21. Key Curriculum Press | Supplementals/Workbooks Calculus Explorations. chaos A Tool Kit of Dynamics activities. Data Matters. FiftyFathoms. fractals A Tool Kit of Dynamics activities. Probability activities. http://www.keypress.com/catalog/products/supplementals/

Home Customer Service Ordering Information Contact Us ... Site Map Resource Centers The Geometer's Sketchpad Fathom Dynamic Statistics Discovering Algebra Discovering Geometry ... IMP Professional Development General Information One-Day Workshops Three-Day Workshops Summer Institutes ... Custom Workshops General Information Ordering Information Customer Service Contact Us Meet Our Authors ... Press Room Other Key Sites Key College Publishing KCP Technologies Keymath.com Supplemental Math Materials Key's supplemental materials support your core curriculum with motivating activities that explore connections among mathematical ideas as well as connections to history, art, science, and other disciplines. These products represent the best ideas from innovative teachers who like to offer students a wide variety of learning experiences. BOOKS 50 Mathematical Puzzles and Problems Advanced Euclidean Geometry Agnesi to Zeno The Ambitious Horse ... Geometric Graphics Coming Jan. '03! Geometry in Action Coming Jan. '03! Graphic Algebra A Graphing Matter Inversions Is Democracy Fair? ... Writing Math Research Papers BOOKS + Books with Software, Manipulatives, Posters

22. 0.3 Links To The Chaos Hypertextbook Ideas and activities, sitesforteachers.com; Ideas and activities, Vicki F. RichardM. Sharp Works Cited, Michael McGoodwin; World of chaos fractals, Larry D http://hypertextbook.com/chaos/links.shtml

Prefaces The Chaos Hypertextbook Fair Use Encouraged prev index next 515 Chaos , BUBL LINK, Strathclyde University Abilene Christian University Library Reference About The Chaos Hypertextbook , A Learning in Motion Top Ten Selection About "The Chaos Hypertextbook" , The Math Forum at Drexel University About the School: Maths Resources - Links , University of Birmingham ACU Library Reference , Abilene Christian University Amara's Science Links , Amara Graps Amatuer [sic] Mathematics Analisi Numerica Applied Dynamical Systems , Allan P. Fordy, University of Leeds Astrophysics , Todd BCPL Physics Center , Bensenville [Illinois] Community Public Library Biotechnology Information Directory - Information Sources , Cato Research Bob's Fractal Links , by Bob I assume Bookmarks for Gustav Nelhans Bookmarks for Jamie Cromartie , Richard Stockton College Bookmarks for James Kay , University of Waterloo Bookmarks for Pekka Orponen Bookmarks for Peter Yoachim , University of Washington BorderLink Project: Academic Success Resources Bridge Program for Math and Science: Fractals and Chaos , University of the South Busse Library - Virtual Mathematics , Mount Mercy College Cardinal Cushing Library Mathematics , Emmanuel College Chaos , Glossary of Terms Used in Time Series Analysis of Cardiovascular Data, Centro di Bioingegneria Chaos in Power Electronics , Switching-Mode Power Supply Design Chaos-links , Chaosforum

23. Ideas And Activities Ideas and activities Bamdad's Math Comics Page. Bamdad's Math Comics Page, frequently updated with new comics, features a collection of over 200 cartoons scanned from newspapers and magazines for grades 512. Ideas and activities. About.com's Homework 40 mathematics Web based activities and projects for K-12 Elert's chaos Hypertextbook is an online illustrated primer on fractals and choas http://www.csun.edu/~vceed009/activities.html

Ideas and Activities 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.

24. Chaos And Fractal Geometry Tutorials And/or Resources For Teaching Chaos. They H fractals and chaos An Illustrated Course Paul S. Addison. fractals for the Classroom Strategic activities Vol 1 - Heinz-Otto Peitgen, Hartmut http://metastore.metaculture.net/science/fractal/learning/default.asp

Learning Fractal Geometry "History does not long entrust the care of freedom to the weak or the timid." -Dwight D. Eisenhower Book Search at bottom of page. Submit books in bottom-level categories. metastore Home Up One Level Home metasearch ... 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 Visit ScanStore.com Paperless Office Systems from Meta Enterprises These resources are instructional in nature versus research-oriented material. It is divided into categories by age group the particular item targets. There is material in here that an 8-10 year old can easily grasp, and don't believe they can't. Links to Learning Fractal Geometry (20) Related Categories Fractals for Children (2 Items) Fractal tutorials and resources for beginners and grade school children. Fractals for Young Adults (10 Items) Fractal tutorials and resources for high school students and those with intermediate math skills. College Chaos (30 Items) Fractal tutorials and resources for college students and those proficient in math.

