81. SPIRITUALITY AS EXPERIENCE chaos theory considers the edge of chaos as a special region in the state the complexity and number of our activities in both teaching and research, http://www.zulenet.com/VladimirDimitrov/pages/spirituality.html

SPIRITUALITY AS EXPERIENCE AT THE EDGE OF CHAOS Bob Hodge and Vlad Dimitrov University of Western Sydney-Hawkesbury E-mail: B.Hodge@uws.edu.au V.Dimitrov@uws.edu.au Introduction Chaos theory considers the edge of chaos as a special region in the state space of nonlinear systems, where order and chaos meet to give birth to dramatic changes in systems' dynamics. It is a region where all established patterns dissolve their rigid boundaries and become permeable and fluid, able to coalesce and evolve, percolate and urge forward new emergent phenomena. In social systems the edge of chaos is where 'social magic' manifests. By 'social magic' Young means "appearance of events which do not follow logically and coherently from what has gone before"; social magic relates to happening of wondrous things "which surprise, astonish and bemuse those of us who are accustomed to orderly and routine consequences in every day life" [1]. Individual experience is full of such 'wondrous things' as our living is mostly at the edge of chaos - it neither unfolds as a sequence of orderly-organized patterns nor disintegrates into an entire chaos. At the edge of chaos, self-organizing capacity of complex life dynamics manifests its potential not only to sustain the integrity of each individual's life but also to support its unfolding. The unfolding of human life reflects the process of evolving of the whole universe. Both processes are like fractals nested within each other - they keep centered at one and the same spiritual core. The ability to experience the attracting power of this core we refer to human spirituality.

82. Math On The Web CHANCE This data base contains materials designed to help teach a CHANCE course. The Fractal Microscope - Further discussion of fractals, http://www.uwp.edu/academic/mathematics/math_on_the_web.htm

Math on the Web From Cornell University General Topics Ask Dr. Math - College students and professors helping K-12 students with their math questions, based at Swarthmore College and staffed mainly by Swarthmore students, staff, and faculty. Students are encouraged to send in their math questions. Algebra For Everyone - A collaborative math project with Carnegie Mellon University in Pittsburgh that uses computer and artificial intellignce tutors to revitalize math education in local public schools. 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. CHANCE - This data base contains materials designed to help teach a CHANCE course. CHANCE is a new introductory course being developed cooperatively by several colleges and universities. It is a case study course based upon current chance events as reported in the daily newspapers. CHANCE is designed for undergraduates, but may be of interest in high schools, as well. 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 I'm including it anyway. Enjoy, and show it to your kid sister or brother!

83. NSU ICAMP Topic 2 fractals and chaos. chaos theory and fractal geometry are cutting edge knowledge Teaching Focus Exploring mathematics using World Wide Web. http://polaris.nova.edu/MST/ICAMP/

Governor's Summer Program 1997 (June 23, 1997-July,11, 1997) Institute for Computer Aided Mathematics Program (ICAMP) Math, Science and Technology Farquhar Center for Undergraduate Studies Nova Southeastern University ICAMP Features Build up a strong background in mathematics Develop problem-solving skills Learn applications of mathematics Explore math on World Wide Web Tour various university research labs Build a bridge to future college studies 1. ICAMP '97 The purpose of the ICAMP '97 is to provide gifted, talented and creative youngsters opportunities to pursue their interests in the relaxed summer atmosphere of a university campus environment with other youngsters of similar abilities. The learning activities are designed to provide students with interesting, challenging, and unique experiences. The ICAMP '97 provides math enrichment to help students develop a sense of discovery and problem-solving skills in both applied and theoretical mathematical situations with the computer and Internet as tools. The ICAMP helps students to understand that studying mathematics and science now will be key to career opportunities in the technology driven 21st century. Research Lab experiments, field studies, Web exploring, challenging projects, collaborative learning and recreational activities such as tennis, swimming and basketball will add fun and excitement to the ICAMP. 2. Program Goals and Objectives

