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Communicating Mathematics : A Problem Solving Approach

Explore the innovative use of technology in teaching mathematics at all levels with a focus on teacher time-saving tools and collaboration. Includes software, materials, workshops, and a support system. Join the movement towards improved math education today!

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Communicating Mathematics : A Problem Solving Approach

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  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 Studentquery Instructor response

  14. Instructor Web Page (part 3) Link to wqs system Link to online text 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 System response Student answer Email window System answer Problem and answers

  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)

  20. How students watch the videos

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

  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. Preparing Materials CD burner and blanks food coffee

  25. 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

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

  27. 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

  28. 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

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

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

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

  32. Sharing: Laura and Jody Do Ma123 Lectures

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

  34. Joe Mahoney and Avinash Sathaye did Videos for MA322

  35. Unified Format: Video link LaTeX math formatting

  36. Web homework is part of text in unified format

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

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

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

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

  41. 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

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

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