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
– Course (with text)
– Workshops
• Support System for teachers
• Very much a work in progress
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
Current Approach to
Advancing these Objectives
is through the application of
Technology To Save Teacher
Time
•Automation of tedious tasks
•Collaboration on materials
development
•Sharing resources
•Facilitating parental/community
involvement with students
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
The most obvious (to us)
source of time saving is in the
management of homework
• Assignment
• Checking*
– Feedback
• Logistics
– Collection
– Return
– Record Keeping
The Tools: Part 1 (WQS)
• Used for two years in basic calculus and linear
algebra
• Handles:
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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
Primary Student Interface:
Instructor’s Web Page
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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 emails
from homework
system
with responses
Links to lecture
notes for video
lectures
Responses to Student Questions:
Page references
particular
assignment
Student query
Instructor
response
Instructor Web Page (part 3)
Link to wqs
system
Link to online
text
Links to lecture
slides for video
lectures by
chapter
WQS System: login screen
Students select
video lectures
menu
or their class
homework
menu
Group logins and
work are
encouraged
Typical Section Menu
Chapter 1 homework
Review for test II
Homework Page: Basic Format
System
response
Student
answer
System
answer
Problem
and
answers
Email
window
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 lecture
segment (10-30 min)
How students watch the videos
Test Review with video solutions:
Model for current experiments
Problem
statement
with
diagram
Link to
video
solution
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
Preparing Materials
CD burner and
blanks
food
coffee
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
Maple Source: WQS Homework
Problem
Question
Tag:( Q_ )
“SKIP”
Tags
Code for
Figure
(section)
Answer Tags:
( A_ )
Correct
Answer Tag
SAMPLE WQS TAGS
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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
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
LOAD
SHARING
Student login 1
To B’s class
5
B’s Files
ma123
control
homework
3
5
2
4
materials
wqs
Wqs
system
2
Student login
To A’s class
lecture
3
B’s Files
wqs
ma123
control
1
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:
Video link
LaTeX
math
formatting
Web homework is part of text
in unified format
Experience with WQS:
It does work. But …
• Works much better with motivated, advanced
students
• Primary problem is compliance
• Problem with misinformed faculty, advisors
Student response to Ma123 as
reported in the student paper
Tools: Part 2 (MathClass)
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Currently under development
Subsumes WQS
Very general format
Promotes sharing/collaboration across net:
– development
– individual problems
• Better data management
MathClass Visuals:
MathClass does homework grading in
advance – “frontloads”
Format: Print out problems – work
them away from computer –
Perhaps use computer to work
problem
MathClass Dissemination
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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
Course needs to provide
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Serious introduction to Maple
Comprehensive overview of system structure
Facility with tools
Experience
– Use of the system
– Collaborative materials development
Philosophical Difficulties:
Formally not a Math Class
• Looks on its face like an elementary computer
skills course
• What is the intellectual content?
• Where does it fit in a crowded curriculum?
Observations
• WQS materials move readily to MathClass
(something is conserved)
• Effort is mathematical problem-solving at a nontrivial level
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Creating diagrams, answers (WQS)
Creating solver (MathClass)
Verification
Requires wide variety of math tools even for
elementary problems
• MathClass environment permits development of
non-traditional types of problems .
Conclusion
• The material fits nicely into a mathematical
communications/problem solving course
• Basic Activities are creation, presentation and
solution of problems
– Diagrams,
– Checkers,
• Substitutes for conventional problem solving
course
• Provides communications skills
• Excellent introduction to instructional
technology
Ma375:
Communicating Mathematics
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Course description
Walkthrough
Math prerequisites
Communication
– Written, oral, collaboration, continuation,
community building
Layout of Ma375
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Text/software required
Topics
Operation
Testing
Connection with student teaching
NSF support –
Looking for collaborators/testers
Services
Layout continued
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Security
Intellectual property considerations
Design of modules as executables
NSF requirements
Workshops
Materials
Math 375 (General Outline)
• Using MathClass (2 wks)
• Using Maple to Create Problems (6 wks)
– Basic techniques
– Graphics techniques
– Solvers
• Additional topics and techniques (2 wks)
– Security, intellectual property,
– Video, and other advanced techniques
• Materials development lab (6 wks)
1. Hand sketch
3. Assign values to variables
4. Realize image
2. Abstract Object in Maple
1. Add property (e.g. color)
2. Explore simple
extensions
3. Have students extend it further.
Making Compound Objects
Exercise: Remake
the “K” Cube with
a properly
Formatted “K”
Animation
Basic Drawing/Annotation:
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DL ( “Draw Line”)
PT (“Put Text”)
PP (“Put Point”)
GP (“Graph
Paper”)
• PA (“Put Arc”)
• ARRW (“Dbl or
Sngl Arrow”)
Workshop: Live development of
a problem set
• Make video prompt(s)
Lab Activities:
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Making CD/DVD
Operating personal site
Evaluation
Collaboration
Making/integrating video
JAVA and other tools