1. Communicating Mathematics: A Problem Solving Approach The creation, implementation, sharing, and management of web-based mathematics instructional materials

2. Project Focus The Appropriate Application of Technology to Conserve Teacher Time and Energy

3. At this time “appropriate” Includes: – automating record-keeping, – document and instructional supplement preparation and presentation –automated homework presentation, checking Does not include: –Automated testing, –Computer-based instruction,

4. With Regard to Time Our Experience has Been: The development of high quality web-based “multi-media” materials takes from four to ten times the time and resources that an experienced teacher would need to prepare and present the same ideas in a traditional instructional format

5. Project Components Suite of tools for collaborative development and presentation of mathematics on the web Course through which prospective teachers can learn and effectively employ these tools Long-term R&D program to continually improve the tools and course

6. The Tools Support Automated homework –Presentation –Checking –Record-keeping Fast, efficient development of supplements such as tests, handouts, etc. Collaborative development and efficient sharing of materials among colleagues at the same or different institutions.

7. Current System: WQS Effectively Multiple choice Only Central distribution –Not possible for individual to set up and run Login required Effectively supports sharing Requires server Supports video Two years experience Refer to graduate student presentations for experience Relatively simple to develop materials –Maintenance requires effort –Ideosyncratic at present

8. 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)

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

10. Class Roll:

11. 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

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

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

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

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

16. Homework Page: Current Format Problem and answers System response Email window Student answer System answer

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

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

20. How students watch the videos

21. Test Review with video solutions Problem statement with diagram Link to video solution Maple worksheet With links exported to html

22. 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

23. Log Data

24. WQS Video Materials prepared by faculty lectures by faculty and graduate students tapes converted to ASF and edited by grad students and staff separate video and homework (original system) text/homework/video merged in next edition

25. Graduate Student Editing Video Files

26. WQS and Video Lecture Materials Preparation Materials developed by faculty using a variety of standard tools (e.g. Maple, LaTeX, Perl). Individual item described by a file called “data” in directory specific to item. It describes how construct the item. locations placed in control file called wqs- dirs which is known to server and describes the section menu page

27. Faculty Preparing Materials coffee food CD burner and blanks

28. 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 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

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

30. 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

31. 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

32. The “data” file which describes the final document These correspond to tags in source document These correspond to segments of html in exported document which were delimited by the tags

33. Sharing Materials: Paul’s control file Paul made homework set number 7 Ken made homework set number 8

34. WQS Sharing: Instructor A can use instructor B’s entire menu simply by copying B’s control file (with permission) Instructor A can use any item in instructor B’s menu simply by copying the corresponding entry from B’s control file (with permission) In either case student email from A’s students will be routed to A and activity logged for A

35. 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

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

37. Sharing: Laura and Jody Do Ma123 Lectures

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

39. Joe Mahoney and Avinash Sathaye did Videos for MA322

40. Unified Format: LaTeX math formatting Video link

41. Web homework is part of text in unified format

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

47. Lessons from WQS Students like posted homework and feedback All students printed problems out and asked system for answer Very few lower division students watch instructional videos – most upper division students watch them. Many lower division students watched short “test review” problems. Bandwidth a major problem with video (CD’s an effective way to address the problem) Most viewed any video-watching outside of class as an extension of class. Lower division students complain about “having to teach themselves” and “can’t learn from a computer” Very few complaints and high level of success from upper division students Resource ratio approximately 5:1 for ma123 this semester (all materials new – short videos), less than 1:1 in 322 (re-using last semester materials) Sharing is very efficient on same system

59. The course Serious mathematics problem solving course Only technology to be learned is Maple (or Mathematica, etc.) –Creative work embedded in Maple source –Protection against changes in software –Solid Knowledge of Mathematics required Emphasis on sharing/collaboration

60. Log format

61. Planned Format Each Problem is a single executable which logs itself –Portability –Security –Will run locally (often requires Maple) Simple Maple source + gui interface

62. Ma375 General Outline Using MathClass (1 wk) Introduction to Maple as Graphing Calculator (1 wk) Elementary Editing and Diagram creation (3 wks) Developing and illustrating problems (2 wks) Constructing solution procedures (2 wks) Collaborative Materials Development Projects (5 wks)

63. Course Outcome: Pre-service teachers will work as part of a team to develop and fully implement a substantial set of materials appropriate to their anticipated practice teaching assignments. Prospective technical graduate students would typically work on courses such as college algebra or basic calculus.

64. Software Sharing The MathClass course materials, preliminary texts, syllabi, etc. will be freely available to faculty at any college interested in experimenting. The MathClass courseware (with source) will be freely available for implementation on any school or college system Student materials will be hosted on UK servers and student accounts maintained through their initial teaching years – regardless of where they took the course All materials developed in these courses would be made available to the non-profit teaching community

65. Examples Need some sample problems – Need to include videos