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COURSE ORIENTATION

This is a distance learning course, concentrating on uses of the Internet for teaching, learning and professional development. It also is intended to give you enough web sites and leads-in to more web sites to be a continuously useful resource for your learning and doing.

This is a PASS/FAIL course. Therefore, SELECT and BASE YOUR WORK on those areas that best match your current interests. You can return any time to areas that match future concerns and changing interests--one of the many advantages of on-line learning

Assessment is based on work you produce in series of essays/listings for each Essential Question or topic you "connect with," and with an annotated lists of sites supporting your views and reflecting your web work. Note the Rubric for Course Portfolio Assessment.

For instance, you might write “The site XXXX [http://www.xxx.com] gave me a different perspective on how to help students learn _____. It also cleared up for me something I was confused about, and that is what educators mean by __________.” Certainly you would want to elaborate more.

This work may be emailed to me at ozpk100@aol.com, or snail-mailed to me at Chad C. Osborne 923 W. Mission St., Santa Barbara, CA 93101. If you email the work, you may wish to put it in a Zip file, which compresses text and makes it easier to send over the 'Net.


TEACHING & LEARNING MATH MORE EFFECTIVELY

An Online Course, Producing a Project of Ideas and Resources with Discussion Board Interaction

May be taken twice for 8 credits total.

Note our other Teacher Development Network Courses and Workshops!

Because of the extensive number of links, the most important are signified with a *1* sign. These also cover the widest array of Certification Standards. Be sure your course work reflects your having learned from these sites.

*1* Either develop and answer an essential question for each section of the course, or use and re-use the following "ESSENTIAL MEGA-QUESTION": IN WHAT WAYS MIGHT YOU USE (selected) TEACHING STRATEGIES TO TEACH THE SUBJECT MATTER (selected) FROM THE RESOURCES BELOW? [A "rubric" for this question: Use Individual Brainstorming to list at least five items, each indicating both content and strategy. Try to "think outside the box" in your ideas, and then * star what you regard as the best idea(s) for each section.]

Be sure to read the COURSE POLICY

ESSENTIAL QUESTION 1: Based on the following sites, in what ways might you make the most out of reform?

Standards

Teachers in this decade must keep an eye toward standards and discuss with each other how best to prepare students to take standardized tests, particularly the high stakes tests being required for high school graduation in many states. You need to have your own copy of standards for the state where you teach, available from the Department of Education in your state. Five sources of current standards and frameworks are
  1. *1* Massachusetts Frameworks,
  2. *1* SELECTED PRINCIPLES from the Massachusetts MATH FRAMEWORKS
  3. California Mathematics Standards {most textbooks are based on these}, and
  4. The National Council of Teachers of Mathematics Standards.
  5. National and State by State Standards are also on the Web.
  6. *1*Is Your School Ready for Standards-Based Reform? -- Anne Wheelock's "rubric" to help balance "outcomes" based reform with meaningful contexts from "best practices"
  7. Preparing Your High School Students to Take Standardized Tests
  8. *1*Test Content and Tips for Preparing Your Students for Standardized Math Tests

Begin with this third document, and first read Chapters 1 and 2--the Vision and the Six Principles. Then survey the Standards for the grade level(s) you will be teaching.

Compare and contrast these with the Massachusetts and California Frameworks and Standards. See if you can detect results of the "culture wars" going on between teachers who want to teach for UNDERSTANDING and the conservative political agenda of teaching for rote memorization. Write about your impressions from these standards in Part 1 of your Project Notebook.

**While there are many questionable aspects of the Ed. Reform, there are two positive yet difficult directions for school-wide, positive, productive reform: 1) Small Schools By Choice, meaning breaking big schools down into "houses" or "clusters" of 70-120 students each. This helps students and teachers to know each other better--and results in higher attendance, achievement, and less violence. Smaller school units also make it easier to bring about 2) *1* Parent and Family Engagement as a Reform Strategy. Give consideration to both of these dimensions of reform in this section.

Also realize how central the issue of *1* DEPTH vs. COVERAGE becomes in light of the extent of standards and the climate of high-stakes testing. Take particular note of the counter-intuitive idea in the DEPTH vs. COVERAGE link that wide coverage does NOT produce higher scores. Write about this idea in Part 1 of your Project Notebook, as well.

Advanced Challenge: Based on links from any single or combination of sections of course work, develop a WEB QUEST you can use with your classes. My web page, *1* QUESTING the WEB: Web Quests as Essential Questions, gives further examples of this format.

