1. Creating Virtual Instructors for Mathematics The Exponential Principle The Exponential Principle Constructivism - J. Bruner (1966) http://www.pindling.org/Math/Video/exponential_principle.html http://www.pindling.org/RT

2. The Virtual Instructor The Virtual Instructor Think about the greatest teacher you knew / know. Think about the greatest teacher you knew / know. What made that teacher great? What made that teacher great? If that teacher were to appear to us online today would he / she be still great? If that teacher were to appear to us online today would he / she be still great?

3. How Students View the Internet A virtual textbook and reference library A virtual textbook and reference library A virtual tutor and study shortcut A virtual tutor and study shortcut A virtual study group A virtual study group A virtual guidance counselor A virtual guidance counselor A virtual locker, backpack, and notebook. A virtual locker, backpack, and notebook. 78% of children between the age of 12 and 17 go online (Levin & Arafeh, 2002).

4. "As every thinking teacher knows, the trouble with education is that it is too often about teaching and not enough about learning." Evans, Peter and Deeham, Geoff, In The Descent of Mind

5. Instructors’ Roles Online Helping students acquire (or construct) knowledge, Helping students acquire (or construct) knowledge, Assisting students to understand and take greater control of their learning processes, Assisting students to understand and take greater control of their learning processes, Providing students with emotional support and motivation, and Providing students with emotional support and motivation, and Carrying out administration and organizational duties.. Carrying out administration and organizational duties.. (Annand & Haughey, 1997)

6. Required Skills for Online Instructors Generic Skills (in educational disciplines) Generic Skills (in educational disciplines) Core Distance Education, DE skills (DE, analysis and course development) Core Distance Education, DE skills (DE, analysis and course development) Specific DE skills (e.g., specific use of technology, issues related to specific interest, etc.) Specific DE skills (e.g., specific use of technology, issues related to specific interest, etc.) Cognate DE skills (e.g., computer programming, understanding of learning and instructional theory, statistical skills, etc.) Cognate DE skills (e.g., computer programming, understanding of learning and instructional theory, statistical skills, etc.) (Ally & Coldeway, 1999) – DE is Distance Education

7. Mathematics and Virtual Learning Mathematics requires the active participation of the student Mathematics requires the active participation of the student Mathematics is well adapted to self- directed learning Mathematics is well adapted to self- directed learningself- directed learningself- directed learning Mathematics requires a student to master certain topics before proceeding to new topics Mathematics requires a student to master certain topics before proceeding to new topics (Strasser, 2000) 2x+10=y

8. Problem 1 If a times a equal 4, what is a?

9. The Virtual Instructor Toolkit Dynamic Textbook (Non-Linear) Dynamic Textbook (Non-Linear) Dynamic Interactive Homework Assignments Interactive Homework Assignments Interactive Video Learning (Game / Fun) Video Learning (Game / Fun)Game / FunGame / Fun e-Study (Instant Feedback) e-Study (Instant Feedback)Instant FeedbackInstant Feedback Learning - By Example Learning - By Example LearningBy Example LearningBy Example Visual Learning Tools (Visual / Graphics) Visual Learning Tools (Visual / Graphics)Visual / GraphicsVisual / Graphics Community Learning (Workshops) Community Learning (Workshops)Workshops The Multimedia Instructor (Almost Live) The Multimedia Instructor (Almost Live)Almost LiveAlmost Live

10. Dynamic Textbook Non-Linear Learning Non-Linear Learning Non-Linear Learning Non-Linear Learning Drill-down for more details Drill-down for more details Drill-down Multi-learning Opportunities (Tony’s Research) Multi-learning Opportunities (Tony’s Research)Tony’s ResearchTony’s Research Eliminates note taking – offsets short term learning Eliminates note taking – offsets short term learningnote taking note taking Interactive text – optimize learning Interactive text – optimize learning Interactive text Interactive text

11. Interactive Homework Provides Immediate Feedback Provides Immediate Feedback Adjusts to Student Performance / Knowledge Adjusts to Student Performance / Knowledge Provides a Forum to Practice Concepts / Application (Learn by Doing) Provides a Forum to Practice Concepts / Application (Learn by Doing)Learn by DoingLearn by Doing Provides for Instructor’s Interaction with Students Provides for Instructor’s Interaction with Students Analyzes Areas of Concerns Analyzes Areas of Concerns Optimizes Various Learning Styles Optimizes Various Learning Styles

12. Problem 2 Fill in each box (blue) with a number from 1 to 8 (no duplicates). No numbered box should have a number adjacent to it (also diagonal) that is one more than itself (e.g. 4 cannot be next to 5).

13. Multimedia Toolkit Interactive Educational Video Games Interactive Educational Video Games –e-Math (Wiley) e-Math (Wiley)e-Math (Wiley) –Simulated Learning Video Games Simulated Learning Video GamesSimulated Learning Video Games Learning by examples Learning by examplesby examplesby examples –Math text now have more worked out examples and –answers to every problem –Studies show that student learn math better by examples learn math betterlearn math better Lectures Online Lectures Online –Lecture Notes –Streaming Video / Audio VideoAudioVideoAudio Interactive Learning Tools Interactive Learning Tools –Math Function Graphing (MathGv) MathGv –Interactive Online Tools Interactive Online ToolsInteractive Online Tools Learning Communities Learning Communities –WebCT WebCT –Blackboard Blackboard

14. References http://www.pindling.org/Math/Video/ref/de_biblio.html

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16. Towards the Creation of A great virtual instructor is first a great physical instructor! The Virtual Instructor is an integration of: 1. Technology – hardware and software 2. The Instructor’s Presence a. Intellectual Essence (knowledge transfer) b. Perceived Physical Presence c. Ability to Interact Online 3. Student Interactions 4. Virtual Communication Between Student and Instructor Pindling, 2000