25. BSU 96-98 Graduate Math Course Descriptions Presents and analyzes mathematical activities, models, games, and related backgroundmaterial that can be used 540 INTRODUCTION TO fractals chaos (4 credits http://www.bemidjistate.edu/BSUCatalog/GRADCATALOG/MATH/Courses.html

BSU Catalog Home Undergraduate Math Program All-University Courses and Descriptions Mathematics Graduate Course Offerings (MATH) College-Program Codes: 17-10 Unless otherwise specified, the prerequisite for the graduate courses in mathematics is an undergraduate major in mathematics or MATH 520 or equivalent. 500 MATH MODELS, GAMES, AND ACTIVITIES FOR THE PRIMARY GRADES (2 credits). For teachers of grades K-3. Mathematical background including teaching-aids, games, projects and activities that relate to the primary level will be presented. The basic mathematical operations will be presented from a "concrete" standpoint. 501 MATH MODELS, GAMES, AND ACTIVITIES FOR THE INTERMEDIATE GRADES (2 credits). For teachers for grades 3-6. Mathematical background including teaching-aids, games, projects, and activities that relate to the intermediate level will be presented. The basic mathematical operations will be presented from a "concrete" standpoint. 502 MATH MODELS, GAMES, AND ACTIVITIES FOR ELEMENTARY CLASSROOMS (4 credits). An intensive introduction to activities, models, projects, and ideas needed to effectively teach using contemporary text materials. Materials usable at every ability level will be included. Prerequisite: Teaching experience or consent of instructor.

26. BSU Updated 2002-04 Graduate Mathematics Course Descriptions FOR THE SECONDARY CLASSROOM (3 credits) Presents and analyzes mathematical activities,models, games, and 5440 INTRODUCTION TO fractals AND chaos (3 credits http://www.bemidjistate.edu/Catalog/0204upcatalog/GradCatalog/Math/courses.html

BSU Catalog Home Graduate Mathematics Program All-University Courses and Descriptions Graduate Course Offerings Mathematics (MATH) College-Program Codes: 7-10 NOTE: Please see your advisor regarding course sequencing and any expected preparation. 5010 MATHEMATICS FOR PRE-K TO GRADE 3 (3 credits) Students gain understanding of appropriate mathematics and pedagogy for young children from pre-K through the primary grades. 5050 MATH MODELS, GAMES, AND ACTIVITIES FOR THE PRIMARY GRADES (2 credits) For teachers of grades K-3. Mathematical background including teaching-aids, games, projects, and activities that relate to the primary level will be presented. The basic mathematical operations will be presented from a "concrete" standpoint. Set theory, numeration, and the systems of whole numbers and rational numbers will be considered. Prerequisite: Teaching experience or consent of instructor. 5051 MATH MODELS, GAMES, AND ACTIVITIES FOR THE INTERMEDIATE GRADES (2 credits) For teachers of grades 3-6. Mathematical background including teaching-aids, games, projects, and activities that relate to the intermediate level will be presented. The basic mathematical operations will be presented from a "concrete" standpoint. The systems of integers, rational numbers, and real numbers; ratio and proportion; percentiles; and elementary functions will be considered. Prerequisite: Teaching experience or consent of instructor. 5052 MATH MODELS, GAMES, AND ACTIVITIES FOR THE ELEMENTARY CLASSROOM

27. Powell's Books - Used, New, And Out Of Print Creative activities in both the arts and the sciences depend upon an ability to modelthe fractals The Patterns of chaos A New Aesthetic of Art, Science http://www.powells.com/subsection/MathematicsPopularChaosandFractals.html

Technical Books Kids' Books eBooks more search options ... Materials Science Mathematics Mechanical Engineering Media Metal Metaphysics ... view all sections... Popular Chaos and Fractals There are 176 books in this aisle. Browse the aisle by Title by Author by Price See recently arrived used books in this aisle. Featured Titles in Mathematics -Popular Chaos and Fractals: Page 1 of 6 next Used Trade Paper Chaos: Making a New Science by James Gleick Publisher Comments read more about this title check for other copies New Hardcover Chaos and Fractals: New Frontiers of Science by Heinz Otto Peitgen Publisher Comments The definitive book on chaos and fractals, covering the central ideas and concepts of chaos and fractal theory, and including spectacular illustrations. Rigorous mathematics are also included for those desiring more detailed explanations. Named the Most... read more about this title check for other copies Used Trade Paper Does God Play Dice?: The Mathematics of Chaos

