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Gateway to Mathematics

Gateway to Mathematics

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Gateway to Mathematics

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  1. Gateway to Mathematics

  2. Purpose A shortage of well-qualified workers in many science, mathematics, and engineering/ technology (SMET) fields limits Idaho corporate competitiveness, just as a shortage of well-qualified K-12 mathematics and science teachers limits our children’s educational opportunities. Gateway to Mathematics and the University of Idaho are creating a statewide partnership of Idaho educational stakeholders, including state agencies, corporations, communities, and K-12 schools, focused on making high quality university level courses and professional development activities and services available statewide. Funded by grants from the US Department of Education and the Idaho State Board of Education

  3. Guiding Principles • Academically --- Courses should reflect the values and standards of mathematics and mathematics education faculty throughout the Idaho university system and related educational, governmental, and industrial associations; • Pedagogically --- Courses should implement “best practices” identified by mathematics education researchers, rather than imitate traditional, face-to-face instruction;

  4. Goals • Practically --- Courses should be easily transferable between university campuses and readily recognized by accrediting agencies (e.g., the Idaho Department of Education); and • Theoretically --- Courses should be systematically studied by researchers focused on the evaluation and improvement of web-based teaching and learning.

  5. Partnership • Partners • University of Idaho • K-12 Schools & Corporations • Idaho Department of Education • Collaboration Principles • Courses are only available via K-12 and corporate partners; and • Policies & procedures are developed collaboratively by project partners.

  6. Community of Inquiry Model Community of Inquiry Model (Garrison et al, 2000) http://cade.athabascau.ca/vol14.2/rourke_et_al.html

  7. Learning Model • Data Analysis • SNA (NetMiner II) • Statistics

  8. Future Courses • Fall 2006 • Math 170 Calculus and Analytic Geometry I • Spring 2007 • Math 170 & 175 Calculus and Analytic Geometry I & II • Geometry & Measurement for Middle School Teachers • Number & Operations for Middle School Teachers • Fall 2007 • Repeat Spring 2007 Courses • Probability & Statistics for Middle School Teachers • Spring 2008 • Repeat Fall 2007 Courses • Algebra for Middle School Teachers

  9. Math 170 --- WebCT Home Page

  10. Math 170 --- Assumptions • Students are mathematically ready [SAT/ACT/Compass]. • Students are technologically ready [Technology Readiness Test]. • Students are independent learners, patient, confident, and collegial [Recommendation of local principal]. • Students have a daily 50 minute “opening” in their schedule for study and synchronous chats [Coordinated by local Administrative Liaison]. • Partner high schools coordinate recruitment, registration, and other administrative aspects of the course, including daily attendance and examination proctoring. [Coordinated by local Administrative Liaison]. • Partner high schools will provide and maintain a networked student workstation [Coordinated by local Technical Liaison].

  11. Math 170 --- Overview • Calculus & Analytic Geometry I Traditional topics delivered using non-traditional pedagogies & technologies.

  12. Collaborative Groups Research on web-based university courses has shown that individual student satisfaction and achievement are strongly related to the sense of community and cohesiveness engendered by the course. In Gateway to Mathematicscourses, students participate in two types of communities: Whole class and small collaborative groups.

  13. Beta-test Spring 2006 Enrollment • 14 students from 4 Idaho high schools • 12 seniors and 2 juniors • 10 males and 4 females

  14. Math 170 --- Content • Spring 2006 • Partial Table of Contents • Links to lessons • Links to videos

  15. Math 170 --- Scientific Notebook Traditional expository mathematics MacKichan (2005). Scientific Notebook. Available on-line at http://www.mackichan.com/

  16. Math 170 --- Scientific Notebook Interactive practice [Answers and occasional hints]

  17. Math 170 --- Videos Video presentations of key concepts and procedures

  18. Math 170 --- WorldWideWhiteboard Synchronous mathematical demonstration & dialogue www.link-systems.com

  19. Math 170 --- Bernoulli Menu Algorithmically generated & scored practice & quizzes [Partial list of homework sets] www.link-systems.com

  20. Math 170 --- Bernoulli Item

  21. Math 170 --- Bernoulli Item

  22. Math 170 --- Bernoulli Item

  23. Math 170 --- Bernoulli Item

  24. Math 170 --- Bernoulli Item

  25. Exam #1 Exam #1: First WebCT Quiz Score vs. Examination Score

  26. Exam #1 Exam #1: Average WebCT Quiz Score vs. Examination Score

  27. Exam #4 Exam #4: First WebCT Quiz Score vs. Examination Score

  28. Exam #4 Exam #4: Average WebCT Quiz Score vs. Examination Score

  29. Overall Achievement

  30. Sample Student Survey Items Q: Are you satisfied with the course? A: Yes, 14-0. Q:  Would you recommend this course to a friend? A:  Yes, provided they are self-motivated and responsible. Q: What have you learned so far that has interested you the most? A: Application of calculus in real life, science, etc. Q: What is the most beneficial/enjoyable aspect of the course? A: Bernoulli, WorldWideWhiteboard, getting a start on college mathematics. Q:  On average, how many hours do you speed each week on this course? A:  6 - 8 hours

  31. Instructor Observations • Students need about a month to become proficient in the use of course technologies. • Students adapt somewhat reluctantly to printed readings and video lectures. They would prefer to receive daily direct instruction in WorldWideWhiteboard. • Differences in local school calendars, field trips, and so on require flexibility on the part of both project partners and students.

  32. Complex Networks • Telephone networks • Computer networks • Military command & control • Corporate communications • Social networks • Biological networks • Neurons • Animal behavior • Learning networks

  33. Network Matrix

  34. Network Graphics

  35. Learning Networks • Students (Actors) • Leaders • Followers • Lurkers • Emergent structures, roles & attributes • Cohesiveness • Cliques • Brokers • Status

  36. Research Questions • How is cohesiveness associated with achievement? • How does cohesiveness originate and evolve? • Is there an optimal level of cohesiveness? • Is cohesiveness associated with student satisfaction? • What other factors are associated with individual achievement and student satisfaction? • Readiness [mathematics, technology, learning style] • Synchronous & asynchronous dialogues • Automated practice & quizzes [Bernoulli]

  37. Professional Opportunities The Gateway to Mathematics Project invites interested mathematics faculty and educational researchers to contact project leadership to discuss R&D opportunities related to the design, development, delivery, and investigation of web-based mathematics, statistics, and mathematics education courses.

  38. Contact Information

  39. Thank you for your attention and interest in the Gateway to Mathematics Project