Since a Web Quest is a series of linked web pages, you may want to begin with HOW TO CREATE WEB PAGES. Also take note of the *1* Examples of Student-Produced Web Quests, and especially, *1* Think Quest projects for your subject area!

  • *1* Project Based Learning: What Works -- Check out Math Projects on this page!

    ESSENTIAL QUESTION 2: Teaching the HEART of Math

    The HEART of math refers to the humanistic side of teaching, of being an "ambassador" for math--realizing it is a foreign country to many students. More effective math teaching addresses aspects of math anxiety and uses collaborative small group learning in order to engage students. But first, consider the question, what is the HEART?

    1. What IS the HEART? Most of us have "learned" it is basically a pump, a kind of organic machine. Neurocardiology, a recent medical specialty, is developing a far different picture of the human heart. The current scientific view is aligning more with poets, with conventional and "metaphorical" sense of the word, and with Howard Gardner's multiple intelligences of intrapersonal and interpersonal intelligence.

    2. What is Heart Intelligence?, Heart Intelligence , and HeartMath are three fascinating sites showing educational work being done based on "heart intelligence."

      What implications do you see for learning in general and your teaching in particular? Reflect on your thoughts in Part 2 of your Project.

    Consider the links about *1* Coping With Math Anxiety, and ideas on the place of *1* Collaborative Groups in the Math Classroom from the same source. Part 2 of your Project Notebook should have a list of ideas from these sites with a 2-5 line annotation for each idea and a collection of web page reprints you choose to support them.

    ESSENTIAL QUESTION 3: Based on links in this section, in what ways might I help students btter understand and master Part/Whole and Probability Relationships?

    Nearly all students can do decimal/fractions when counting money or making change. The relation of parts (Quarters) to wholes (Dollars) is a lot more concrete to them, and a field where their past experience helps. But fewer than 25% of students can consistently do Percents, Decimals and Fractions well.

    THE CORE of MATH--PART/WHOLE RELATIONS has over 40 valuable links centered on this core math area. It can be a KEY resource for you in teaching, a site you may want to put on your own web page for students and their families, and one you may want to use to brush up on this critical area of math.

    Understanding systems, being able to analyze situations, as well as more specific functions as doing taxes and shopping for bargains, are all based in this type of thinking. It really separates adults from children when it comes to both math and life! Give it the priority it is due!

    *1* PROBABILITY is the area where MCAS Tests shows students needing the most help. This page has sites for both Middle and High School!

    ESSENTIAL QUESTION 4: Based on the following array of sites with ideas from numerous Math teaching links, what appeals to you most to bring Math to life for students and utilize tecnology intelligenlt?

    1. Resources for Middle School Mathematics
    2. Math Sites
    3. *1* The EISENHOWER NATIONAL CLEARING HOUSE FOR MATH AND SCIENCE TEACHERS,
    4. *1* The Math Forum,
    5. *1*Math Library
    6. High School Hub:Math,
    7. Big Chalk's PreK-ELEMENTARY MATH Note the Algebra links!
    8. *1* Big Chalk's MIDDLE SCHOOL MATH Links,
    9. *1* Big Chalk's HIGH SCHOOL MATH Links, and
    10. BLUE WEB'N Mathematics
    11. *1* Thinkquest Math Projects - A+ Resources!
    12. *1* Teachers@Work Over 200 Math teaching sites, rated and annotated!

      The above sites are the source for your work in Part three of your Project Notebook. *1* Make this a considerable part of your work to find

      1. Ideas for making Math more concrete and practical (see Site 2 above) and
      2. *1* a self-assessment of your STRENGTHS and UNDERDEVELOPED AREAS in your knowledge of Math from sites 1 and 3 above.
      *1* Chart these in Part 3 of your Project Notebook, and collect web reprints that you think will be useful for you.

      *1* Also, compose an imaginary Journal entry for a student who has tried an activity you select. Have them write about a project idea they might like to propose, based on the activity.

    13. *1* **Rubrics! Great site to help you evaluate students most fairly and to help them learn to self-evaluate in all areas of Math!
    14. *1* **Types of Assessment
    15. *1* **Assessment Resources
    16. *1* **Assessment in Mathematics Teaching
    17. *1* **ASSESSMENT IN MATH TEACHING
    18. *1* **AUTHENTIC ASSESSMENT IN MATHEMATICS HOME PAGE

      *1* Work out your views on assessment in a brief paper, written as a Draft Proposal to your department. Include this in your notebook.

