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  1. InterMathProfessional and Cognitive Development through Problem Solving and Technologyhttp://www.intermath-uga.gatech.edu/ Evan Glazer Learning and Performance Support Laboratory University of Georgia eglazer@coe.uga.edu http://www.arches.uga.edu/~eglazer/NECC2001.html

  2. Overview • My Background • About InterMath • Professional Development • Cognitive Development • Teachers’ Activities http://www.intermath-uga.gatech.edu/

  3. Background • Doctoral Candidate in IT at UGA http://www.intermath-uga.gatech.edu/

  4. Baptism Bulldawg Style

  5. Background • Doctoral Candidate in IT at UGA • InterMath - problem solving with TEMIs. http://www.intermath-uga.gatech.edu/

  6. Under the direction of Jim Wilson and others http://www.intermath-uga.gatech.edu/

  7. Background • Doctoral Candidate in IT at UGA • InterMath - problem solving with TEMIs. • Taught high school mathematics in Glenview, Illinois http://www.intermath-uga.gatech.edu/

  8. You might be a “real” teacher if... • You grade papers in the car, during commercials, in faculty meetings, in the bathroom, and (at the end of the six weeks) have been seen grading in church. • You have a disjointed neck from writing on boards without turning your back on the class. • You are written up in medical journals for the size and elasticity of your kidneys and bladder. http://www.intermath-uga.gatech.edu/

  9. You might be a “real” teacher if... • You have been timed gulping down a full lunch in 2 minutes, 18 seconds. Master teachers can eat faster than that. • You know it is better to seek forgiveness than to ask permission. • You buy Excedrin and Advil at Sam's. • You know secretaries and custodians run the school http://www.intermath-uga.gatech.edu/

  10. You might be a “real” teacher if... • You hear the heartbeats of crisis; always have time to listen; know you teach students, not just a subject; and you are absolutely non-expendable. http://www.intermath-uga.gatech.edu/

  11. Background • Doctoral Candidate in IT at UGA • InterMath - problem solving with TEMIs. • Taught high school mathematics in Glenview, Illinois • Web-based development since 1993. http://www.intermath-uga.gatech.edu/

  12. Background • Doctoral Candidate in IT at UGA • InterMath - problem solving with TEMIs. • Taught high school mathematics in Glenview, Illinois • Web-based development since 1993 • I have a passion for working with kids, teaching, learning, mathematics, and running http://www.intermath-uga.gatech.edu/

  13. Mathematicians have the unique talent of determining howfast they are running, and how much faster they need to runby the end of the race in order to set a personal record. http://www.intermath-uga.gatech.edu/

  14. Unflattering portrait: How one child perceives mathematicians Source: http://www.thetimes.co.uk/article/0,,2-61352,00.html

  15. Background • Doctoral Candidate in IT at UGA • InterMath - problem solving with TEMIs. • Six years of teaching high school mathematics in Illinois • Web-based development since 1993 • I have a passion for working with kids, learning, mathematics, and running • Research and writing interests include communities of practice and technology integration. http://www.intermath-uga.gatech.edu/

  16. Available September 1, 2001 Greenwood Publishing

  17. About InterMath • What is InterMath? • Who is involved in InterMath? • What is the rationale for InterMath? • What are the goals of InterMath? About InterMath Professional Development Cognitive Development http://www.intermath-uga.gatech.edu/

  18. What is InterMath? • A five year, NSF-funded Internet-based professional development project • A community of middle school mathematics teachers and administrators • An effort to strengthen teachers’ conceptual understanding • A program that uses technology to explore problem solving situations • About InterMath • What is InterMath? • Who is involved? • Rationale • Goals • Professional Development • Cognitive Development http://www.intermath-uga.gatech.edu/

  19. A Sad Excuse for Problem Solving • About InterMath • What is InterMath? • Who is involved? • Rationale • Goals • Professional Development • Cognitive Development

