Maple T.A. Overview

André Heck

Amsterdam Mathematics, Science and Technology Education Laboratory

AMSTEL InstituteUniversity of Amsterdam

Helsinki, March 9, 2005

Contents 1. Background

AMSTEL, related projects

2. Maple T.A. Overview demonstration: creating questions & assignments

3. Strengths & Weaknesses illustrative examples

1. The AMSTEL Institute

improve education in the MST-subjects in general for all levels of education

take care of the relation between secondary and higher education concerning content

explore the possibilities of ICT and New Media in MST education and take care of the implementation

Our mission:

Projects related with CAS-based testing and assessment

Higher Education

- Foundation Year- Diagnostic testing of new students- Webspijkeren- MathMatch

preparing a heterogeneous group of students in making the transition - from school to university math- from bachelor to master

Secondary Education

GALOIS geïntegreerde algebraïsche leeromgeving in school

developing a framework at school forpupils to: - assess their own progress- have access to a large amount of exercise material (CAS-based tests, applets, ….)- get intelligent feedback on their work- store their activities and answers (+ the route to the answers) in the ELO

Major constraint: open source software

Main roles of assessment in the projects

Diagnostic tests identify strengths & weaknesses

Self-testsfast feedback on progress in knowledge & skills

Summative assessmentgrades that count in a portfolio

2. Maple T.A.

A web-based system for- generating exercises and automatically assessing students’ responses- delivering tests and assessments- administering students’ results and giving them feedback

Main software ingredients:- Maple- Brownstone’s EDU Campus- (if required) Blackboard Building Block

Components of Maple T.A.

Short Demonstration ofMaple T.A.

To get a quick impression of: Student view Instructor view Author view (QBE)

Student view

variety of assignmentswith different policiesanonymous practice, homework, study session, mastery session, proctored exam

variety of feedback modes ranging from no grading up to immediate gradingand full solutions (set by the instructor)

variety of question types view on grades and feedback from

teacher

Instructor view

variety of assignmentswith different policies to choose from

variety of feedback modes to select variety of question types to choose view on and control of grades and

feedback from teacher variety of item banks to select questions

from possibility to test, edit, construct

questions

Question types in Maple T.A. Selection type

multiple choice, multiple selection, true/false, matching, menu, list

Text-basedblank (text or formula), essay

Graphical typeclickable image, sketch of a graph

Mathematical & scientific free response(restricted) formula, multiformula, numeric, list,

matrix, Maple-graded Miscellaneous

multipart, inline

Author view

editing EDU code (plain-text script file)online or offline; error-prone

using the question bank editor (QBE)online; large risk of loosing items or item bank

using the LaTeX2EDU conversiononline; peculiar behavior with Maple-graded items

(not yet) using a Maple documentoffline; immediate testing of Maple code would be possible

I prefer LaTeX mode of authoring

Various modes of authoring:

A simple LaTeX example

\begin{question}{MultipleChoice}

\name{example 1}

\qutext{Given $f(x)=(x+3)^2$, find $f(x+5)$}

\choice*{$(x+8)^2$}

\choice{$x^2+6x+14$}

\choice{$x^2+10x+24$}

\choice{none of these}

\end{question}

Features of creating items in Maple T.A.

The use of HTML, MathML in questions & answers algorithmic variables Full power of Maple to create questions,

grade (free) responses, provide hints & solutions

Maple plots in exercise material

Free response question

Maple is used for grading in \answer statement;

it takes care of algebraic equivalence testing

\begin{question}{Formula}

\name{example 2}

\qutext{Given $f(x)=(x+3)^2$, find $f(x+5)$.}

\answer{(x+8)^2}

\end{question}

With algorithmic parameters

\begin{question}{Formula}\name{example 3}\qutext{Given $f(x)=(x+\var{a})^2$,

find $f(x+\var{b})$}\answer{(x+\var{c})^2}\code{$a=range(1,6); $b=range(1,6); $c=$a+$b; $ans=mathml((x+$c)^2);}\comment{Correct answer is \var{ans}}\end{question}

