1. Web Advanced Learning Technologies WebALT EDC-22253 Mika Seppälä

2. March 9, 2005 Mika Seppälä WebALT Technical Meeting Goal The WebALT project showcases a significant application that uses a combination of existing standards for representing mathematics on the web and existing linguistic technologies in order to enable the creation of language-independent mathematical content. The WebALT project will create software and sample content for an XML database of mathematical problems to be used in undergraduate university courses in mathematics. The technological solutions to be developed by the project can be directly applied to any middle and high school mathematics instruction.

3. March 9, 2005 Mika Seppälä WebALT Technical Meeting Web ALT System CCD -Course Content Definition Third Party Exercise Administration GUIs: Publishers, Serving Mathematics, WebPearls, Maple TA, etc. Problem Tree XML Database On-line Text Traditional Texts Adams Hughes-Hallet et al. Stewart Etc. … Automatic Testing Multilingual Generator

4. March 9, 2005 Mika Seppälä WebALT Technical Meeting Main Deliverables Structure for the Problem Database allowing detailed classification of the problems and the problem trees – Course Content Definitions (CCD) XML vocabulary that enables the creation of language independent mathematical content Editors for Problems, Problem Trees and for the CCD High quality sample content

5. March 9, 2005 Mika Seppälä WebALT Technical Meeting Components of Algorithmic Problems Problem body Code for algorithmic problems Code to evaluate the answer Hints (several levels with links) Solutions Feed-back – can be used to build problem trees Problem body, hints, solutions and feed-back contain language independent text fragments.

6. March 9, 2005 Mika Seppälä WebALT Technical Meeting Example (MapleTA Problem) Problem $var=switch(rint(5),x,t,u,s,v); $pf = maple('simplify(($d1)/(($var)+($a1))+(($c1)*($var)+ ($d2))/(($var)^2+($b1p)))'); $f=maple('sort(numer($pf))/denom($pf)'); $ff=maple('printf(MathML:-ExportPresentation($f))'); Here the parameters $a1, $c1, $d1 and $d2 have the range from -5 to 5 and must be different from 0. The parameter $b1p has the range from 1 to 10. This generates 100 000 different versions of the same problem.

7. March 9, 2005 Mika Seppälä WebALT Technical Meeting Remarks on the Algorithm $var=switch(rint(5),x,t,u,s,v); $pf = maple('simplify(($d1)/(($var)+($a1))+(($c1)*($var)+ ($d2))/(($var)^2+($b1p)))'); $f=maple('sort(numer($pf))/denom($pf)'); $ff=maple('printf(MathML:-ExportPresentation($f))'); Variable names can be selected algorithmically.

8. March 9, 2005 Mika Seppälä WebALT Technical Meeting Remarks on the Algorithm $var=switch(rint(5),x,t,u,s,v); $pf = maple('simplify(($d1)/(($var)+($a1))+(($c1)*($var)+ ($d2))/(($var)^2+($b1p)))'); $f=maple('sort(numer($pf))/denom($pf)'); $ff=maple('printf(MathML:-ExportPresentation($f))'); Variable names can be selected algorithmically. Maple can be used to build and to manipulate mathematical expressions.

9. March 9, 2005 Mika Seppälä WebALT Technical Meeting Remarks on the Algorithm $var=switch(rint(5),x,t,u,s,v); $pf = maple('simplify(($d1)/(($var)+($a1))+(($c1)*($var)+ ($d2))/(($var)^2+($b1p)))'); $f=maple('sort(numer($pf))/denom($pf)'); $ff=maple('printf(MathML:-ExportPresentation($f))'); Variable names can be selected algorithmically. Maple can be used to build and to manipulate mathematical expressions. Maple can be used to create MathML expressions that can be used in the question body, hints, solutions and in the feedback.

10. March 9, 2005 Mika Seppälä WebALT Technical Meeting Grading evalb(whattype($RESPONSE)=`+` and (degree(denom(op(1,($RESPONSE))),($var))=1 or degree(denom(op(1,($RESPONSE))),($var))=2) and (degree(denom(op(2,($RESPONSE))),($var))=1 or degree(denom(op(2,($RESPONSE))),($var))=2) and simplify(($RESPONSE)- ($ANSWER))=0); The code that grades students’ answers may be a rather sophisticated Maple program. In this example the grading is done by one command only.

11. March 9, 2005 Mika Seppälä WebALT Technical Meeting Answer Problem Answer The possibility to create algorithmic problems makes all the difference. Students can practice as many times as they want with the same question and get a different version of it every time.

12. March 9, 2005 Mika Seppälä WebALT Technical Meeting WebALT editor Has to support all the features of MapleTA/AiM question banks, especially the problem programming languages Has to add META information to problems to make it possible to easily retrieve problems of a given type (CCD) Text fragments need to be encoded so that versions of problems can be generated in many languages automatically Debugging needs to be solved in a good way

13. March 9, 2005 Mika Seppälä WebALT Technical Meeting WP 1: State of Art and Requirements Mile Stone 1: Report, ready by Month 3 WP 2: CCD vocabulary beta development WP 3: Multilingual tools beta development Mile Stone 2: CCD with a prototype, Month 9 Mile Stone 3: Multilingual tools and a prototype, Month 11 WP 5: WebALT beta WP 6: Dissemination, Month 18 WP 4: Evaluation, Month 24 Mile Stone 4: WebALT beta, Month 17 WP 7: Final Showcase of WebALT Mile Stone 5: Final Showcase of WebALT by Month 24