Mathematical Interactive Exercise Generation From Static Documents

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Mathematical Interactive Exercise Generation From
Static Documents
Manolis Mavrikis School of
MathematicsUniversity of Edinburgh
Alberto González PalomoToledo Spain
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Motivation
Content for (mathematical) educational systems
- authoring is time consuming - not easily
reusable, shareable
common specifications for content are necessary
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Exercises
- Question and Test Interoperability (QTI) no
consideration for mathematical questions - OMDoc
no particular structure for exercises (until
MKM Bertinoro) - others ?
There are many systems that use different
techniques and their own format - WALLIS
(JavaScript templates and JSPs) - Alice
Interactive Mathematics (own programming
language) - MapleTA (Maple specific syntax) -
CUE, SToMp (their own XML structures)
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Exercises
- complex structures e.g nested multiple
parts - adaptive feedback - interactivity -
mathematics !
example
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The rest of the talk
Examples from an exercise description language
that - separates content from
presentation - achieves question
randomisation - represents multiple structures
interaction - helps in providing adaptive
feedback/presentation
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Mathematical entities
ltOMOBJgt ltOMAgt ltOMS cdrelation1"
name"eq"/gt ltOMV name"A"/gt ltOMAgt
ltOMS cd"linalg2" name"matrix"/gt ltOMAgt
ltOMS cd"linalg2" name"matrixrow"/gt
ltOMI id"m_1_1"gt1lt/OMIgt ltOMI
id"m_1_2"gt2lt/OMIgt lt/OMAgt ltOMAgt
ltOMS cd"linalg2" name"matrixrow"/gt
ltOMI id"m_2_1"gt3lt/OMIgt ltOMI
id"m_2_2"gt4lt/OMIgt lt/OMAgtlt/OMAgt
lt/OMAgt lt/OMOBJgt
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Mathematical entities
XHTML or OpenMath ? presentation
MathML ?
HTML (with CSS)
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Exercises with Mathematical Entities
Use a ltmatch-textgt element to replace the parts
where we want to create blanks or any type of
questions
ltreplacegt ltblank for"m_1_1" size"2"
id"blank_1"/gt ltblank for"m_1_2" size"2"
id"blank_2"/gt ltblank for"m_2_1" size"2"
id"blank_3"/gt ltblank for"m_2_2" size"2"
id"blank_4"/gt lt/replacegt
This separates further the presentation from
content and makes authoring easier.
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this could work for other schemes
XML is ltspan idmatch1gtgreatlt/spangt because it
ltspan idmatch2gtseparateslt/spangt content from
ltspan idmatch3gtpresentationlt/spangt.
ltreplacegt ltblank for"match1" size10"
id"blank_1"/gt ltblank formatch2" size10"
id"blank_2"/gt ltchoice formatch3"
multiplenogt lt/choicegt lt/replacegt
example
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Randomisation variable use

can help speed up authoring - declared
manually once and used in several places in
the document or feedback elements to produce
a different question OR - randomised by the
system (need more care)

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ltvariablesgt lt!--mix and max are
inclusive--gt ltvar id"m" minvalue"1"
maxvalue"3"/gt ltvar id"f_tmp" minvalue"0"
maxvalue"1"/gt ltvar id"f"
expression"Yes"gt2f_tmp-1lt/vargt ltvar
id"n_tmp" minvalue"1" maxvalue"3"/gt ltvar
id"n" expression"Yes"gtn_tmpm1lt/vargt ltvar
id"z" minvalue"1" maxvalue"10"/gt ltvar
id"a" expression"Yes"gtm4nflt/vargt ltvar
id"b" expression"Yes"gt4(m-nf)lt/vargt ltvar
id"hb" expression"Yes"gtb/2lt/vargt ltvar
id"c" expression"Yes"gt4mnflt/vargt ltvar
id"d" expression"Yes"gt5zlt/vargt lt/variablesgt
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11?x22?x?y3?y24
ltOMAgt ltOMS
cd"arith1" name"power"/gt ltOMV
name"x"/gt ltOMIgt2lt/OMIgt lt/OMAgt
lt/OMAgt ltOMAgt ltOMS cd"arith1"
name"times"/gt ltOMV name"b"/gt ltOMV
name"x"/gt ltOMV name"y"/gt lt/OMAgt
ltOMAgt ltOMS cd"arith1"
name"times"/gt ltOMV name"c"/gt
ltOMAgt ltOMS cd"arith1" name"power"/gt
ltOMV name"y"/gt
ltOMIgt2lt/OMIgt lt/OMAgt lt/OMAgt
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Interaction
Define a structure - easy to author, maintain,
database - represent the directed graph but with
a shallow structure - general enough - clear
separation of interactive layer from
content Benefits - speed authoring
process - makes document manageable
and reusable
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Response conditions
ltmap-action type"reply"gt ltcond
xref"1st_part_misconception1"gt
ltnum_equal for"blank_1"gt2lt/num_equalgt
ltnum_equal for"blank_2"gt3lt/num_equalgt
lt/condgt lt/respconditiongt
ltitem id"1st_part_misconception1"gt
ltmaterialgtltmattextgt No it's not correct
because... lt/mattextgtlt/materialgt lt/itemgt
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Response conditions (using variables)
ltmap-action type"reply"gt ltcond
xref"1st_part_misconception1"/gt ltnum_equal
forblank_1gt ltvar_valuegt2blt/var_valuegt lt/
num_equalgt lt/condgt lt/map-actiongt
ltitem id"1st_part_misconception1"gt
ltmaterialgtltmattextgtNo it's not correct...lt/mattext
gtlt/materialgt lt/itemgt
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Response conditions for hints
ltmap-action typehint"gt ltcond
xref"hint_rhs_1"gt ltnum_equal forblank_2gt3lt/nu
m_equalgt lt/condgt ltcond xref"hint_rhs_2"gt
ltnum_equal forblank_2gt4lt/num_equalgt
lt/condgt ltdefaults xrefdefault_hint
gt lt/map-actiongt
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Response conditions for CAS
ltmap-action typereply"gt ltcond
xrefcorrect"gt ltcas_test forblank_2gt
omobj lt/cas_testgt
lt/condgt lt/map-actiongt
ltmap-action typereply"gt ltcond
xrefcorrect"gt ltcas_test forblank_2gt
test/Diff(U) lt/cas_testgt
lt/condgt lt/map-actiongt
example
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Conclusion
An exercise description language - shallow
structure - general enough - declarative -
separates presentation from content
Further Work
- limitations wtr to different content -
finalise details of the language - finalise
two different implementations (client
server)
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Part of WALLIS DTD for reference
lt!ELEMENT exercise (variable,preamble?,statement
) lt!ATTLIST variable id (text) REQUIRED gt
lt!ELEMENT preamble (text)gt lt!ELEMENT statement
(text,(exercise interaction))gt lt!ELEMENT
interaction (text,match-text,map-action)gt lt!ELEM
ENT map-action (cond?,system?,message?,
statement,default)gt lt!ATTLIST map-action type
(hint answer solution onEnter)
REQUIRED gt lt!ELEMENT cond textgt lt!ATTLIST cond
xref (text) type (cas js) REQUIRED return
(boolean value) IMPLIED gt
This has now being mapped to QTI but with the
necessary extensions