Highlighting of some parts:Introduction of algorithmic parameters in \code

\begin{question}{Formula}\name{example 3}\qutext{Given $f(x)=(x+\var{a})^2$,

find $f(x+\var{b})$}\answer{(x+\var{c})^2}\code{$a=range(1,6); $b=range(1,6); $c=$a+$b; $ans=mathml((x+$c)^2);}\comment{Correct answer is \var{ans}}\end{question}

Use of algorithmic parameters elsewhere

\begin{question}{Formula}\name{example 3}\qutext{Given $f(x)=(x+\var{a})^2$,

find $f(x+\var{b})$}\answer{(x+\var{c})^2}\code{$a=range(1,6); $b=range(1,6); $c=$a+$b; $ans=mathml((x+$c)^2);}\comment{Correct answer is \var{ans}}\end{question}

Maple-graded question

\begin{question}{Maple}

\name{example 4}

\type{formula}

\qutext{

Give an example of an even function on the

interval (-1,1). Only specify the function body.

\newline

You can also plot the graph of your answer on

this interval to verify your answer.

}

\maple*{ expr := $RESPONSE; var:= remove(type, indets(expr,name), realcons); if nops(vars)<>1 then check := false; else var := op(var); check := evalb( simplify(expr - eval(expr, var=-var))=0 ); end if; evalb(check);}

\plot*{ expr := $RESPONSE; plot(expr,x=-1..1);}\comment{ If your answer is marked as wrong, this is because the vertical axis is not a symmetry axis for the graph of your function.}\end{question}

Because of the \plot statement a student can see the graph of his/her response and verify the property

Avoiding Maple syntax in answer and providing a solution\begin{question}{Maple}

\name{example 5}

\qutext{Compute the derivative of $\sin(x^2)$.}

\maple*{

expr := $RESPONSE;

evalb([0,0]=StringTools[Search](["diff","D"],

"$RESPONSE")) and

evalb(simplify(expr-$answer)=0);

}

\code{ $answer = maple("diff(sin(x^2),x)"); $answerdisplay = maple( "printf(MathML:-ExportPresentation($answer))");}\comment{ Use the chain rule to differentiate this formula. The correct answer is \var{answerdisplay}.}\hint{ Use the chain rule: $$(f(g(x)))'=f'(g(x))\,g'(x),$$ for differentiable functions $f$ and $g$.}

\solution{ The chain rule is: $$(f(g(x)))'=f '(g(x)) g'(x),$$ for differentiable functions $f$ and $g$. In this exercise $f(x)=\sin x$ and $g(x)=x^2$. So, $f '(x)=\cos x$ and $g'(x)=2x$. Therefore $$(\sin(x^2))'=\cos(x^2)\,2x = 2x\cos(x^2).$$}\end{question}

3. Strengths & Weaknesses

Strong points of Maple T.A. - variety of question types- large amount of exercise material can be created effectively- algorithmic variables can also be used in hints, solutions, feedback- rather good display, input, and creation of formulas; HTML can also be used - easy authoring knowing Latex and Maple - smoothly working together with Blackboard

Weaknesses of Maple T.A. - no good question chaining and combining of response fields- limited partial credit- limited feedback to student’s response- no good standalone authoring at present- ruling out Maple syntax is clumsy- no good facilities to test Maple code first- user interface is more rooted in software engineering than in educational design- no easily adaptable user interface- no language adaptation possible

Major difficulties of CAS-based assessment tools Author must be familiar with CAS Questions must sometimes be

rephrased for easy marking Intelligent feedback and

marking of free-text responses require rather sophisticated programming

Difficult to foresee the construction of an unsolvable or trivial problem when algorithmic parameters come into play

Key Issues for success Flexible authoring Algorithmic parameters Intelligent & immediate feedback Integration with ELO Functionality in practice

And they are all equally important!

Good luck to WebALT-teams

The End

Questions? Remarks?