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Communicating Mathematics:A Problem Solving Approach
The creation, implementation, sharing, and management of web-based mathematics
instructional materials
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Project Focus
The Appropriate Application of Technology to Conserve Teacher
Time and Energy
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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,
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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
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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
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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.
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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
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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)
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Student Interface: Instructor’s Web Page (part 1)
System tutorial
Course syllabus
Visual class rolls
Exam schedule
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Class Roll:
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Instructor’s Web Page (part 2)Link to wqs system server
Student emailsfrom homework systemwith responses
Links to lecturenotes for videolectures
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Responses to Student Questions:Page referencesparticular assignment
Student query
Instructorresponse
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Instructor Web Page (part 3)
Link to onlinetext
Link to wqssystem
Links to lectureslides for videolectures by chapter
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WQS System: current login screen
Students selectvideo lecturesmenuor their class homeworkmenu
Group logins andwork are encouraged
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Typical Section Menu
Chapter 1 homework
Review for test II
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Homework Page: Current Format
Problem and answers
Systemresponse
Email window
Student answer
System answer
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Most students print the problem sets out and record their solutions or solutions from class
directly on the printouts
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Video Lectures Menu
Lecture Slides (html)
Video of lecturesegment (10-30 min)
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How students watch the videos
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Test Review with video solutions
Problemstatementwithdiagram
Link to videosolution
Maple worksheetWith links exported to html
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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
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Log Data
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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
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Graduate Student Editing Video Files
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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
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Faculty Preparing Materials
coffeefood
CD burner andblanks
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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
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Maple Source: Homework Problem
Question Tag:( Q_ )
“SKIP”Tags
Answer Tags:( A_ )
Correct Answer Tag
Code forFigure(section)
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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
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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
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The “data” file which describes the final document
These correspond to tags in source document
These correspond to segments ofhtml in exporteddocument which were delimited bythe tags
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Sharing Materials: Paul’s control file
Paul madehomework setnumber 7
Ken madehomework setnumber 8
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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
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B’s Files
control
materials
homework lecture
wqs
ma123
Wqs system
Student loginTo B’s class
1
2
3
4
5
Student loginTo A’s class
B’s Fileswqs
ma123
control
1
2
3
5
LOADSHARING
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Sharing: Laura’s Ma123 Control File and class menu
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Sharing: Laura and Jody Do Ma123 Lectures
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Sharing: Control File for Joe Mahoney’s Paducah, KY Section of Ma322
Carl Eberhart created the homework for the Ma322 sections
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Joe Mahoney and Avinash Sathaye did Videos for MA322
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Unified Format:
LaTeX mathformatting
Video link
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Web homework is part of text in unified format
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Student response to Ma123 as reported in the student paper
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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
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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
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Log format
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Planned Format
• Each Problem is a single executable which logs itself– Portability– Security– Will run locally (often requires Maple)
• Simple Maple source + gui interface
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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)
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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.
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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
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Examples
• Need some sample problems –
• Need to include videos