1. MathAssess Maths in QTI http://www.sourceforge.net/qtitools MathAssess is a JISC Demonstrator project

2. Partners Liverpool John Moores University – plus Graham Smith and Sue Milne University of Glasgow University of Portsmouth University of Edinburgh - SnuggleTeX Kingston University - AQuRate University of Southampton - ASDEL University of Cambridge - Minibix

3. Item and Test Use Cases Item Author Author questions Edit questions Store questions Student Attempt questions Get new questions Take tests Test Constructor Construct tests Store tests Tutor Assign tests Administer tests

4. Now add Maths... We must be able to: Display maths expressions Manipulate maths expressions Create randomised items, i.e. use templates Compare input and expected answer algebraically, not just string matching...and there’s more!

5. The finer points... templateProcessing  Compute mathematical values (in more complex ways than standard QTI allows)  Use a Computer Algebra System (CAS)  Do not (usually) select from “canned” examples  Set default values and constants as maths expressions responseProcessing  Compare variables with mathematical values algebraically:  Equal? Equivalent? Greater/Less?  Compare expressions involving mathematical variables:  Functions, Coefficients, Terms Feedback  Target student errors – “coeff of is incorrect”  Use mathematical variables in feedback

6. What does a Maths Variable look like? It must have Visual form expressions are displayed as mathematics Semantic meaning expressions can be manipulated Input form for students as “natural” as possible Input form for authors expresses meaning and hence appearance So the variable contains Presentation MathML annotated with Content MathML CAS code – Maxima Input string - ASCIIMathML (if any) CAS code – Maxima used in authoring (if any)

7. Using CAS For Computing groups of maths expressions Computing a single maths expression Comparing two expressions (variables of baseValues) Evaluating a condition customOperator scriptRule casProcess casCompare casCondition customOperators all use Maxima CAS. All can be used in template and response processing.

8. SnuggleTeX & ASCIIMathML SnuggleTeX converts: – LaTeX to XHTML and MathML – PMathML to CMathML – CMathML to CAS code (Maxima) ASCIIMathML converts String input to – (slightly strange) PMathML Maxima can output (strange) PMathML The maths glue joins these up...

9. JAssess New implementation with maths features Has been testbed for “upconversion” Investigating MathAssess requirements Prototype implementation Proof of concept rendering Uses maths glue classes

10. JAssess Rendering Desktop renderer MathAssess functionality

13. MathAssess Tools MathQurate Item Author JQTI 2 Rendering API QTI Assessment Delivery Classes (+XSLT)‏ Test Constructor+ ASDEL+ Assessment Delivery Minibix+ Item and Test Storage JAssess+ Preview Applet Minibix+ Item Storage API QTI Assessment Test and Item Banking Mathqurate Authoring API QTI Assessment Item Data Classes Applications Libraries QTI Engine Question Render AuthorStoreDeliver Local Question Preview Server Question Preview Store / Retrieve Questions Store / Retrieve Tests Deliver Tests Render Questions

14. MathQurate New features: New interface based upon Eclipse Uses Java API for XML binding (JAXB)‏ Uses JQTI 2 library for preview Question features: – Templates – randomisation – Maths input via LaTeX – customOperator for CAS computations – customInteraction for maths input

15. Step 1: Create new or import a question

16. Step 2: Review and edit meta-data Edit the meta-data – Identifier – Title – Adaptive attribute

17. Step 3: Declare template and outcome variables Template variables are used for randomisation Outcome variables are used in response processing, after question submission Edit the variables – Define each variable's identifier – Assign its base type – Assign the cardinality – Set the default value, if any – For template variables also set the mathVariable and parameter flags

18. Step 4: Declare the response variables Some response variables are bound to the student input and compared with the expected answer Response variables are defined for different purposes: – The question response Contains the student input May define a correct answer – Feedback requests e.g. Hint or Solution

19. Step 5a: Editing the item body Edit the content for display to the student Insert and edit MathML where required Insert and edit ChoiceInteraction Basic preview

20. Step 5b: Editing MathML SnuggleTex approach LaTeX input MathML output Re-editing supported

21. Step 5c: Editing Choice Interactions Breaks up the XML into digestible information – Metadata editor – HTML and MathML Prompt editor – List of Simple Choices

22. Step 5d:Editing Simple Choices Each simple choice can contain HTML and MathML Metadata editing Editing of Feedback provided to the student inline when this choice is selected

23. JQTI JQTI is a pure Java library for handling, validating & interpreting QTI 2.x, released under a BSD licence – JQTI v.1 – Full support for the assessment model, partial expression and reporting model support – JQTI v.2 – Adds full support for item, expression and reporting models – Plug-in support for customOperators and customInteractions JQTI-Rendering is a Java library for rendering QTI using a series of XSLTs JQTI-Controller is a library for coordinating the presentation of assessments

24. JQTI + MathAssess No changes to JQTI 2 required for MathAssess CAS support – MathAssess functionality provided by a plug-in library that just needs to be placed on the classpath!

25. Test Constructor+ New features: Use JQTI2 library Take items from item bank (Minibix) using the Maths taxonomy Package as test and deposit back into bank (Minibix)

26. QTIEngine QTIEngine is a new QTI rendering and responding engine for both individual items AND complete assessments – Built on top of JQTI 2, JQTI-Rendering and JQTI- Controller Aims to implement the entirety of the QTI specification! – (currently support for rendering mediaInteraction and drawingInteraction is missing, although they are supported in JQTI) – Includes MathML support for IE+MathPlayer & Mozilla Demo: http://qtiengine.qtitools.org

29. Minibix+ New features: Maths capability Store both items and tests Better search and metadata editing Support organisation by taxonomy Offer support and advice for online testing

33. Coming soon... In MathAssess – Completion of work in progress – Moodle integration – CARET training materials And then... – Content – Live diagrams – Live graphs – Graphical interactions in maths items