28. WWNFF Teacher Outreach dynamical systems, data analysis, fractals, and chaos. and Escher art, geometricdesigns, fractals, soap bubble The activities focus on the integration of http://www.woodrow.org/teachers/outreach/math.html

2000 TORCH Workshop Descriptions Math Algebra Contact David Heckman for more information You are invited to experience with us an introduction to Algebra for the 21st century. Transportation will be provided by manipulatives, graphing calculators, computer algebra systems, and spreadsheets. Pedagogical strategies modeled include cooperative learning, writing across the curriculum, inquiry- and discovery-based learning and real-world modeling. Technology demonstrations include applications of graphing calculators and calculator based laboratories. Computer algebra systems and graphing spreadsheets will augment this excursion. Hand-held Technology: TI-80,-81,82,-83,-92 and CBL Computer Needs: Change Contact Allen E. Martin

29. ThinkQuest Internet Challenge Library : Fractals Through lessons, a Fractal Explorer, and interactive activities, our goal is to makemath interesting to even the most nonmath-inclined fractals and chaos http://www.thinkquest.org/library/cat_show.html?cat_id=162&cid=1

30. Karen L. Shuman Teaching Interests In finite mathematics, I used pairs activities in which partners could practice new learningworkshops, one on graph theory and one on fractals and chaos. http://www.math.uiuc.edu/~kshuman/teachingindex.html

Teaching Interests Classes VIGRE Research Assistant Professor, UIUC, 2000-2002 After teaching three classes at UIUC using a traditional lecture format (Math 384 and Math 361), I decided to experiment with including active learning activities in my classes every day. To see recent examples of active learning exercises I have created and used in my classes at UIUC, see the following links: Statistics and probability Proof-writing and problem-solving (under the green headings) A typical day in a class such as Math 247 or Math 308 consisted of a short lecture and a long activity or a longer lecture and a short activity. In Math 285, my students used the Calculus and Mathematica courseware, and students spent almost every day interacting with mathematics problems on the computer. My class sizes at UIUC ranged from 8 to 52, and many of my students were engineers or mathematics majors, except in Math 308, where all the students were future actuaries. Mathematics 247 , Honors SectionFundamental Mathematics. Math 247 is a bridge course to rigorous mathematical thought focusing on problem-solving and proof-writing. Mathematics 285 Differential Equations with Calculus and Mathematica . Go to Syllabi, then Math 285 for a syllabus for this course. The course web page is password-protected.

31. NETS For Students for the classroom Introduction to fractals and chaos. fractals for the classroomComplex systems and Spreadsheet activities in middle school mathematics (2nd http://cnets.iste.org/students/s_rbooks.html

NETS Main NETS for Students Essential Conditions Standards for Students ... Distinguished Achievement Award 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).

32. JC's Link Page classroom that will help them teach their students to follow when using the activitiesand discussions fractals, chaos Includes a link to a good introduction http://jwilson.coe.uga.edu/emt668/emt668.folders.f97/weber/links.html

Local UGA library Email - The email server for UGA College of Education. Mathematics Education UGA College of Education UGA Department of Mathematics Education Jim Wilson's Homepage Math Forum A great set of resources for mathematics education. JRME J ournal of R easearch in M athematics E ducation, a publication of NCTM. Begle's Homepage NCTM's N ational C ouncil of T eachers of M athematics. Origami Teaching mathematical thinking through origami. Knowledge Mathematics Network Geometry, Measurement and Trigonometry resources. Angie's Geometry Page Angie invented this page in order to help teachers plan different activities in the classroom that will help them teach their students about geometry in a fun manner. Golden Ratio The purpose of this web page is to provide an introduction to the Golden Ratio and Fibonacci Sequence. The idea is to have the student work through several activities to discover the applications of the Golden Ratio and Fibonacci Sequence. Cut-the-Knot A resource that would help to learn, if not math itself, then, at least, ways to appreciate its beauty. Investigating Patterns A resource of various number patterns, curves and topology.

