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http://rutherglen.ics.mq.edu.au/~macqtex

MacQTEX—Online, Randomised,Self-Marking Quizzes

Frances Griffinfgriffin@maths.mq.edu.au

Ross Mooreross@maths.mq.edu.au

Copyright c© 2003 MacQTEXLast Revision Date: July 4, 2003

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Features

• Online interactive quizzes in mathematics.• Self marking, providing feedback to the student.• Numerical parameters are randomised, allowing students to repeat

the same quiz many times with different numbers.• Fully worked solutions become visible once the quiz is completed.• Quizzes are personalised for each student, including name and Stu-

dent Id, personalised message appears on completion.• Delivered as PDF [2, 4, 5] documents containing JavaScript [1, 8]

controlled form fields.• Platform independent, students only need Acrobat 5 running inside

a web browser.• Typeset with pdfLATEX [6, 7] using exerquiz [9] (D.P. Story, Uni

of Akron) for high quality typsetting and forms capability.• Quiz serving and creation system runs in Mac OS X (or other

UNIX platform) using free software.• Three levels of server interaction: a) personalised and records all

results, b) personalised but does not record results, c) stand-alone,with all messages and functions fully self-contained.

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Motivation for the project

• School leavers often lack basic skills in mathematics, leading to con-siderable difficulties in units requiring a reasonable level of math-ematical proficiency.

• Ensure that students do essential revision at beginning of semester,as concepts and techniques are quickly forgotten after exams.

• Encourage students to practise until they understand the materialand can perform the techniques.

• Quizzes are used in first and second year units as compulsory as-sessment tasks, but do not attract marks.

• Indicate to students with insufficient mathematical backgroundthat they might withdraw from the unit before it is too late.

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Online delivery

Student’s browser

Quiz loginpage

(HTML)

Quiz request

Validuser?

Record request

Quizexpired?

Student’s browser

+Acrobat

Apologymessage(HTML)

Attemptlogged

Enoughquizzes?

Wait message(HTML)

Update quizcounters

Make morequizzes

Record quizsent

Error?

Update quizcounters

Delete usedquiz

Send uniquequiz

(FDF — PDF)

Warningmessage(HTML)

No

No

Yes

Yes

No

Yes

Sending a quiz to the student’s browser

Recordaccess denied

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Recording student’s quiz scores

Student’s browser

+Acrobat

Record resultin student’s

individual log

Record resultin main log

Personalizedwarningmessage(FDF)

Check if thisversion isalready

submitted

Result submitted

(URL-encoded)

Student completes quiz

(PDF and JavaScript)

Request log

Personalizedresult message

(FDF)

Yes

No

Recording results from a quiz

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Staff interface

• View student and class logs as tables, graphs or in raw form.

• Make or edit a quiz choosing from existing questions, without writ-ing any LATEX code or JavaScript.

• Reconstruct an old quiz which has been deleted.

• Set or change quiz expiry dates and pass marks.

• Add students to class list.

• Reinstate access for students who have missed the due date.

• Customise messages which display on completion of the quiz, incase of unauthorized login, and in response to a student beingdenied access after due date.

• Get lists of students who are still to complete quiz requirements.

• Generate a skeleton login page containing URLs to the requiredquizzes and appropriate JavaScript for reducing user error.

• Housekeeping (priviledged users only).

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How a quiz is made

The exerquiz package• Provides general mechanism for including form fields and JavaScript

in PDF documents, with special functionality for quizzes.• Quizzes are interactive, eg. answers can be changed at any time,

immediate feedback is given for various user errors.• Self marking, so that quizzes need not communicate with a server.• Solutions are visible after quiz is completed.• Multiple choice questions.• Fill-in-the-answer questions, as text or mathematical expressions.• Text fill-ins use regexps to compare user answer to alternative

forms of the correct answer.• Parses mathematical expressions and randomly selects values for

the variable (default x), evaluating user answer and correct answerat these points. The user answer is considered correct to a givenprecision. Equivalent expressions are recognised.

• Fill-in questions use syntax similar to most programming languages.• Alerts user when invalid expression is entered, such as unbalanced

parentheses, unknown variable, syntax error etc.

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MacQTEX extensions to exerquiz

• Server interaction (although this is now present is the standardversion of exerquiz).

• Different mechanism for linking to and displaying the solutions.

• Different mechanism for displaying correct answers to fill-in ques-tions.

• Hints for multiple choice questions, which indicate why a particularanswer choice is wrong. Visible on completion of the quiz.

• New look and feel using customised version of pdfscreen [11].

• Many extensions to the JavaScript controlling the fill-in questions,including options to

– disallow decimal answers;– evaluate factorials and binomial coefficients, or disallow these,

making students find the numerical answer;– extend the random value selection to only choose integers

when evaluating expressions such as (−3)n;– answers which are lists, such as elements of a set, can be

entered in any order;– parse and test strings in a regular language.;

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• Other extensions to JavaScript in order to– disallow multiple attempts at the same version of the quiz,

this is also checked by the server when quiz results are recorded;– display progress messages on completion of the quiz, either

supplied by server via FDF [3], or internal to the quiz;– implement timings and display the time taken when student

gets perfect score.

