heck
DESCRIPTION
WebALTHelsinkAndré HeckTRANSCRIPT
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Maple T.A. Overview
André Heck
Amsterdam Mathematics, Science and Technology Education Laboratory
AMSTEL InstituteUniversity of Amsterdam
Helsinki, March 9, 2005
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Contents 1. Background
AMSTEL, related projects
2. Maple T.A. Overview demonstration: creating questions & assignments
3. Strengths & Weaknesses illustrative examples
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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:
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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
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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
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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
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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
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Components of Maple T.A.
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Short Demonstration ofMaple T.A.
To get a quick impression of: Student view Instructor view Author view (QBE)
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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
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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
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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
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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:
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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}
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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
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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}
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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}
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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}
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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}
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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.
}
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\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);}
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\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
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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);
}
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\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 $g$.}
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\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}
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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
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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
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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
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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
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The End
Questions? Remarks?