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André Heck

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  1. 1. Maple T.A. Overview <ul><li>André Heck </li></ul><ul><li>A msterdam M athematics, S cience and T echnology E ducation L aboratory </li></ul><ul><li>AMSTEL Institute </li></ul><ul><li>University of Amsterdam </li></ul><ul><li>Helsinki, March 9, 2005 </li></ul>
  2. 2. Contents <ul><li>Background AMSTEL, related projects </li></ul><ul><li>Maple T.A. Overview demonstration: creating questions & assignments </li></ul><ul><li>Strengths & Weaknesses illustrative examples </li></ul>
  3. 3. 1. The AMSTEL Institute <ul><li>improve education in the MST-subjects in general for all levels of education </li></ul><ul><li>take care of the relation between secondary and higher education concerning content </li></ul><ul><li>explore the possibilities of ICT and New Media in MST education and take care of the implementation </li></ul>Our mission:
  4. 4. Projects related with CAS-based testing and assessment <ul><li>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 </li></ul>
  5. 5. <ul><li>Secondary Education GALOIS g eïntegreerde a lgebraïsche l eer o mgeving i n s chool </li></ul><ul><li>developing a framework at school for pupils 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 </li></ul>
  6. 6. <ul><li>Main roles of assessment in the projects </li></ul><ul><li>Diagnostic tests identify strengths & weaknesses </li></ul><ul><li>Self-tests fast feedback on progress in knowledge & skills </li></ul><ul><li>Summative assessment grades that count in a portfolio </li></ul>
  7. 7. 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
  8. 8. Components of Maple T.A.
  9. 9. Short Demonstration of Maple T.A. <ul><li>To get a quick impression of: </li></ul><ul><li>Student view </li></ul><ul><li>Instructor view </li></ul><ul><li>Author view (QBE) </li></ul>
  10. 10. Student view <ul><li>variety of assignments with different policies anonymous practice, homework, study session, mastery session, proctored exam </li></ul><ul><li>variety of feedback modes ranging from no grading up to immediate grading and full solutions (set by the instructor) </li></ul><ul><li>variety of question types </li></ul><ul><li>view on grades and feedback from teacher </li></ul>
  11. 11. Instructor view <ul><li>variety of assignments with different policies to choose from </li></ul><ul><li>variety of feedback modes to select </li></ul><ul><li>variety of question types to choose </li></ul><ul><li>view on and control of grades and feedback from teacher </li></ul><ul><li>variety of item banks to select questions from </li></ul><ul><li>possibility to test, edit, construct questions </li></ul>
  12. 12. Question types in Maple T.A. <ul><li>Selection type multiple choice, multiple selection, true/false, matching, menu, list </li></ul><ul><li>Text-based blank (text or formula), essay </li></ul><ul><li>Graphical type clickable image, sketch of a graph </li></ul><ul><li>Mathematical & scientific free response (restricted) formula, multiformula, numeric, list, matrix, Maple-graded </li></ul><ul><li>Miscellaneous multipart, inline </li></ul>
  13. 13. Author view <ul><li>editing EDU code (plain-text script file) online or offline; error-prone </li></ul><ul><li>using the question bank editor (QBE) online; large risk of loosing items or item bank </li></ul><ul><li>using the LaTeX2EDU conversion online; peculiar behavior with Maple-graded items </li></ul><ul><li>(not yet) using a Maple document offline; immediate testing of Maple code would be possible </li></ul><ul><li>I prefer LaTeX mode of authoring </li></ul>Various modes of authoring:
  14. 14. A simple LaTeX example <ul><li>egin{question}{MultipleChoice} </li></ul><ul><li> ame{example 1} </li></ul><ul><li>qutext{Given $f(x)=(x+3)^2$, find $f(x+5)$} </li></ul><ul><li>choice*{$(x+8)^2$} </li></ul><ul><li>choice{$x^2+6x+14$} </li></ul><ul><li>choice{$x^2+10x+24$} </li></ul><ul><li>choice{none of these} </li></ul><ul><li>end{question} </li></ul>
  15. 15. <ul><li>Features of creating items in Maple T.A. </li></ul><ul><li>The use of </li></ul><ul><li>HTML, MathML in questions & answers </li></ul><ul><li>algorithmic variables </li></ul><ul><li>Full power of Maple to create questions, grade (free) responses, provide hints & solutions </li></ul><ul><li>Maple plots in exercise material </li></ul>