    19. *1* Teaching Strategies for All Subjects

    20. Elementary Math
    21. Math is Elementary: Basic Math Operations
    22. Kids Did This in Math! On-line projects
    23. Skewl MATH Primary, Intermediate, and Secondary Sites
    24. *1*REAL WORLD MATH & SCIENCE
    25. Middle and High School Math Resources
    26. Brown Middle School (Newton, Mass.) Math Page -- Check the links!
    27. Math Lessons
    28. Great Math Sites!
    29. *1*Teaching Math 7-12 With the Internet
    30. Teaching Math K-6 With the Internet
    31. COLOR MATH PINK Sites to develop girls' math interests
    32. *1* A Career in Mathematics - A Web Quest for student inquiry into this topic
    33. MATH RESOURCES
    34. Math Instruction
    35. MATH WEB SITES AND RESOUCES
    36. HIGH SCHOOL HUB: MATH
    37. Regents Review: Math A
    38. Regents Review: Math B
    39. Math for Morons Like Us: Algebra
    40. MATH RESOURCES
    41. MATH INSTRUCTION
    42. TEACHING MATH WITH STRAW, RAISINS, CONSTRUCTION PAPER, and GREEN SLIME
    43. Bringing Mathematics to Life
    44. Connecting Math To Our Lives
    45. EVERYDAY MATH EDUCATORS' HOMEROOM
    46. WHAT GOOD IS MATH?
    47. MATH SCHOOLNET
    48. INTERACTIVE MATH PUZZLES
    49. *1* BASEBALL PREDICTION
    50. Word Problems For Kids
    51. A+ Math
    52. All Math - Flashcards and much more!
    53. MathOurWayTwo -- Awesome links for Primary, Intermediate & Secondary levels!
    54. Virtual Library: Math Education -- Great links!
    55. ALGEBRA!
    56. Three Skills for Algebra
    57. GEOMETRY RESOURCES
    58. CALCULUS
    59. MONEYOPOLIS
    60. MATH TEACHING MATERIALS
    61. MATHEMATICS WEB LINKS
    62. *1* EVERYDAY MATH
    63. Math Comics Page
    64. Math Jokes
    65. STATISTICS
    66. MATH RESOURCES from Carrie's Crazy Quilt
    67. PITSCO'S LAUNCH TO MATH RESOURCES
    68. PLATONIC REALMS - MATH Encyclopedia
    69. *1* BLUE WEB'N MATH PROBLEM SOLVING SITES
    70. NASA MATHEMATICS SITES for EDUCATORS
    71. *1* NEW MATH TEACHER'S HOME PAGE
    72. TOPICS IN MATHEMATICS
    73. MIDDLE SCHOOL MATH BOOKMARKS
    74. MATH--Resources Galore!
    75. HOW STUDENTS LEARN MATHEMATICS
    76. ALGEBRA STORY AND WORD PROBLEMS
    77. THE BASICS OF PROBLEM SOLVING
    78. ELI'S MATH AND LOGIC PUZZLES
    79. MEGA MATH
    80. MATH RESOURCES Compiled by MISS AUEN
    81. SCIENCE AND MATH RESOURCES
    82. SECONDARY MATHEMATICS ASSESSMENT and RESOURCE DATABASE
    83. DoYourMath - offers interactive practice tests, puzzles, expert advice and more for the PSAT, SAT, A.P. tests and calculus
    84. Algebra Online - free private tutoring, live chat, and a message board, among many other features
    85. Math Goodies - interactive math lessons which use a problem-solving approach and actively engage students in the learning process
    86. This is MegaMathematics! - Diverse, interesting links from Los Alamos Labs
    87. Math in Daily Life - explores the universal impact of math in many facets of everyday living
    88. Absurd Math - interactive mathematical problem solving game series in which the player proceeds on missions in a strange world where the ultimate power consists of mathematical skill and knowledge
    89. Making Schools Work for Every Child - create educational equity using math and science materials to help improve the ways in which students with varied needs are educated
    90. Totally Tessellated: An Introduction to Tessellations - history and construction of different types of tessellations
    91. MathMagic! - pairs students over the Internet to solve math questions
    92. Mathematics of Cartography - maps, map history, mathematical concepts behind maps, and map activities
    93. The Boxer Learning Channel - complete math tutorials over the Internet for high school students, teachers and parents
    94. The Math Forum: Internet Resource Collection - links to math and other education resources.
    95. Explorer - math and natural science curriculums, searchable by topic
    96. Center of Excellence for Science and Math Education - professional development, classrooom resources, scholarship, and special projects for science and mathematics classrooms
    97. *1* Mega-Mathematics! - math games, lessons, and activities
    98. MathCentral - resource room and chats for K-12 mathematics teachers
    99. TI Calculators - Texas Instruments' Web site
    100. Ask Dr. Math - ask about specific math problems and topics
    101. Ask the Math Tutor - ask questions ranging from basic mathematics to calculus
    102. Pitsco's Ask an Expert - search for experts in your field of study and ask specific questions
    103. Ask an English as a Second Language Expert - work with ESOL experts to best meet the needs of ESOL students
    104. The Geometry Center - geometry projects and references
    105. Study Web's Puzzles and Problems - links to numerous math puzzle sites from basic to advanced levels
    106. Centre for Innovation in Mathematics Teaching - resources, games, and puzzles to use in the classroom
    107. Beat the Calculator - tips for math computations that you can do faster in your head
    108. The History of Mathematics - biographies of mathematicians, chronologies of mathematics discoveries, and other historical topics
    109. Interactive Mathematics Online - algebra, trigonometry, geometry, chaos, and stereogram topics
    110. Math Humor Links - connects you to cartoons, jokes, poems, and other humorous math-related sites on the Web
    111. The Eisenhower National Clearinghouse - collects both physical and virtual resources useful to math and science educators
    112. Essential Question 5:

