consultation, TABS CREC Jobs CREC News Direct Care Training Disability Resources Edu-Links EHGEMS Employee Assistance Program EQUAL Family Day Care Farm Valley Diagnostic Center Hartford Mag Middle School Human Resources Instructional Technology Integrated Program Models Links Literacy Center Magnet Schools at CREC Metropolitan Learning Center Minority Teacher Recruiting Montessori Magnet School Parent Aide Program Polaris Preschool Intervention REACT Reading Recovery Resource Sharing River Street School School To Career Sister Schools Sm/Reg School District Svcs Soundbridge Student Services Summer Programs Summer Youth Emp Trng Tech Prep Technology Services Technology Training Theater of the Performing Arts Transition to Employment Tunxis Middle College HS Two Rivers Magnet MS Univ of Hartford Mag School Young Educators' Society Choice Programs
Conference Brochure with Registration Form (in pdf format) October Thinking Conceptually
Paul Hewitt - Keynote Presenter November 2nd Annual Trinity College/GHAMAS Professional Development Conference
with Keynote Speaker Dr. Henry Lee

12. Enrichment - Secondary School
secret solutions to these problems and activities. Using the Newspaper to teach Math,Science chaos, fractals, and Dynamics Computer Experiences in Mathematics
Titles for Enrichment
Seconday Level Reading, Writing, and Doing Mathematical Proofs
Daniel Solow (Grades 10-12)
SS6-0-86651-148-2, 288 PP, $29.10
The little insights and ideas we all so laboriously discovered for ourselves come together in this carefully-structured, systematic book about mathematical proofs. Once students understand and analyze the structure of proofs, theyll be able to follow the more informal versions in texts and learn to create their own.
  • two workbooks tailored to the high school curriculum
  • short, easy-to-follow lessons followed by exercise sets with solutions
Number Treasury
Stanley Bezuszka and Margaret Kenney (Grades 7-12)
SS6-0-86651-078-8, 208 pp., $29.10
This resource offers an extensive source of information about number patterns, classical and modern.
  • covers prime and composite numbers, plane and figurate numbers, digital patterns, and more
  • solutions included
Math Space Mission
Regional Math Network

Kay Merseth, Director (Grades 7-9)
SS6-0-86651-439-2, 256 pp., $33.45 Students explore the outer realms of our solar system and learn estimation, geometry, and problem solving with this four-module, spiral-bound kit.
  • activity book includes teaching notes, reproducible student worksheets and problem cards, answers, and more

13. Michigan Mathematics Prize Competition
students who have taken calculus; and chaos, fractals, and Dynamics A Tool Kit ofDynamics activities, all aimed on all continents so if you teach at South
The Forty-Sixth Annual
Michigan Mathematics Prize Competition
An Activity of the Michigan Section of the Mathematics Association of America
Robert Devaney
Boston University
(return to Awards Day
A native of Methuen, Massachusetts, Professor Robert L. Devaney is currently Professor of Mathematics at Boston University. He received his BA from Holy Cross College in Worcester, MA in 1969 and his PhD from the University of California at Berkeley in 1973 under the direction of Stephen Smale. He taught at Northwestern University, Tufts University, and the University of Maryland before coming to BU in 1980. His main area of research is dynamical systems, primarily complex analytic dynamics, but also including Hamiltonian systems, planar mappings, and computer experiments in dynamics. Lately, he has become intrigued with the incredibly rich topological aspects of dynamics, including such things as indecomposable continua and Cantor bouquets. He is the author of over seventy research papers in these fields. He is also the author or editor of ten books on various aspects of dynamical systems theory. These include "An Introduction to Chaotic Dynamical Systems," a text for advanced undergraduate and graduate students in Mathematics and researchers in other fields; "A First Course in Chaotic Dynamical Systems," written for undergraduate college students who have taken calculus; and "Chaos, Fractals, and Dynamics: Computer Experiments in Modern Mathematics" and the series of four books collectively called "A Tool Kit of Dynamics Activities," all aimed at high school students and teachers as well as college faculty teaching introductory dynamics courses, including courses aimed at non-science majors.

14. 2002 NATM Summer Conference - Program Speakers
Play a chaos game Come see how to generate your own fractals using spreadsheets, paperfolding Basic rocketry for the beginner with fun, safe activities to teach

Nebraska Association of Teacher of Mathematics
NATM 2nd Annual Summer Conference
Doane College, Crete, Nebraska
Thursday, July 25, 2002 Time: 7:30 - 8:30 AM Registration - Hallway outside Heckman Auditorium Time: 8:30- 8:50 AM Session #1 General session - all participants
Heckman Auditorium, Communications Building
Speaker: Tom Price 1st Vice-President of NATM (President next year)
Introductions and Welcome Time: 9:00 - 9:50 AM Session #2 Level 9-12 Lied - Room 152
Speaker: Jim Foley, NCTM Affiliate Representative, Coon Rapids, MN
(repeated on Friday) "I Finally Get to Teach Reform Algebra
but I had to Move to the Community College to Do It" Time: 9:00 -9:50 AM Session #3 Level 6-8 Lied - Room 223
Speaker: Mary Lynn Reiser, UNO Center for Economic Education, Omaha "Show Me the Money" Introducing curriculum for integrating personal finance topics into the middle level math classes. The session will provide an overview of the lessons. Participants will get copies of a guide; information will also be given on the Nebraska Council on Economic Education Stock Market Game. Time: 9:00 - 9:50 AM Session #4 Level 2-6 Lied - Room 224 Speaker: Nancy Kunkel, Hebron Elementary School, Hebron, NE