84. Ooooo O O O M S T O +-+-+-+-+-+-+-+-+-+-+-+-o * * * O-+-+-+-+-+-+ ICAMP Faculty Jerry Bartolomeo, Associate Professor Teaching focus Number Theory, Enter the strange and beautiful world of fractals and chaos 2. http://polaris.nova.edu/MST/FOCUS/focus2.1.html

85. Teachers Empowering Teachers In addition, each teacher will teach a fractal Scenario, or adaptation thereof, There is a continuum of teaching activities between routine basic skills http://thales.cica.es/icme8/wgtg/tg19/allen/allen.poster2.html

Teachers Empowering Teachers Vertically-integrated, Inquiry-based Geometry in School Classrooms Project Back to Page 1 Investigators: Richard J. Allen (Director), Judith N. Cederberg, Dale G. Pearson, Martha L. Wallace St. Olaf College, Northfield, MN 55057 Summary. The central aim of the project is three-fold: to help teachers integrate and use manipulatives, computer software, and calculator technology to make the teaching and learning of secondary school geometry an engaging, dynamic, inquiry oriented activity consistent with the recommendations of the NCTM Curriculum and Evaluation Standards to use their work with geometry as a springboard for vertically integrating geometric and visual methods and techniques into other courses that they teach in the secondary mathematics curriculum; and to engage and assist in efforts that will help transfer the project work to the classrooms of their district and regional colleagues. Project Philosophy. The goals of the first year of the project for the participants are: * To learn new geometry in new ways - Finite geometries as examples of axiomatic systems - Non-Euclidean geometry - Transformational geometry - Fractal geometry * To consider what we know and believe about - what geometry is - how children learn geometry - how geometry could be taught in an inquiry-based manner * To provide time - to investigate appropriate manipulative tools, computer software, and calculator technology

86. Points And Angles A Multimedia Fractal chaos Presentation An essay not to exceed 400 words on “Why I would like to teach mathematics.” Please send all information to http://www.mmcchicago.org/dinners00-01/P&AMar01.htm

Points and Angles Online March 2001 Table of Contents: Current Speaker Answers to last month's Mathacrostic Application For The MMC Scholarship Professional Development Units ... This month's puzzle that will Infuse You With Amazement Monica Neagoy Mathematics Consulting Services Rare is the student who is not fascinated by the beauty of fractals, or the teacher who is not captivated by the surprises of chaos. Multiple media will be used to illustrate the interplay between fractals and chaos, and their connection with mathematics and our world. Monica Neagoy was educated in France, Asia and the U.S. with her Ph.D. in mathematics from the University of Maryland. Her exposure to many cultures, her mastery of several languages, and her professional involvement in both the arts and sciences give her a unique perspective on the learning and teaching of mathematics. She is a national mathematics consultant (ie., The Annenburg/CPB Channel, The American Association for the Advancement of Science, PBS) and the head judge for MATHCOUNTS organization. Since 1985, she has worked with in-service teachers independently and through Georgetown University. She is also a professional actor and is the artistic co-director of the professional LE NEON Theater in Washington, D.C. This will be an exciting evening with Monica Neagoy on March 9, 2001.

87. Internet International Journal for Mathematics Teaching and Learning Contains many images and exploration opportunities for fractals and chaos http://wwwstaff.murdoch.edu.au/~kissane/internet.htm

The Internet and Mathematics Education Educational Student resources Teacher resources Maths software ... Interactive maths This page is mainly designed to try to keep track of some of the possibilities for mathematics education of the Internet, especially of the World Wide Web (WWW). There seems to be several potential uses of the Internet in mathematics and mathematics education. These are still rather severely constrained in many cases by accessibility issues, although time has seen these diminish, a trend that will presumably continue. Opinions about the Internet appear to lie on a wide continuum from one extreme, reminiscent of a Brave New World A global classroom is now a desirable possibility; we should think of ourselves as residents of the global village and take advantage of the possibilities offered by email and the WWW Students are more likely to engage fruitfully with Internet-based materials than traditional media Education can and should be restructured to take advantage of online learning. This seems to be especially so in tertiary education. The penetration of the Internet into homes is happening so fast that home learning via the Internet TV is not far away and a serious alternative to formal schooling; already very many Australian students have better access to the Internet at home than at school.

