1. Maple T.A. Overview André Heck Amsterdam Mathematics, Science and Technology Education Laboratory AMSTEL Institute University of Amsterdam Helsinki, March 9, 2005

2. Contents 1. Background AMSTEL, related projects 2. Maple T.A. Overview demonstration: creating questions & assignments 3. Strengths & Weaknesses illustrative examples

3. 1. The AMSTEL Institute n improve education in the MST-subjects in general for all levels of education n take care of the relation between secondary and higher education concerning content n explore the possibilities of ICT and New Media in MST education and take care of the implementation Our mission:

4. Projects related with CAS-based testing and assessment n 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

5. n Secondary Education GALOIS geïntegreerde algebraïsche leeromgeving in school 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 softwareapplets

6. Main roles of assessment in the projects n Diagnostic tests identify strengths & weaknesses n Self-tests fast feedback on progress in knowledge & skills n Summative assessment grades that count in a portfolio

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. Components of Maple T.A.

9. Short Demonstration of Maple T.A. To get a quick impression of: n Student view n Instructor view n Author view (QBE)

10. Student view n variety of assignments with different policies anonymous practice, homework, study session, mastery session, proctored exam n variety of feedback modes ranging from no grading up to immediate grading and full solutions (set by the instructor) n variety of question types n view on grades and feedback from teacher

11. Instructor view n variety of assignments with different policies to choose from n variety of feedback modes to select n variety of question types to choose n view on and control of grades and feedback from teacher n variety of item banks to select questions from n possibility to test, edit, construct questions

12. Question types in Maple T.A. n Selection type multiple choice, multiple selection, true/false, matching, menu, list n Text-based blank (text or formula), essay n Graphical type clickable image, sketch of a graph n Mathematical & scientific free response (restricted) formula, multiformula, numeric, list, matrix, Maple-graded n Miscellaneous multipart, inline

13. Author view n editing EDU code (plain-text script file) online or offline; error-prone n using the question bank editor (QBE) online; large risk of loosing items or item bank n using the LaTeX2EDU conversion online; peculiar behavior with Maple-graded items n (not yet) using a Maple document offline; immediate testing of Maple code would be possible I prefer LaTeX mode of authoring Various modes of authoring:

14. 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}

15. Features of creating items in Maple T.A. The use of n HTML, MathML in questions & answers n algorithmic variables n Full power of Maple to create questions, grade (free) responses, provide hints & solutions n Maple plots in exercise material

16. 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}

17. 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}

18. 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}

19. 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}

20. 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. }

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. \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. 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); }

24. \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 $g$. }

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 $$(\sin(x^2))'=\cos(x^2)\,2x = 2x\cos(x^2).$$ } \end{question}

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. 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. Major difficulties of CAS-based assessment tools n Author must be familiar with CAS n Questions must sometimes be rephrased for easy marking n Intelligent feedback and marking of free-text responses require rather sophisticated programming n Difficult to foresee the construction of an unsolvable or trivial problem when algorithmic parameters come into play

29. Key Issues for success n Flexible authoring n Algorithmic parameters n Intelligent & immediate feedback n Integration with ELO n Functionality in practice And they are all equally important! Good luck to WebALT-teams

30. The End Questions? Remarks?