      Considering the following "EXTRA TOPICS" sites, how might you make your teaching more relevant and reach more students? Particularly, through a) working with parents and families, b)using alternative assessment to help students learn more, c) confronting the dilemma of depth vs. coverage. d) teaching the gifted and talented, the learning disabled, and English Language learners likely to be in your classes via "inclusion", e) coping with challenges of (beginning) teaching, including mastering the dynamics of questioning, and f) helping students with career planning and transition to life after high school.

      1. Working With Parents: What Parents Should Do, What Is the Teacher's Role
      2. Teacher Web.com -- A fast and easy way to create a great connection to students and parents. You can use many of the links you find in this course!
      3. **Rubrics! Great site to help you evaluate students most fairly and to help them learn to self-evaluate in all subjects!
      4. Depth vs. Coverage in Teaching and Preparing Students for Standardized Tests
      5. Teaching Gifted and Talented Students
      6. Teaching Strategies and Techniques -- Matched to types of diabilities students may have
      7. Free Translation.com -- A site that can be used to translate handouts, tests, and texts into Spanish and several other languages
      8. Teaching English Language Learners
      9. Guides for New (And Not So New) Teachers
      10. *1*TEACHERS ON TEACHING Discussions by classroom teachers on what they wish they'd known when they started.
      11. *1*My Hero: Teacher Heroes Inspiring!
      12. *1*Teacher Tools Page -- On-line tools for making quizzes, puzzles, rubrics, webquests, and more.
      13. Custom Classroom -- Free tools
      14. SchoolNotes.com FREE! Easily develop homework assignments and class information, posting it on the Web!

        *1***Consider, too, the importance of WAIT TIME. Most teachers ask questions at an extremely rapid rate, and average only one second of wait time after each question and after each student answer.

        When teachers increase wait time by 5 seconds, the following results occur:

        1) Longer student answers;
        2) More appropriate answers;
        3) More frequent student responses;
        4) More answers on the analysis and synthesis levels;
        5) More questions and responses from slow learners; and
        6) More confidence by students in their answers.

        An excellent site to inquire further into the dynamics of questioning and wait-time is *1*Changing the Questions.

      15. Careers.org -- Resources for Job Seekers and links to numerous career information sites.
      16. Exploring Careers
      17. Career Paths Online

        FINAL TASK

        *1* Go through your Project Notebook. Make an annotated Table of Contents for each section, and **star the sites you want to be sure to make reference to in teaching Math more effectively.

        *1*Describe in a brief essay how you intend to us the Internet as an instructional/learning tool in your teaching.

        *1* Last, compose an imaginary letter to a friend who has written, asking you about teaching. Tell the friend about one class based on ideas from this online course—the kinds of students you have, the work they’ve done, how you’ve evaluated them, and what you want to try to add next year.

        Mail your completed Project work to:

        Chad C. Osborne
        923 West Mission St.
        Santa Barbara, CA 93101


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