88. Lesezeichen Für Siegfried Zseby Q23 What are some general references on fractals and chaos? modify their teaching according to suggestions from the research literature, http://userpage.fhw-berlin.de/~zseby/bookmark/bmdidakt.htm

Lesezeichen für Siegfried Zseby Ordner "Persönliche Symbolleiste" Resources for GDM 1 Gesellschaft für Didaktik der Mathematik - GDM Mathematical Museum and Exhibitions The Mathematical Museum is a very personally selected collection of links referring to - History informations - Digital Art and Galleries - Visualizations and Animations - Didactical Items - Scientific and Technical Expositions - Other Museums and Galleries. Frequently Asked Questions in Mathematics - Contents This is a compilation of Frequently Asked Questions (and their answers) about Mathematics. Topics range from trivia and the trivial to advanced subjects such as Wiles recent proof of Fermat's Last Theorem. Deutsche Mathematiker- Vereinigung (DMV) Dieser Server bietet Ihnen Informationen über die Deutsche Mathematiker-Vereinigung: - Was ist die DMV? / On the DMV (English) - Organisatorisches / Aktuelles / Tagungen / Publikationen der DMV / Personen und Adressen - Andere Server Karte von WWW-Servern mathematischer Fachbereiche und Fakultäten Wenn Sie auf die roten Rechtecke klicken, werden Sie mit dem jeweiligen Server verbunden. Fakultät für Mathematik der Universität Bielefeld Neben Uni-Infos: - Mathematische Gesellschaften, Journale, Server, Bibliotheken:

89. Connect-ME - Weblinks Our innovative approach to teaching mathematics enables students to quickly break down complex problems fractals are chaos and order, math and beauty. http://educ.queensu.ca/connectme/weblinks/strands.htm

Classroom Resources for Teachers Curriculum Strands Measurement Magic Squares - Math Forum http://mathforum.org/alejandre/magic.square.html Late Primary - Intermediate The Math Page - Skill In Arithmetic http://www.themathpage.com/ARITH/arithmetic.htm Multiplication: An Adventure in Number Sense http://naturalmath.com/mult/index.html This site illustrates patterns in multiplying 2 numbers up to 10 x 10. By using patterns and and 'twin facts' a 10 by 10 multiplication table is reduced to only 13 facts to be memorized. Numbers: Facts, Figures and Fiction http://richardphillips.org.uk/number/ Primary/Junior Numbers: Facts, Figures and Fiction Place Value http://www.sedl.org/scimath/compass/v03n02/place.html Primary The activities described in this lesson reinforce students' understanding of place value by using rhythm, physical action, and introspection. Simply Number Sense http://library.thinkquest.org/17888/opening.shtml

90. Mathematics And Teaching Project The Mathematics and Teaching Project was run by the Department of fractals and chaos (Helen L. Chick); Patterns and continuous change (John D. http://staff.edfac.unimelb.edu.au/~chick/homepage_files/MathsTeaching.html

