MathAssess

Maths in QTI

http://www.sourceforge.net/qtitools

MathAssess is a JISC Demonstrator project

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

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

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!

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

• responseProcessingCompare 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

3x

What does a Maths Variable look like?

It must have• Visual form

expressions are displayed as mathematics

• Semantic meaningexpressions can be manipulated

• Input form for studentsas “natural” as possible

• Input form for authors expresses meaning and hence

appearance

So the variable contains• Presentation MathMLannotated with• Content MathML• CAS code – Maxima

• Input string - ASCIIMathML(if any)

• CAS code – Maximaused in authoring (if any)

Using CASFor• 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.

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...

JAssess

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

JAssess Rendering

• Desktop renderer• MathAssess functionality

MathAssess Tools

MathQurate

Item Author

JQTI2 Rendering API

QTI Assessment Delivery Classes (+XSLT)

TestConstructor+ ASDEL+

Assessment Delivery

Minibix+

Item and Test Storage

JAssess+

Preview Applet

Minibix+ Item Storage API

QTI Assessment Test andItem Banking

Mathqurate Authoring API

QTI Assessment ItemData Classes

Applications

Libraries

QTI Engine

Question Render

Author Store Deliver

Local QuestionPreview

Server Question Preview

Store / RetrieveQuestions

Store / RetrieveTests

DeliverTests

Render Questions

MathQurateNew features:• New interface based upon Eclipse• Uses Java API for XML binding (JAXB)• Uses JQTI2 library for preview• Question features:

– Templates – randomisation– Maths input via LaTeX– customOperator for CAS computations– customInteraction for maths input

Step 1: Create new or import a question

Step 2: Review and edit meta-data

• Edit the meta-data– Identifier– Title– Adaptive attribute

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

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

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

Step 5b: Editing MathML

• SnuggleTex approach• LaTeX input• MathML output• Re-editing supported

Step 5c: Editing Choice Interactions

• Breaks up the XML into digestible information– Metadata editor– HTML and MathML

Prompt editor– List of Simple Choices

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

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

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!

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)

QTIEngine

• QTIEngine is a new QTI rendering and responding engine for both individual items AND complete assessments– Built on top of JQTI2, 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

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

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