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How randomisation is achieved

Quiz creationscript (perl)

Create quiz directoriesAssemble perl sourceLink to LATEX sources

Create LATEX master files

Complete quiz (PDF)

Run LATEX job

Run perl source

for quiz

LATEX definitions

files

HTML form

perl headerperl sources for questions

LATEX sources for questions

Display samplequiz (PDF)

Generate firstbatch of quizzes

Question choicesQuiz title, topicColour scheme

File name

Incomplete quizPDF containing solutions

PDF containing hints

QuizOK

Quizneeds

editing

Final LATEX job

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Programming practicality vs. educational considerations• Multiple choice or fill-in-the-answer?

– Wrong answers for multiple choice questions are based oncommon errors, but sometimes these are not predictable.

– Use multiple choice rather than fill-in for elementary skills.– Correct answer may be too obvious in multiple choice.– Fill-in expressions should be as short as possible.– Fill-in questions require less programming effort than multiple

choice.• How much variation in a single question?

– Questions covering a large number of cases may be elegant,but it can be more time efficient to make several simpler ques-tions instead.

– Lecturers often prefer to have control over which cases arepresented, so these are done as separate questions.

• How much detail should be in the solutions?– Space limits the amount of detail, but students like to see

every step!– If a solution is too long, lead up questions are included, which

establish the techniques needed to answer the more compli-cated question.

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Designing randomisation of questions• Need enough variation to make question interesting, but not so

much that it requires huge effort to program.

• Most programming effort goes into generating the intermediateresults for the solutions.

• Must avoid parameters which give trivial answers or overly tediouscalculations, or duplicate answers in multiple choice questions.

• TEX and JavaScript expressions are passed through filters to re-move silliness such as +− 3x, 1x, x0 etc.

• Simple mathematics sometimes creates tricky programming or type-setting problems.

• Develop algorithms for gcd calculations, nPr,(nr

), reducing frac-

tions and surds to simplest terms, set operations, truth tablesfor randomly generated logical expressions, randomly construct-ing regular languages,. . .

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Why Perl [10] rather than Mathematica or Maple?• Perl ’s string handling provides ease in producing strings in TEX

format.

• Perl ’s overheads are much less than those of specialised algebrapackages.

• Algebra packages still require special programming to generate in-termediate results for solutions.

• Perl ’s special functions such as regexps and eval make it preferableto lower level languages such as C.

• Construction of TEX and JavaScript strings can be built into analgorithm.

• Output of intermediate results becomes part of an algorithm ratherthan a separate task.

• Perl is free, already installed on most UNIX systems.

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Acknowledgements

MacQTEX has received support in the form of• An equipment grant from Apple Computer, Australia Pty Ltd, via

the Apple Universities Consortium;

• Funding via a Targeted Flagship Grant from the Centre for FlexibleLearning, Macquarie University, and the Division of Informationand Communication Sciences, Macquarie University.

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References

[1] Adobe Systems Inc.; “Acrobat Forms JavaScript Object Specifica-tion, Version 5.0.5”; Technical Note #5186; Revised: September 14,2001. 2

[2] Adobe Systems Inc.; Acrobat Reader, viewer for PDF format [4]documents, available free of charge from http://www.adobe.com/.2

[3] Adobe Systems Inc.; “FDF Toolkit Overview”; Technical Note#5194; Revised: August 10, 1999. 9

[4] Adobe Systems Inc.; “PDF Reference second edition AdobePortable Document Format Version 1.3”; July, 2000. 2, 15

[5] Adobe Systems Inc.; “pdfmark Reference Manual, Version: Acrobat5.0”; Technical Note #5150; Adobe Developer Relations; Revised:June 25, 2001. 2

[6] Han, The Thanh; pdf-TEX, free software for generating documentsin PDF format, based on the TEX typesetting system. Available forall computing platforms; see http://www.tug.org/applications/pdftex/. 2

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[7] Lamport, Leslie; LATEX, a Document Preparation System. This isfree software available for all computing platforms. Consult the TEXUser’s Group (TUG) website, at http://www.tug.org/. 2

[8] Netscape Communications Corporation; Core JavaScript Reference,2001; available online at http://developer.netscape.com/docs/manuals/javascript.html. 2

[9] Story, Donald; exerquiz & AcroTEX, packages for including specialeffects in PDF documents, using TEX and LATEX. Dept. of Mathe-matics and Computer Science, University of Akron. Software avail-able online from http://www.math.uakron.edu/~dpstory/webeq.html. 2

[10] Wall, Larry; Perl, a general purpose scripting language for allcomputing platforms. This is Free Software, available from http://www.perl.com/. 13

[11] Radhakrishnan, C.V.; pdfscreen Manual, available from http://www.river-valley.com. 8

[12] Verbruggen, Martien; GDGraph Documentation, available fromhttp://theoryx5.uwinnipeg.ca/CPAN/data/GDGraph/Graph.html.