Mathematics and Teaching Project PME29 Home Page Helen's Home Page DSME Home MATHS ED Research Interests List of Publications Teaching MATHS General Interests Research Interests List of Publications Maths Poem MISCELLANY The Mathematics and Teaching Project was run by the Department of Mathematics and the School of Education at the University of Tasmania during 1993, and was designed to provide professional development for teachers in mathematics. It comprised a number of courses offered at the Graduate Certificate level and catered for teachers across the whole curriculum range, from K to 12 and TAFE. All teachers participating were required to enrol in the Core Unit plus at least one Extension Unit. The core unit was designed to introduce teachers to a number of mathematical topics, presented in such a way as to be suitable for a general audience. The Extension Units - one for teachers of the K-4 curriculum, one for 5-8 teachers, one for 9-12 teachers and the fourth for TAFE teachers - were intended to extend the mathematical ideas in a way that was appropriate for the particular group of teachers involved and to put things in an educational context. The program was funded by a grant won from the Commonwealth Government's Department of Employment, Education and Training, and was presented by staff from the University's Mathematics and Education Departments as well as involving a number of well-qualified Consulting Teachers from around the state. The courses were very well received by teachers and the program won a Teaching Excellence Award from the University of Tasmania.

91. Teacher Resources All are arranged alphabetically by book title for teaching literature at the elementary level Information on fractals and chaos ..lots of higher level http://www.scsb.org/nhs/teacher_resources.htm

Resources for the Faculty of Northwood High School The Northwood High School Faculty Handbook (Only accessible to teacher accounts from Northwood HS) Defining the School’s Beliefs and Mission - Team 2 1/31/2003 Title Page Narrative Description Virginia's Standards of Quality for Public Education Virginia's Standards of Accreditation for Public Education Weblinks to Various Resources ENGLISH / LANGUAGE ARTS http://www.teachervision.com This site offers many links to lesson plans, curriculum materials, assessments, etc. for teachers. http://www.cbcbooks.org/pubs/thirteen.htm Check out these 13 ways to connect children to books. Most can be adapted to suit different age groups and are intended to introduce readers to the joys of literature. http://www.classroom.com/edsoasis/ Enter the Teachers’ Guild Library for language arts lesson plans and more! http://www.theteacherscorner.net/reading/activities/index.htm This site offers many successful teacher-created activities and lessons such as teaching point of view. http://www.homeworkheaven.com

92. Curriculum Vitae 19831987 - participation at research activities organized by the Central supporting information flow on fractal physics, chaos theory, synergetics, http://www.csc.matco.ro/CURRIFM.htm

Curriculum Vitae Surname: MUNTEANU Given name: Florin Date and place of birth : March 27, 1952, Brasov, Romania. Sex : male. Nationality : Romanian. Marital Status : married, 1 child (1976) Studies : 'Politehnica' University Bucharest, Faculty of Technology. Graduation date: June 1976. Professional activity: since 1998 - general manager of the AsTech Solutions ltd. since 1996 - president of the ‘ Center for Complexity Studies ’ - Bucharest 1998 - 2001 member in the advisory board of the Ministery for Research and Technology (ANSTI) 1990 - 2001 senior researcher in the Institute of Geodynamics of the Romanian Academy 1988-1990 - assisting professor, 'Politehnica' University Bucharest, Department of Materials Science and Welding Technology 1979-1988 - assistant, 'Politehnica' University Bucharest, Department of Materials Science and Welding Technology 1976-1979 - teacher, "Grivita Rosie" College Teaching activity: 1979-1985 - discipline of Materials Science; teaching and devising didactic material (Laboratory handbooks), modernization works for the laboratory didactic activity, mainly in the field of nonconventional technologies and nondistructive defectoscopy; 1985,1987 and 1989 - chair owner in 'Materials Technology', teaching at the Faculty of Technology, the Faculty of Electronics and the Faculty of Computer Science. The courses were improved using new notions from fields like fractal measurement methodology, notions of synergetics, stability of dynamic systems with self-regulation and self-organization, chaos theory;

93. Physics Course Descriptions, SIUE PHYS 494 (3) Methods of Teaching Physics in Secondary Schools — Current teaching normal modes; waves; numerical methods; percolation; fractals; chaos. http://www.siue.edu/PHYSICS/coursedesc.html

