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 involvement

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

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 SLIDES/VISUALS Experience with WQS: It does work

Student response to Ma123 as reported in the student paper

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 s 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 online text Link to wqs system Links to lecture slides for video lectures by chapter

WQS System: current 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: Current 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

Test Review with video solutions Problem statement with diagram Link to video solution Maple worksheet With 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 coffee food CD burner and blanks

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 for Figure (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 of html in exported document which were delimited by the tags

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

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 from A’s students will be routed to A and activity logged for A

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

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

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 Course description Walkthrough Math prerequisites Communication –Written, oral, collaboration, continuation, community building

Layout of Ma375 Text/software required Topics Operation Testing Connection with student teaching NSF support – Looking for collaborators/testers Services

Layout continued 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 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”)

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

Lab Activities: Making CD/DVD Operating personal site Evaluation Collaboration Making/integrating video JAVA and other tools