15. ECOO97 Session D Friday, May 2, At 2:30
D14 Follow the Bouncing Ball D15 chaos, fractals and the all students use IBM notebooksfor their daily activities. that teachers aren't using it to teach.
ECOO '97 Keys for Learning
May 1, 2, 3, 1997
Regal Constellation Hotel
Toronto, Ontario, Canada
Conference Hompage General Information
Workshops A B C Saturday E F G H ... Next
Session D Friday, May 2, 2:30-3:30
Contents of this page
Click on a session number or scroll down for details of each session. Who is Steering the Ship?
The Power Within
SIG-Tel Annual Meeting
From Chalk Dust to Microchips: Creating a Technology Capable School
Archiving the Web
E-STAT - Electronic Learning in Action!
Introduction to World-Wide-Web Home Page Design
Redefining the Student, Teacher and the Day Technology Trends and Direction The Intranet Improve Teaching and Increase Collaborative Learning in Your Computer Lab An Integrated Computer System - From Classroom to Central Office Student Tracking System Follow the Bouncing Ball Chaos, Fractals and the Mandelbrot Set Integrating Science, Technology, Mathematics and Language Arts using Outcomes Integrating Canadian Multimedia in Language Arts and Science Animation for All When is a Word Processor NOT the Best Tool?

16. HRUMC IX - More Information
from modern mathematics such as chaos, fractals, and dynamics This network offersoutreach activities in science of explorations designed to teach students at
HRUMC IX: Hamilton College, Clinton, NY
April 27, 2002
Sponsored by SALLIE MAE Directions to Hamilton College Hamilton Campus Map Lodging Information - link now active Conference Parking
Parking near the center of campus is very limited so we ask that you park in North Lot (or Siberia as it is known to the students). We will run a shuttle service although it is an easy walk. As you reach the top of the hill on College Hill Road, you will see signs for North Lot to your right or you may proceed several hundred yards father to the registration site (ELS) on your left. You can drop off students there and then head for North Lot. HRUMC IX - Schedule of Sessions.
(Click on the details links for room numbers and lists of talks for each session.)
  • 8:30 - 9:50 AM - Registration and Coffee - Emerson Hall (known locally as ELS)
  • 10:00 - 10:55 AM - SESSION I (details)
    • Number Theory I
    • Abstract Algebra I
    • Geometry I
    • Analysis I
    • Analysis/History of Mathematics
    • Differential Equations I
    • Graph Theory I
    • Game Theory I
    • Statistics I
    • Computer Science
    • Applied Mathematics IA
    • Applied Mathematics IB
  • Welcome and Invited Address - Wellin Hall Title: Chaos Games and Fractal Images Robert Devaney, Boston University

17. Updated URL Addresses For Using INTERNET Primary Sources To Teach Critical Think 1 http// 2 http//
A leading publisher of academic, reference, trade, general interest, and professional books and electronic media
Updated URL Addresses for
Using INTERNET Primary Sources to Teach Critical Thinking in Mathematics

By Evan Glazer . ISBN: 0-313-31327-X
Last Update: January 16, 2003 Please contact the author about additional or bad links. ABSOLUTE VALUE OF A LINEAR FUNCTION
Related Internet Sites: Absolute Value of a Quadratic Function
Related Internet Sites: Airplane Noise Simulator Site 1: [updated 2/6/02] Site 2: Traffic Simulation Site 1: [updated 6/21/02]

Site 2: [updated 1/16/03]

18. More About Aggie
PARTICIPANT fractals, chaos, and Dynamics brings calculators, overheads, handouts,writing activities, and manipulatives to teach and motivate
Most Important Press Release End of page MC,i. Home ... MSH! Home
  • MOTHER: of Michael Anthony Vinik: 7/16/79 - present;
  • ASSISTANT PROFESSOR: Mathematics, Middlesex CC, Edison, NJ: 9/80 - present;
  • PRESIDENT: AMTNJ, 10/02 - present.
  • AMATYC 1997 Award for Teaching Excellence , Mid-Atlantic Region Recipient. MATYCNJ 1999 Outstanding Service Award
    (Standard Math Teacher Certificate (NJ), and Supervisor Certificate (NJ))
    Northern Valley Reg. HS, 9/72-6/73;
    Randolph HS, 9/73-6/75;
    Piscataway HS, 9/75-6/79;

    Paramus PS, 3/76;
    West Morris Central PS, 10/77

    Math Lady, MCC DCC, 9/85-5/90;

    Middlesex CC, 9/80 - present;
    Rutgers, '88 (Adjunct Faculty);
    Montclair SC, '89 (Graduate Asst.);

  • INSERVICE: in Hackensack, Lakewood, Jackson, Franklin Township, E. Brunswick, Bayonne, Swedesboro, Plainfield, Newark, Belleville, Roselle Park, Neptune, West New York, and others places;
    1996 Papers 1997 Papers 1998 Papers 1999 Papers ... 2002 Papers ICME-7; NCTM, MAA-NJ, ATOMIC, NADE, NJADE, AMTNJ, NJEA, MAA-SIAM-AMS, NCSM, conferences at Fairleigh Dickenson U, Montclair State College, Moravian College, Brookdale CC, Rutgers U, Suffolk University, Raritan Valley CC.

19. Math Ideas And Activities M-Z
a handson approach to teach geometry using sites with classroom paper folding activitiesfor geometry fractals, chaos is another good tutorial by the author.

projects articles resources people about nua ... email
These pages has links to many sites related to math. If you have any corrections or additional information please email NUA . The pages are arranged by the following categories
Ideas and Activities A - L

Ideas and Activities M - Z


Online Math Applications
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.

20. Easy Reader
fractals Images of chaos Penguin Books (1991 teach people with computers how tomake fractals themselves Number activities and Games Edwards R., Williams A.

easy reader online
Education Schools National Curriculum Resources for Teachers Maths Resources
MW Educational
MW Educational
MW Educational
MW Educational
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