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Communicating Mathematics : A Problem Solving Approach

Communicating Mathematics : A Problem Solving Approach. Paul Eakin, Carl Eberhart, Ken Kubota, Dan Chaney,. General Program. R&D on effective application of communications technology to the teaching of mathematics software, methodology, materials Associated Dissemination Project

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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 involvement

  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 • Can be used independently of local school 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. WQS SLIDES/VISUALSExperience with WQS:It does work

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

  11. 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)

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

  13. Class Roll:

  14. 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

  15. Responses to Student Questions: Page references particular assignment Studentquery Instructor response

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

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

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

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

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

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

  22. How students watch the videos

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

  24. 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

  25. Log Data

  26. 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

  27. Graduate Student Editing Video Files

  28. 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

  29. Faculty Preparing Materials CD burner and blanks food coffee

  30. 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

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

  32. 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

  33. 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

  34. 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

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

  36. 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

  37. 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

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

  39. Sharing: Laura and Jody Do Ma123 Lectures

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

  41. Joe Mahoney and Avinash Sathaye did Videos for MA322

  42. Unified Format: Video link LaTeX math formatting

  43. Web homework is part of text in unified format

  44. Tools: Part 2 (MathClass) • Currently under development • Subsumes WQS • Very general format • 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

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