  20. A Consequence of Bad Problems • About InterMath • What is InterMath? • Who is involved? • Rationale • Goals • Professional Development • Cognitive Development

  21. Who is Involved? • LPSL - UGA (Hannafin, Wilson) • Research scientists, SMEs, Web and curriculum developers • CEISMC - Georgia Tech (Ohme) • Web designers and technical support • Workshop Participants • Middle school teachers/administrators and instructors at UGA, Kennesaw State, Valdosta State, and state INTECH centers. • About InterMath • What is InterMath? • Who is involved? • Rationale • Goals • Professional Development • Cognitive Development http://www.intermath-uga.gatech.edu/

  22. Rationale for InterMath • New approaches to teaching and learning • About InterMath • What is InterMath? • Who is involved? • Rationale • Goals • Professional Development • Cognitive Development

  23. Learning over the Past 50 years Teaching Math in 1950: A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price. What is his profit? • About InterMath • What is InterMath? • Who is involved? • Rationale • Goals • Professional Development • Cognitive Development

  24. Learning over the Past 50 years Teaching Math in 1960: A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price, or $80. What is his profit? • About InterMath • What is InterMath? • Who is involved? • Rationale • Goals • Professional Development • Cognitive Development

  25. Learning over the Past 50 years Teaching Math in 1970: A logger exchanges a set "L" of lumber for a set "M" of money. The cardinality of set "M" is 100. Each element is worth one dollar. Make 100 dots representing the elements of the set "M". The set "C", the cost • About InterMath • What is InterMath? • Who is involved? • Rationale • Goals • Professional Development • Cognitive Development of production contains 20 fewer points than set "M". Represent the set "C" as a subset of set "M" and answer the following question: What is the cardinality of the set "P" of profits?

  26. Learning over the Past 50 years Teaching Math in 1980: A logger sells a truckload of lumber for $100. His cost of production is $80 and his profit is $20. Your assignment: Underline the number 20. • About InterMath • What is InterMath? • Who is involved? • Rationale • Goals • Professional Development • Cognitive Development

  27. Learning over the Past 50 years Teaching Math in 1990: By cutting down beautiful forest trees, a logger makes $20. What do you think of this way of making a living? Topic for class participation after answering the question: How did the forest birds and squirrels feel as the logger cut down the trees? • About InterMath • What is InterMath? • Who is involved? • Rationale • Goals • Professional Development • Cognitive Development

  28. Learning over the Past 50 years Teaching Math in 2000: A company outsources all of its loggers. The company claims that contracting workers will Ultimately save them on expenses for benefits and salaries when demand for their product is down. The union requests that you take a closer look at historical employment, salary, benefits, and contracting data located on the web. Was outsourcing a good move? Use a cognitive tool like a spreadsheet or simulation to develop and support your reasoning. • About InterMath • What is InterMath? • Who is involved? • Rationale • Goals • Professional Development • Cognitive Development

  29. Rationale for InterMath • New approaches to teaching and learning • Insufficient content background in teacher training programs • Resilient and pervasive beliefs about teaching mathematics • About InterMath • What is InterMath? • Who is involved? • Rationale • Goals • Professional Development • Cognitive Development http://www.intermath-uga.gatech.edu/

  30. Is this what mathematics teaching is about? • About InterMath • What is InterMath? • Who is involved? • Rationale • Goals • Professional Development • Cognitive Development

  31. Rationale for InterMath • New approaches to teaching and learning • Insufficient content background in teacher training programs • Resilient and pervasive beliefs about teaching mathematics • Escalating demands for teachers and little support • About InterMath • What is InterMath? • Who is involved? • Rationale • Goals • Professional Development • Cognitive Development http://www.intermath-uga.gatech.edu/

  32. Teacher Support • About InterMath • What is InterMath? • Who is involved? • Rationale • Goals • Professional Development • Cognitive Development

