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: formatted Mathematics Chat groups Student-teacher Visual rolls Video lectures Sharing of problem sets Has primitive data handling Multiple choice format Too much data

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

Class Roll:

Instructor’s Web Page (part 2) Link to wqs system server Student s from homework system with responses Links to lecture notes for video lectures

Homework Page: Basic Format Problem and answers System response 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 lecture segment (10-30 min)

How students watch the videos

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 coffee food CD burner and blanks

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

Responses to Student Questions: Page references particular assignment Student query Instructor response

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

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 Answer Tags: ( A_ ) Correct Answer Tag Code for Figure (section)

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: Paul made homework set number 7 Ken made homework set number 8 This is Paul’s Control file

B’s Files control materials homeworklecture wqs ma123 Wqs system Student login To B’s class Student login To A’s class B’s Files wqs ma123 control LOAD SHARING

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 math formatting Video link

Web homework is part of text in unified format

Student response to Ma123 as reported in the student paper

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

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

Phase II: (MathClass) Currently under development Subsumes WQS Very general format Promotes sharing/collaboration across net: –development –individual problems Better data management

Now Have Two Years’s Experience With Technology Development Program –Useful, –Improving Systematic testing and evaluation program

Must Begin to Address Dissemination to users User training User support –Materials distribution

MathClass Dissemination Software and Service Software freely distributed (except Maple) Materials sharing features also provide free source of materials Problem (apparent) is hosting of service –Need reliable, convenient, efficient, persistent site location –Need full contol –Need after-hours access

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

Initial Focus is on Pre-service Teachers They have TIME –Learn operation, tools, techniques –Set up and operate personal site –Prepare and implement complete, operational material sets –Form collaborative relationships for continuation They can provide collegial consultation at their host schools

Course for Pre-Service Teachers Needs to Provide: Introduction to Maple (including graphics) Comprehensive overview of how such systems work Facility with tools Experience in: –Use of system –Collaborative development of materials (teamwork)

Philosophical Difficulties: Not a math class as describes Looks like an elementary computer skills class Thin intellectual content? Fit in a crowded curriculum?

Observations WQS materials move readily to MathClass (something is conserved) Effort is mathematical problem-solving at a non- trivial level –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.

Mathematical Content Designing problems –Includes solving them Creating diagrams, answers (WQS) Creating Solvers –Validation Math required for even elementary problems: –Geometry, algebra, trig, formal logic, calculus, linear algebra,..

Conclusions The material fits nicely into a mathematical communications/problem solving course Basic activities: creation, presentation, solution of problems –Illustrations –Solvers Excellent introduction to instructional technology in mathematics Communications skills

Ma375: Communicating Mathematics Course description Walkthrough Math prerequisites Communication –Written, oral, collaboration, continuation, community building

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)

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

Basic Maple Technique Quick start: Maple as graphing calculator –Notes developed by Carl Graphics techniques Basic programming –In context of solving problems and developing solvers for problems

MathClass Training Requirements 1 day workshop for introduction as user 2-day workshop for operational site 3 day materials development workshop for experienced teacher familiar with Maple 2 week materials development workshop for experienced teacher familiar with Maple Comprehensive one-semester course for pre-service teacher

1. Hand sketch 2. Abstract Object in Maple 3. Assign values to variables 4. Realize image

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: DL ( “Draw Line”) PT (“Put Text”) PP (“Put Point”) GP (“Graph Paper”) PA (“Put Arc”) ARRW (“Dbl or Sngl Arrow”)

Early Lab ACtivities Operating individual MathClass sites –Student chats, s –Managing data Working with extant materials Making/integrating graphics/video –Class rolls Making CD/DVD etc

Major Course Project: Development and Implementation of Student Teaching Materials Done with student team In consultation with supervising teacher Site will be maintained throughout student teaching and beyond

Workshop: Live development of a problem set Make video prompt(s)