Mathematical instructional delivery supported by technology:

1. Mathematical instructional delivery supported by technology: A case study of the new and innovative SFU Cooperative Lab (CoLab) CMPT 873 Final Project Karen, Bob, Hamid, Maria

2. Introduction • We observed several sessions of graduate level math classes conducted by Dr. Jonathan Borwein in the new and innovative Cooperative Lab (CoLab) at SFU. • Specifically, we observed the use of large touch screen displays as used in the delivery of math instruction.

3. Research Question How do technologies such as large screen displays, support, enhance or hinder instructional delivery in Experimental Mathematics

4. Methodology Laboratory Experiment Experimental Simulation • Field Study • Case Study • Direct observation Judgment Study Field Experiment Sample Survey Field Study • Formal Theories • Ethnography • Constructivism Computer Simulation Formal Theory

5. Case Study and Ethnography • Qualitative descriptiveresearch • Small groupof participants • Observedover a longer time period • Multiple sourcesof evidence • Accountsof the participants • Conclusionsonly about thatgroupinaspecific context

6. Personal interpretation Exploration Social interaction Problem Discovery Experience Constructivism • Intuition of concept is actively created by the student

7. Direct observation Focus group with students Video recording Interviews Data Analysis Categorization of events Experts: Mathematics Education HCI Frequency of events Conceptual Maps Task analysis Methodology

8. Measurements • Time and frequency of interaction issues • Windows manipulation • Use of Electronic pen / eraser • Keyboard issues • Typing in wrong display • Traveling between displays Qualitative Quantitative • Conceptual Context of Participants • Teaching style • Attitude towards technology • Assessment of interaction issues

9. Teaching Style • Constructivist (hands-on approach) • Has a good understanding of each student’s abilities and needs • Interactive • Promotes Discussion and Questions • Provides tips to students as required • Provides coaching • Suggests alternatives • Involves students with the technology • Encourages students to be self starters • Offers stories (historical references, anecdotes)

10. Instructional Environment • Graduate level mathematics • Experimental mathematics • Mathematical analysis • CoLab is small • Technology “Rich” • Enhances effectiveness of delivery • Cooperative Idea sharing • Brainstorming • Interactive

11. Room Layout

12. Software Maple Custom designed modules Math Resource (dictionary) interactive visual output without learning commands easy access to reference materials Smartboard Browser / Acrobat Reader online books and articles

13. Maple Interactive Session • Teach students Maple • Apply the theory to practice • Highly interactive process • Student uses keyboard • Instructor helps him with the process and commands. “I like to see what the prof is talking about i.e. they often say –we could do this…- and leave it at this, but in this class we actually do the could’s”

14. Math Resource Dictionary • Definitions of mathematical terms with a hyperlink structure • Biographies and historical data • Interactive problem-solving of examples • Maple engine • plotting “I appreciate the database of math concepts, which provides quick and accurate information”

15. Smart Board

16. Activity Flow

17. Activities and Events • Activities • different instructional delivery components • we identified 6 distinct activities (see list) • 15 - 45 minutes in duration • Events • elements of unproductive time associated with technology use • several specific events were recorded • we identified 22 distinct events • usually quite short (2 - 8 seconds)

18. Events time • Relatively low (3%) • Would be higher for less experienced users • It seemed more to students • Instructor was very efficient (using the technology)

20. Large Screen Displays • Easy to point to the place you want • Finger vs. mouse • Harder window manipulation

21. Large Screen Displays Used as E-board • No dust, no switching between projectors and overhead • Saving ability: size of the board unlimited • Bring up a new slide with no time • Easy to go back and forth between the slides

22. Windows Issues Multiple-screens • More displaying space • Multiple SW applications displayed concurrently • Students split focus • Pointing to the screen • Locate window • In which display? Locating Window

23. 7% of the total unproductive time Would be much higher for less experienced user Difficulties locating keyboard trouble using it while standing Keyboard Issues

24. Keyboard Issues Keyboard while sitting Keyboard while standing

25. Keyboard Issues • Maple session • Collaboration • (pointing-typing) • Dialogue • Instructions • Clarification • Keyboard handoff • Traveling time

26. Keyboard hand off • Aneffective work-around • Not by design, but by chance • A very substantial time saver • requires knowledgeable user (student) • increased collaboration • helped to pace the class “I learn and understand by doing and follow better when I have control over the steps we’re taking”

27. Electronic Pens • Pen / holder problem every pen has to be in the right slot. • Can not bring up cursor on another connected screen without placing the pen back on the right slot • Require more pressure to write

28. Electronic Pens • Never run out of ink • Always available • Can be improved as user gets used to the technology • Used to click • Registration problem • Writing formulas or cursively • “Handwriting” not legible Writing cursively Using pen to click

29. Instruction in the CoLab • Advantages / benefits • Presentation is more dynamic and engaging • Individual involvement is encouraged • Increased use of demos is facilitated (I.e. maple) • Instantly accessible material. • electronic notes • research documents • Math Resource Dictionary • Quick mechanism for refreshing previously learned concepts • Maple • “allowed us to do experimental mathematics” • Helps visualization of abstract data / concepts

30. Instruction in the CoLab (cont.) • Disadvantages / problems • Parallax and lag time associated with the whiteboards. • Pens / pen holder problem (requires practice). • Electronic whiteboard readability (sometimes not legible) • Eraser (it often erases too much) • Lighting • Glare on display screen (visibility) • Tiring (eye strain)

31. Effectiveness of Method • Realism of context • Precision • Quantitative • Qualitative • Validity • “Rich” data • Feedback from Experts • Member checks • Reactivity • Construct validity • Fidelity: quantitative measurements • Not generalizability

32. Conclusions • Effectiveness of tech-oriented environment for teaching depends heavily on the presenter (professor). • Quantitatively • Perceived time • Students comfortable to explore the technology • their attitude towards technology was positive • Feeling of integration

33. Conclusions • Works well for a constructivist approach – not as well for an instructivist approach • Allows flexible and dynamic learning environment • Suits the course: unstructured content • Teaching style of instructor is not affected by the presence of technology (gesturing and visual contact)

34. Aknowledgements • CoLab • Jonnatan Borwein, Lyn Bartrand and Jen Chang • Students • Linda, Tom and Cody • NewMIC • Julia Rylands • SFU • Mark Weiler, Arthur Kirkpatrick, Niklas Rober