  33. Rationale for InterMath • New approaches to teaching and learning • Insufficient content background in teacher training programs • Resilient and pervasive beliefs about teaching mathematics • Escalating demands for teachers and little support • About InterMath • What is InterMath? • Who is involved? • Rationale • Goals • Professional Development • Cognitive Development • Difficulty attaining learning standards http://www.intermath-uga.gatech.edu/

  34. Georgia Test Scores • About InterMath • What is InterMath? • Who is involved? • Rationale • Goals • Professional Development • Cognitive Development

  35. The Truth • About InterMath • What is InterMath? • Who is involved? • Rationale • Goals • Professional Development • Cognitive Development

  36. Compared to the Nation • “Georgia drops to 50th in nation in SAT scores” • “State Board of Education's goal of reaching a 1,000 mean score by 2001 is all but dead.”-Savannah Morning News • About InterMath • What is InterMath? • Who is involved? • Rationale • Goals • Professional Development • Cognitive Development http://www.intermath-uga.gatech.edu/

  37. Goals for InterMath • Promote innovative practices • Revitalize teaching by modeling and applying innovative approaches • Support reform of mathematics teaching and learning • Establish a human and technological support infrastructure • About InterMath • What is InterMath? • Who is involved? • Rationale • Goals • Professional Development • Cognitive Development http://www.intermath-uga.gatech.edu/

  38. Professional Development • Participant Selection • Workshop Procedures • Our Use of Technology • Additional Contributions About InterMath Professional Development Cognitive Development http://www.intermath-uga.gatech.edu/

  39. Participant Selection • Underserved schools will receive priority • Schools where mathematical technologies are available • Teams of middle-school teachers and administrators • About InterMath • Professional Development • Participant Selection • Workshop Procedures • Use of Technology • Additional Contributions • Cognitive Development http://www.intermath-uga.gatech.edu/

  40. “If you can teach middle school, then you can teach anyone.” • About InterMath • Professional Development • Participant Selection • Workshop Procedures • Use of Technology • Additional Contributions • Cognitive Development

  41. Workshop Procedures • 100 hours of training • 45 hour workshop, 55 hour “follow along” development course • Development of portfolio using a web page • Write-ups of investigations • Development of technology lessons • Ongoing support system • Human (experts, community) • Electronic (listserv, bulletin board, email) • Documents (tutorials, guides) • About InterMath • Professional Development • Participant Selection • Workshop Procedures • Use of Technology • Additional Contributions • Cognitive Development

  42. InterMath’s Use of Technology …does not focus on finding answers. • About InterMath • Professional Development • Participant Selection • Workshop Procedures • Use of Technology • Additional Contributions • Cognitive Development

  43. InterMath’sUse of Technology • Cognitive tool for building ideas, organizing thinking, solving problems, and exploring patterns • Multiple technologies promote multiple representations • Provides new learning opportunities • About InterMath • Professional Development • Participant Selection • Workshop Procedures • Use of Technology • Additional Contributions • Cognitive Development http://www.intermath-uga.gatech.edu/

  44. Additional Contributions • Evolving database of investigations • Teacher resources and lesson plans • Discourse through electronic communities • About InterMath • Professional Development • Participant Selection • Workshop Procedures • Use of Technology • Additional Contributions • Cognitive Development http://www.intermath-uga.gatech.edu/

  45. Cognitive Development • Rationale of Workshop Activities • Workshop Content • Investigations • Teacher’s Activities About InterMath Professional Development Cognitive Development http://www.intermath-uga.gatech.edu/

  46. Rational of Workshop Activities • Intrinsically motivating • Appropriate level of challenge • Appeal to curiosity • Learner control • Realistic applications • Ownership of learning • Open-ended exploration • Generative extensions of investigations • About InterMath • Professional Development • Cognitive Development • Rationale of Workshop Activities • Workshop Content • Investigations • Teacher’s Activities