SIUE Home Page Physics Home Page Department of Physics 100- and 200-Level Courses ... SIUE Graduate Program Physics Course Descriptions Numbers in parentheses (...) indicated credit hours earned for the course or each semester of the course. Items in square brackets [...] after the course title indicate General Education requirements fulfilled by the course 100- and 200-Level Courses PHYS 111 (3) Concepts of Physics Prerequisite: Satisfaction of high school math requirements for entering freshmen. PHYS 112 (1) Conceptual Physics Laboratory Prerequisite: Concurrent enrollment in PHYS 111. PHYS 206a,b (5,5) College Physics Prerequisites: (a) MATH 125. (b) PHYS 206a. PHYS 211a,b (4,4) University Physics Prerequisites: (a) MATH 152 or concurrent enrollment, concurrent enrollment in PHYS 212a. (b) PHYS 211a, concurrent enrollment in PHYS 212b. PHYS 212a,b (1,1) University Physics Laboratory Prerequisites: (a) Concurrent enrollment in PHYS 211a. (b) PHYS 212a, concurrent enrollment in PHYS 211b. 300-Level Courses PHYS 301 (3) Waves Applications to light and sound.

94. Internet Science Links, Science Web Sites From The Teaching Tank Math, chaos, fractals, Etc. Helping Kids with Math and Reading Math and Reading Help Creative Teaching Associates - Teaching Tools For Home and School http://www.tchg.com/tt/scilinks.htm

Welcome to Science Education Web Site New! 150 hands-on Science Lessons using Readily Available Materials! The Teaching Tank - Making Hands-on Science A Reality! I have checked these links many times, but the internet is changing rapidly. If you find one of these links isn't working, or if you would like to include new links, please send an e-mail to dburgess@rivier.edu . Thank you. I have also begun a list of sites that aren't about science or math, but may be interesting to Home School families Astronomy Biology Chemistry ... Paleontology Astronomy, Space, Solar System, Etc. The Solar System in Pictures - Astronomy webquests and pictures of all the planets in the solar system. The pages load fast and there are great learning quizzes. Amazing Space - A set of web-based activities primarily designed for classroom use, but made available for all to enjoy. California Space and Science Center - Lesson plans and other resources for teachers. Windows to the Universe - Graphics intensive web site about space science. Thursday's Classroom from NASA - Connection between NASA's latest research and the classroom.

95. NETS For Students Teaching and learning with technology Video and Facilitator s Guide. fractals for the classroom Introduction to fractals and chaos. http://www.cnets.iste.org/students/s_rbooks.html

NETS Main NETS for Students Essential Conditions Standards for Students ... Digital Edge Project Books, Videos, CD-ROMs, and Audiotapes The following resource books, videos, CD-ROMs, and audiotapes from the NETS partners and curriculum organizations are organized by curriculum area technology or software , and technology implementation (ie., planning, evaluating, funding, etc.). Curriculum GENERAL Association for Supervision and Curriculum Development. (1995). How technology is transforming teaching [Special issue]. Educational Leadership, 53 (2). Association for Supervision and Curriculum Development. (1996). Teaching and learning with technology [Video and Facilitator's Guide]. Alexandria, VA: Author. Association for Supervision and Curriculum Development. (1997). Integrating technology into teaching [Special issue]. Educational Leadership, 55 (3). Association for Supervision and Curriculum Development. (1998). Integrating technology into the curriculum [Special issue]. Educational Leadership, 56 (5). Bernhadt, V. (1998).