  16. 16. Free response question <ul><li>Maple is used for grading in answer statement; </li></ul><ul><li>it takes care of algebraic equivalence testing </li></ul><ul><li>egin{question}{Formula} </li></ul><ul><li> ame{example 2} </li></ul><ul><li>qutext{Given $f(x)=(x+3)^2$, find $f(x+5)$.} </li></ul><ul><li>answer{(x+8)^2} </li></ul><ul><li>end{question} </li></ul>
  17. 17. With algorithmic parameters <ul><li>egin{question}{Formula} </li></ul><ul><li> ame{example 3} </li></ul><ul><li>qutext{Given $f(x)=(x+var{a})^2$, find $f(x+var{b})$} </li></ul><ul><li>answer{(x+var{c})^2} </li></ul><ul><li>code{$a=range(1,6); </li></ul><ul><li>$b=range(1,6); </li></ul><ul><li>$c=$a+$b; </li></ul><ul><li>$ans=mathml((x+$c)^2);} </li></ul><ul><li>comment{Correct answer is var{ans}} </li></ul><ul><li>end{question} </li></ul>
  18. 18. Highlighting of some parts: Introduction of algorithmic parameters in code <ul><li>egin{question}{Formula} </li></ul><ul><li> ame{example 3} </li></ul><ul><li>qutext{Given $f(x)=(x+var{a})^2$, find $f(x+var{b})$} </li></ul><ul><li>answer{(x+var{c})^2} </li></ul><ul><li>code{$a=range(1,6); </li></ul><ul><li>$b=range(1,6); </li></ul><ul><li>$c=$a+$b; </li></ul><ul><li>$ans=mathml((x+$c)^2);} </li></ul><ul><li>comment{Correct answer is var{ans}} </li></ul><ul><li>end{question} </li></ul>
  19. 19. Use of algorithmic parameters elsewhere <ul><li>egin{question}{Formula} </li></ul><ul><li> ame{example 3} </li></ul><ul><li>qutext{Given $f(x)=(x+ var{a} )^2$, find $f(x+ var{b} )$} </li></ul><ul><li>answer{(x +var{c} )^2} </li></ul><ul><li>code{$a=range(1,6); </li></ul><ul><li>$b=range(1,6); </li></ul><ul><li>$c=$a+$b; </li></ul><ul><li>$ans=mathml((x+$c)^2);} </li></ul><ul><li>comment{Correct answer is var{ans} } </li></ul><ul><li>end{question} </li></ul>
  20. 20. Maple-graded question <ul><li>egin{question}{Maple} </li></ul><ul><li> ame{example 4} </li></ul><ul><li> ype{formula} </li></ul><ul><li>qutext{ </li></ul><ul><li>Give an example of an even function on the </li></ul><ul><li>interval (-1,1). Only specify the function body. </li></ul><ul><li> ewline </li></ul><ul><li>You can also plot the graph of your answer on </li></ul><ul><li>this interval to verify your answer. </li></ul><ul><li>} </li></ul>
  21. 21. 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); }
  22. 22. 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
  23. 23. Avoiding Maple syntax in answer and providing a solution <ul><li>egin{question}{Maple} </li></ul><ul><li> ame{example 5} </li></ul><ul><li>qutext{Compute the derivative of $sin(x^2)$.} </li></ul><ul><li>maple*{ </li></ul><ul><li>expr := $RESPONSE; </li></ul><ul><li>evalb([0,0]=StringTools[Search]([&quot;diff&quot;,&quot;D&quot;], </li></ul><ul><li>&quot;$RESPONSE&quot;)) and </li></ul><ul><li>evalb(simplify(expr-$answer)=0); </li></ul><ul><li>} </li></ul>
  24. 24. code{ $answer = maple(&quot;diff(sin(x^2),x)&quot;); $answerdisplay = maple( &quot;printf(MathML:-ExportPresentation($answer))&quot;); } 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 $g$. }
  25. 25. 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 $$(sin(x^2))'=cos(x^2),2x = 2xcos(x^2).$$ } end{question}
  26. 26. 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
  27. 27. 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
  28. 28. Major difficulties of CAS-based assessment tools <ul><li>Author must be familiar with CAS </li></ul><ul><li>Questions must sometimes be rephrased for easy marking </li></ul><ul><li>Intelligent feedback and marking of free-text responses require rather sophisticated programming </li></ul><ul><li>Difficult to foresee the construction of an unsolvable or trivial problem when algorithmic parameters come into play </li></ul>
  29. 29. Key Issues for success <ul><li>Flexible authoring </li></ul><ul><li>Algorithmic parameters </li></ul><ul><li>Intelligent & immediate feedback </li></ul><ul><li>Integration with ELO </li></ul><ul><li>Functionality in practice </li></ul><ul><li>And they are all equally important! </li></ul><ul><li>Good luck to WebALT-teams </li></ul>
  30. 30. The End Questions? Remarks?