1. Communicating Mathematics : A Problem Solving Approach Paul Eakin, Carl Eberhart, Ken Kubota, Dan Chaney,

2. General Program R&D on effective application of communications technology to the teaching of mathematics – software, methodology, materials Associated Dissemination Project –Course (with text) –Workshops Support System for teachers Very much a work in progress

3. General Goals Improved Preparation of Pre Service Math Teachers Improved communication/collaboration within mathematics community Effective Application of technology to teaching of mathematics at all levels

4. Current Approach to Advancing these Objectives is through the application of Technology To Save Teacher Time

5. Automation of tedious tasks Collaboration on materials development Sharing resources Facilitating parental/community involvement with students

6. Concentration is on general tools For active use by teacher rather than student Have modest computing resource requirements Are intended for remote and out-of-class use –No infringement on traditional class time Require minimal computer skills –Trade off with very solid knowledge of mathematics Support collaboration across large communities Not dependent on local school computer systems

7. The most obvious (to us) source of time saving is in the management of homework Assignment Checking* –Feedback Logistics –Collection –Return –Record Keeping

8. The Tools: Part 1 (WQS) Used for two years in basic calculus and linear algebra Handles: formatted Mathematics Chat groups Student-teacher email Visual rolls Video lectures Sharing of problem sets Has primitive data handling Multiple choice format Too much data

9. Primary Student Interface: Instructor’s Web Page syllabus links to html text links to chat system and FAQ systems links to “WQS” system for course materials (e.g. homework, review materials, video lectures, etc)

10. Student Interface: Instructor’s Web Page (part 1) System tutorial Course syllabus Visual class rolls Exam schedule

11. Class Roll:

12. Instructor’s Web Page (part 2) Link to wqs system server Student emails from homework system with responses Links to lecture notes for video lectures

13. Responses to Student Questions: Page references particular assignment Student query Instructor response

14. Instructor Web Page (part 3) Link to online text Link to wqs system Links to lecture slides for video lectures by chapter

15. WQS System: login screen Students select video lectures menu or their class homework menu Group logins and work are encouraged

16. Typical Section Menu Chapter 1 homework Review for test II

17. Homework Page: Basic Format Problem and answers System response Email window Student answer System answer

18. Most students print the problem sets out and record their solutions or solutions from class directly on the printouts

19. Video Lectures Menu Lecture Slides (html) Video of lecture segment (10-30 min)

21. How students watch the videos

22. Test Review with video solutions: Model for current experiments Problem statement with diagram Link to video solution

23. Data Logs Every student action is logged with time stamp All activity credited to each member on group login Total number of answers submitted (right or wrong) correlates very well with performance on tests

24. Log Data

25. Preparing Materials coffee food CD burner and blanks

26. Remark on WQS CDs Natural corollary of HTML format –easily made at faculty desk, cheap –Students copy in lab on their own blank (15 min, $1) Originated through necessity (bandwidth, reliability) Strongly favored by upper-level students who tend to live off-campus Not used much by lower level students who tend to live on campus

27. Maple Source: WQS Homework Problem Question Tag:( Q_ ) “SKIP” Tags Answer Tags: ( A_ ) Correct Answer Tag Code for Figure (section)

28. SAMPLE WQS TAGS Q_ Question starts and runs to next tag T_ Text starts and runs to next tag A_ Answer choice for current question A_ANS Correct answer for current question SKIP Omit from here to next tag

29. To create and “post” a simple wqs homework set: Source document is exported to html from Maple menu exported html document is processed by a Perl script to: – create a “data” file which describes the final document to the server –place an entry in a control file which describes the menu

30. Control File is basis for sharing Sharing Materials: Paul made homework set number 7 Ken made homework set number 8 This is Paul’s Control file

31. B’s Files control materials homeworklecture wqs ma123 Wqs system Student login To B’s class 1 2 3 4 5 Student login To A’s class B’s Files wqs ma123 control 1 2 3 5 LOAD SHARING

32. Sharing: Laura’s Ma123 Control File and class menu

33. Sharing: Laura and Jody Do Ma123 Lectures

34. Sharing: Control File for Joe Mahoney’s Paducah, KY Section of Ma322 Carl Eberhart created the homework for the Ma322 sections

35. Joe Mahoney and Avinash Sathaye did Videos for MA322

36. Unified Format: LaTeX math formatting Video link

37. Web homework is part of text in unified format

38. Experience with WQS: It does work. But … Works much better with motivated, advanced students Primary problem is compliance Problem with misinformed faculty, advisors

39. Student response to Ma123 as reported in the student paper

44. Tools: Part 2 (MathClass) Currently under development Subsumes WQS Very general format Promotes sharing/collaboration across net: –development –individual problems Better data management

45. MathClass Visuals: MathClass does homework grading in advance – “frontloads” Format: Print out problems – work them away from computer – Perhaps use computer to work problem

49. MathClass Dissemination Software is freely distributed (except Maple) UK will provide service of problems 2-day workshop on setup 1-day workshop to use “shopping basket” 3-day workshop for experienced teacher familiar with Maple 2-week workshop for experienced teacher not familiar with Maple One semester course for pre-service teacher

50. Course needs to provide Serious introduction to Maple Comprehensive overview of system structure Facility with tools Experience –Use of the system – Collaborative materials development

51. Philosophical Difficulties: Formally not a Math Class Looks on its face like an elementary computer skills course What is the intellectual content? Where does it fit in a crowded curriculum?

52. Observations WQS materials move readily to MathClass (something is conserved) Effort is mathematical problem-solving at a non- trivial level –Creating diagrams, answers (WQS) –Creating solver (MathClass) –Verification –Requires wide variety of math tools even for elementary problems MathClass environment permits development of non-traditional types of problems.

53. Conclusion The material fits nicely into a mathematical communications/problem solving course Basic Activities are creation, presentation and solution of problems –Diagrams, – Checkers, Substitutes for conventional problem solving course Provides communications skills Excellent introduction to instructional technology

54. Ma375: Communicating Mathematics Course description Walkthrough Math prerequisites Communication –Written, oral, collaboration, continuation, community building

55. Layout of Ma375 Text/software required Topics Operation Testing Connection with student teaching NSF support – Looking for collaborators/testers Services

56. Layout continued Security Intellectual property considerations Design of modules as executables NSF requirements Workshops Materials

57. Math 375 (General Outline) Using MathClass (2 wks) Using Maple to Create Problems (6 wks) –Basic techniques –Graphics techniques –Solvers Additional topics and techniques (2 wks) –Security, intellectual property, –Video, and other advanced techniques Materials development lab (6 wks)

58. 1. Hand sketch 2. Abstract Object in Maple 3. Assign values to variables 4. Realize image

59. 1. Add property (e.g. color) 2. Explore simple extensions 3. Have students extend it further.

60. Making Compound Objects Exercise: Remake the “K” Cube with a properly Formatted “K”

62. Animation

63. Basic Drawing/Annotation: DL ( “Draw Line”) PT (“Put Text”) PP (“Put Point”) GP (“Graph Paper”) PA (“Put Arc”) ARRW (“Dbl or Sngl Arrow”)

64. Workshop: Live development of a problem set Make video prompt(s)

65. Lab Activities: Making CD/DVD Operating personal site Evaluation Collaboration Making/integrating video JAVA and other tools