Communicating Mathematics:A Problem Solving Approach

The creation, implementation, sharing, and management of web-based mathematics

instructional materials

Project Focus

The Appropriate Application of Technology to Conserve Teacher

Time and Energy

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,

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

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

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.

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

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)

Student Interface: Instructor’s Web Page (part 1)

System tutorial

Course syllabus

Visual class rolls

Exam schedule

Class Roll:

Instructor’s Web Page (part 2)Link to wqs system server

Student emailsfrom homework systemwith responses

Links to lecturenotes for videolectures

Responses to Student Questions:Page referencesparticular assignment

Student query

Instructorresponse

Instructor Web Page (part 3)

Link to onlinetext

Link to wqssystem

Links to lectureslides for videolectures by chapter

WQS System: current login screen

Students selectvideo lecturesmenuor their class homeworkmenu

Group logins andwork are encouraged

Typical Section Menu

Chapter 1 homework

Review for test II

Homework Page: Current Format

Problem and answers

Systemresponse

Email window

Student answer

System answer

Most students print the problem sets out and record their solutions or solutions from class

directly on the printouts

Video Lectures Menu

Lecture Slides (html)

Video of lecturesegment (10-30 min)

How students watch the videos

Test Review with video solutions

Problemstatementwithdiagram

Link to videosolution

Maple worksheetWith links exported to html

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

Log Data

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

Graduate Student Editing Video Files

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

Faculty Preparing Materials

coffeefood

CD burner andblanks

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

Maple Source: Homework Problem

Question Tag:( Q_ )

“SKIP”Tags

Answer Tags:( A_ )

Correct Answer Tag

Code forFigure(section)

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

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

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

Sharing Materials: Paul’s control file

Paul madehomework setnumber 7

Ken madehomework setnumber 8

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

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

Sharing: Laura’s Ma123 Control File and class menu

Sharing: Laura and Jody Do Ma123 Lectures

Sharing: Control File for Joe Mahoney’s Paducah, KY Section of Ma322

Carl Eberhart created the homework for the Ma322 sections

Joe Mahoney and Avinash Sathaye did Videos for MA322

Unified Format:

LaTeX mathformatting

Video link

Web homework is part of text in unified format

Student response to Ma123 as reported in the student paper

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

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

Log format

Planned Format

• Each Problem is a single executable which logs itself– Portability– Security– Will run locally (often requires Maple)

• Simple Maple source + gui interface

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)

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.

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

Examples

• Need some sample problems –

• Need to include videos