33. ENC ENC Focus Magazine Mathematics And Science In The Real in group discussion and activities, discussion questions for the viewer, and suggestedclassroom activities for students. fractals and chaos theory are http://www.enc.org/focus/realworld/resources_v7n3/pd/1,4893,1949,00.shtm

34. ENC: Curriculum Resources: The Future Of Mathematics (ENC-014210, Brief Record) in group discussion and activities, questions for the viewer to discuss, and suggestedclassroom activities for students. fractals and chaos theory are http://www.enc.org/resources/records/0,1240,014210,00.shtm

Skip Navigation You Are Here ENC Home Curriculum Resources Advanced Search ... Ask ENC Explore online lesson plans, student activities, and teacher learning tools. Search Browse 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. ENC#: ENC-014210 Series: Publisher: Date: Ordering Information Grades: Kindergarten 1 2 3 4 5 6 7 8 Abstract: Record Created: Last Modified: ENC does NOT distribute this resource. Vendor Information: Annenberg/CPB PO Box 2345 South Burlington VT 05407 acpb@ordering.com Fax: (802) 846-1850 http://www.learner.org/ Description Cost ISBN Order # 1 videotape Note: 1 complete series (8 tapes/guide) Note: Professional development; Videotape. Supporting Materials: ENC-014174 Subjects: Applied mathematics. Chaos. Computer uses in education. Discrete mathematics. Fractals. Instructional issues. Mathematical modeling. Mathematics. Modeling. Patterns. Professional development. Real world applications. Recursion. Reform Contributor(s): Alain Jehlen; Carol Jackson;

35. Larry S. Liebovitch science together; based on the new textbook fractals and chaos Simplified for byInternet online materials including lecture notes, activities, and online http://www.ccs.fau.edu/~liebovitch/larry.html

Larry S. Liebovitch Florida Atlantic University Center for Complex Systems and Brain Sciences 777 Glades Road Boca Raton, FL 33431 USA [Here is another picture wearing a tie with Astronomers and Historians of Science at Harvard.] Professor Center for Complex Systems and Brain Sciences Center for Molecular Biology and Biotechnology Department of Psychology Department of Biomedical Science Telephone: (561) 297-2239 FAX: (561) 297-2223 E-mail: LIEBOVITCH@CLIFFORD.CCS.FAU.EDU How to get here: Map B.S. Physics, City College of New York, 1972 Ph.D. Astronomy, Harvard University, 1978 Curriculum Vitae (Resume) Research Biophysics of ion channels. Fractal and nonlinear analysis of molecular, cellular, physiological, and psychological systems. Teaching New Mathematics Curricula Materials for undergraduate students who never liked and never did well in math. Not Your Usual Liberal Arts Mathematics Course. "The Mathematics and Science of Fractals." Electronic curricula materials that use different teaching and learning styles. Supported by grants from the National Science Foundation (DUE-9752226 and DUE-9980715), available on a CD-ROM.

36. Blank based on the new textbook fractals and chaos Simplified for the Life enhanced by Internetonline materials including lecture notes, activities, and online http://www.ccs.fau.edu/~liebovitch/mat1932-1.html

Mathematics of Fractals and Chaos for Pre-College Teachers and Psychology Majors FALL 1999 [click here for link to last year's lecture notes] IN BOCA RATON AND BY LIVE VIDEO BROADCAST TO NORTHERN PALM BEACH (JOHN D. MACARTHUR) Course: MAT 1932 Sequence Number Fall 1999: 4374 Boca Raton Campus, 7362 MacArthur Campus Credits: 3 Time: MWF 10:00-10:50 Room: Boca Raton: Instructional Services Building, Studio 4, MacArthur MLC 270 Enrollment: Boca Raton 35, MacArthur 20 Instructor: LIEBOVITCH This course can be used towards satisfying: the mathematics requirement for teacher certification. the mathematics cognate requirement for the B.A. in psychology. Description: This course will use the mathematics of fractals to help understand concepts in physics, chemistry and biology. It will use different approaches to learning, including: lectures, in-class exercises, web electronic materials, discovery computer exercises, and videotapes. The idea of the course is to teach concepts of mathematics, what math really is, and to illustrate those concepts with real scientific applications. It is intended primarily to expand the math-science knowledge of students training to be pre-college teachers or psychologists. This is a new, innovative and highly unusual course: designed for students training to be elementary, middle, or high school teachers

37. Math Interactive Workshops -- Workshop #8 Finally, we will touch on the connection between fractals and chaos, and see is theuse of a variety of media paper and pencil activities, concrete models http://www.learner.org/channel/workshops/math/work_8.html