96. 1996 Course Descriptions chaos, fractals, and Dynamics Computer Experiments in Mathematics Teaching Science and Mathematics in a Distributed Multimedia Learning Environment http://www.chautauqua.pitt.edu/course.html

WARNING! This is 1996 data. The Apply: Center Links are no longer active. Course: 1 Changing Science Courses to Promote Critical Thinking CRAIG E. NELSON, Department of Biology, Indiana University Mar. 20-22, 1996 in Dayton, OH Apply: DAY Participants should bring with them lecture notes and other teaching materials for some course segments where critical thinking seems especially desirable. Those who wish to examine the framework within which we will work should peruse Perry's Forms of Intellectual and Ethical Development in the College Years and Women's Ways of Knowing by Belenky et. al. A summary of Dr. Nelson's approach is given in Chapter 2 of Enhancing Critical Thinking in the Sciences by Crowe (1989). (Participants in Dr. Nelson's Chautauqua on Creation/Evolution should consider this course an expansion of the opening segment of that workshop in deciding whether to apply for this one.) For college teachers of: all disciplines. Prerequisites: none. Dr. Nelson teaches Biology at Indiana University. He has offered Critical Thinking workshops at the Center for the Study of Higher Education; at meetings of the National Collegiate Honors Council; at the National Institutes on Issues in Teaching and Learning; at the Lilly Conference on College Teaching; and at faculty development institutes in twenty states. Critical Thinking has also been a central component in the other Chautauqua short course he has offered in recent years. Course: 2 THIS COURSE IS NOW CLOSED

97. HRUMC IX - More Information Title chaos Games and Fractal Images In 1994 he received the Award for Distinguished University Teaching from the Northeastern section of the http://www.skidmore.edu/academics/mcs/hrumc9in.htm

98. Special Topics who has used these activities in teaching calculus 10 and differential equations. Fractal Frequently Asked Questions and Answers (Ohio State) http://dimacs.rutgers.edu/Volumes/schools/paper82/node21.html

Next: Acknowledgments Up: World Wide Web Sites Previous: General Resources Special Topics Our next set of recommendations is for Web sites which have proven valuable sources for enrichment material for students or teachers on specific topics, or for classroom activities. MegaMath (Los Alamos National Laboratory) http://www.c3.lanl.gov/mega-math/ The MegaMath site brings important mathematical ideas to elementary school classrooms with unique activities. The site was developed by Nancy Casey and Michael Fellows [ ]. It includes many discrete math activities including the following: The Most Colorful Math of All (map and graph coloring); Games on Graphs Untangling the Mathematics of Knots Algorithms and Ice Cream for All (an interesting problem on graphs); and A Usual Day at Unusual School (logic and paradoxes). This site offers teachers the opportunity to bring discrete mathematics into their classroom with engaging stories. MacTutor for Math History Information http://www-groups.dcs.st-and.ac.uk:80/ history/ Mathematical_MacTutor.html

99. George Ashline, Mathematics, Saint Michael's College Math Archives offers online teaching materials and links, with such focal areas Here are so me interesting sites on fractal geo me try and chaos theory http://academics.smcvt.edu/gashline/

George Ashline Depart me nt of Mathematics Saint Michael's College Colchester Vermont USA You can find below so me information about my current classes other classes I have taught advising information my papers , and ways to reach me . I have also compiled links in a number of areas in which I am interested, including fractal geometry and chaos theory mathematics education the history of mathematics finite mathematics , and St. Michael's College Material for my Fall 2005 classes Ele me ntary Statistics , MA 102. Section C me ets T and Th from to 9:45 AM in Jeanmarie Previous syllabus Homepage of Moore rd edition Information about Minitab Guidebooks to the TI-36X TI-82 TI-83 TI 83-Plus ... HP-48gII An extended t-table Data Surfing on the WWW created and maintained by Robin Lock of St. Lawrence University. Sports Data Page , created by Robin Lock Data and Story Library DASL Quantitative Environ me ntal Learning Projects QELP datasets Datasets and data sources from CAUSEweb Data sets for data mining by KD Nuggets US Census Bureau National Weather Service for Burlington VT Correlation Guessing Game , part of the CUWU Statistical Program at Illinois-Champaign-Urbana.

100. Sorinel Adrian Oprisan, Books, Theoretical Physics, Computational In addition, various other activities may be done in the class to facilitate student learning. Each student is expected to be an active participant in the http://www.cns.uno.edu/~soprisan/Teaching/1031_spring_05.html

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