Workshop #8 The Future of Mathematics: Ferns and Galaxies Content Guide - Andee Rubin Supplies Needed for Workshop #8: 1 die, 1 ruler per pair of participants, worksheets 1-4 pencils, paper, scissors, rulers, calculators, tape, a variety of colored markers About the Workshop What is the theme of the workshop? The advent of new technologies in the mathematics classroom is rapidly changing how, what, and when we teach. Not only do higher-level mathematics become accessible to students at a younger age, but new and fascinating worlds of mathematics can open up to them - in their own classrooms - thanks to the power of computers. We will examine two new mathematical tools, recursion and iteration, and introduce a new geometry, Fractal Geometry, which complements the much older and more familiar Euclidean Geometry. Whom do we see? What happens in the videoclips? We will see many amazing and beautiful things in this workshop. First we will see three different approaches to the creation of a famous fractal, the Sierpinski Triangle. Second, we will see multiple representations of fractals: fractals on paper, on a computer monitor, in nature, and built with manipulatives. Finally, we will touch on the connection between fractals and chaos, and see how beautifully patterned shapes can result from "chaotic" systems. What issues does this workshop address?

38. George Ashline, Mathematics, Saint Michael's College with nonlinear dynamics and chaos and discusses The journal fractals publishes peer-reviewedwork in and learning. Lesson plans and activities in mathematics http://academics.smcvt.edu/gashline/

George Ashline Department of Mathematics Saint Michael's College Colchester, Vermont USA 05439 You can find below some information about my current classes other classes I have taught 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 Spring 2003 classes Finite Mathematics MA 101. The syllabus Amortization calculator from Yahoo! Real Estate Matrix multiplication applet from RPI's Project Links Elementary Statistics, MA 102. The syllabus (soon to appear) Link to Correlation Guessing Game , part of the CUWU Statistical Program at Illinois-Champaign-Urbana. Link to Data Surfing on the WWW , created and maintained by Robin Lock of St. Lawrence University. Calculus II MA 111 The syllabus The current Maple info sheet Copies of previous and current Maple labs: The first Maple lab The second Maple lab The third Maple lab The fourth Maple lab The fifth Maple lab Material for other classes that I teach.

39. BSU 96-98 Undergrad Math Course Descriptions Presents and analyzes mathematical activities, games, models, and related backgroundmaterial that can be used 340 INTRODUCTION TO fractals chaos (4 credits http://www.bemidji.msus.edu/bsucatalog/MATH/Courses.html

BSU Catalog Home Math Program All-University Courses and Descriptions Mathematics Course Descriptions (MATH) College-Program: 17-10 Check with department for quarter when quarter courses are offered. Read each course description for prerequisites. 080 INTERMEDIATE ALGEBRA (4 credits). An algebra course designed for students with an insufficient algebraic background for MATH 112 . This course must be taken for a letter grade and, to use this course as prerequisite for MATH 112 , a grade of C or better must be achieved. Credits are not applicable towards graduation. 106 MATHEMATICS FOR ELEMENTARY TEACHERS I (4 credits). The first of three courses providing the background for teaching contemporary mathematics in the elementary school. The use of mathematics manipulatives for modeling the basic operations will be emphasized. Set theory; numeration; and the systems of whole numbers, integers and rational numbers will be considered. Prerequisite: Elementary education major or consent of instructor. 107 MATHEMATICS FOR ELEMENTARY TEACHERS II (4 credits). One of three courses providing the background for teaching contemporary mathematics in the elementary school. The use of mathematics manipulatives for modeling the basic operations for the rational and real number systems will be emphasized. Ratio and proportion, percentiles, elementary functions and solutions of linear equations will be considered. Prerequisite:

40. Math 8 - Frisbie Middle School is using the Glencoe instructional materials to teach mathematics Graphing and Functions,Linear and Exponential Functions, fractals and chaos Theory, Applied http://www.rialto.k12.ca.us/frisbie/math8.html

Math 8 As part of the Rialto Unified School District, Frisbie Middle School is using the Glencoe instructional materials to teach mathematics. Math 8 is a general mathematics course for eighth grade students not enrolled in Algebra I. Under the Curriculum Links the alignment of the course can be checked against the RUSD Math Matrix, California Framework Standards, and the NCTM Standards. Links are provided to support the Math 8 curriculum for students, teachers and parents. Some of the links are to Internet sites with information, others link to sites with interactive lessons which could be used at home as a supplement or during class and still others could be used as enrichment for students willing to work before or after school. A similar Math 7 page is available for the general mathematics course for all seventh grade students. As you use these pages, comments and/or suggestions would be appreciated. Please send them to Suzanne Alejandre Curriculum Links: Math Matrix - RUSD RUSD Course of Study CA Academic Standards Commission California Mathematics Framework Strands Unifying Ideas for the Middle Grades NCTM Standards Reference Links: Dr. Math FAQ - The Math Forum

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