Standardization of physics exercises Dynamical generation of data J. Parellada Facultat de Física...

Standardization of physics exercises

Dynamical generation of data

J. ParelladaFacultat de FísicaUniversitat de BarcelonaDiagonal 64508028 Barcelona [email protected]

UNIVERITAT DE BARCELONA

1. Introduction

Rationale

Classification: DC; LOM; CEN-ISSS

2. QTI Objectives and tags

3. Our proposals

New tags: <response_physmag> <jump>

Dynamical generation of data

• Approaches: Global and Modular

• Schema for dynamical generation of data


IntroductionRationale:

Exercises as a learning toolThe review complexity Students should be encouraged (to try) to solve exercisesIs it possible to set up an automatic procedure?How can the personal work be reassured?


Exercises as learning objects:Classification

DCLOM

Extensions to LOMCEN-ISSS

Vocabularies

QTI NomenclatureAssesment-Section-Item

Single o multiple response

Inside ItemPresentation

MaterialResponse type : LID; String; Numerical, XY, Group

RenderizationMaterialRenderization type : Choice, Hotspot,

Slider, FIBResponse processing

Response conditionconditionvardisplayfeedback

ItemfeedbackGranularity at section levelNo problem set


Problem as QTI instance


The problem structure

General statement: Normally includes: text, graphs, drawings, .....

physical magnitudes with numerical values and unitsmathematical expression

Sequentially ordered questionsQuestion types: numerical

scalar or vector

numerical with accompanying unit

mathematical expression

single or multiple choice

free form text

Hot spot

grouping and ordering

New Response types


Vectors:

OriginHot spot rendering

Coordinate system

Mathematical expression:

Data introductionMathML

Expression comparison

Physical magnitudeMultiple response type

numerical + single choice numerical + string parsed string (to split between a number and its unit)Equivalence between different answers. Conversion factorsPrecision issueRendering

New Response types


Rendering

Example<item ident="s=vt"> <presentation> <material> A car runs at 65 km/h. What distance will it travel in 50 minutes </material> <response_physmag ident="distance"> <show> <units shuffle="yes">

<unit name="km" factor="1.0" shift=0.0"/> <unit name="m" factor="1000." shift=0.0"/> <unit name="miles“ factor="0.6213881812968"/> <unit name="yards" factor="1093.61329833771"/> <unit name="hours" factor="0.0" /> <unit name="lux" factor="0.0" shift=0.0"/>

<show/> <response/> <response_label ident="unit"/> <response_label ident="value"/> <response_label ident="precision"/> <presentation/><item/>

New Response Type

<no show> tag

magnitud


Schema

Respcondition example


<resprocessing>

<respcondition title="Correct" >

<conditionvar>

<and>

<or>

<varequal respident="unit">km</varequal>

<varequal respident="unit">m</varequal>

<varequal respident="unit">miles</varequal>

<varequal respident="unit">yards</varequal>

</or>

<varequal respident="precision">4</varequal>

<varlte respident="value">54.2</varlte>

<vargte respident="value">54.1</vargte>

</and>

</conditionvar>

<displayfeedback feedbacktype="Response" linkrefid= "correct"/>

</respcondition>

<respcondition continue="No" title="units_error" >

<conditionvar>

<or>

<varequal respident="unit">hours</varequal>

<varequal respident="unit">lux</varequal>

<or>

</conditionvar>

<displayfeedback feedbacktype="Hint" linkrefid="u_err"/>

</respcondition>

<respcondition continue="No" title=" low_precision">

<conditionvar>

<varlt respident="precision">4</varlt>

</conditionvar>

<displayfeedback feedbacktype="Hint" linkrefid="l_p"/>

</respcondition>

<respcondition continue="No" title=" high_precision" >

<conditionvar>

<vargt respident="precision">4</vargt>

</conditionvar>

<displayfeedback feedbacktype="Hint" linkrefid="h_p"/>

</respcondition>

<respcondition continue="No" title="value_error" >

<conditionvar>

<or>

<varlt respident="value"> 54.1 </varlt>

<vargt respident="value">54.2 </vargt>

<or>

</conditionvar>

<displayfeedback feedbacktype="Hint" linkrefid="v_err"/>

</respcondition>

</resprocessing>

<itemfeedback ident="u_err">

<material> Wrong units </material>

</itemfeedback>

<itemfeedback ident="l_p">

<material> Please, write more digits </material>

</itemfeedback>

<itemfeedback ident="h_p">

<material> Too many digits!!! </material>

</itemfeedback>

<itemfeedback ident="v_err">

<material> Wrong numerical answer!. </material>

</itemfeedback><itemfeedback ident="correct"><material> Congratulations, right answer!!! </material>

</itemfeedback>

New sequencing tag: <jump>


Displayfeedback inside an item

Problem (section) have questions (items)

QTI ASI Selection and ordering specification version 1.2Conditional selection on Item Outcome/response

Being studied

<jump> to break sequential orderingEmpty tag with linkrefid attribute

<item ident="1">

......

<resprocessing>

<respcondition>

<conditionvar>.....</conditionvar>

<displayfeedback linkrefid="fb11"/>

<jump linkrefid="2"/>

</respcondition>

<respcondition continue="No">



<jump linkrefid="1.1"/>

</respcondition>

</resprocessing>

<itemfeedback ident="fb11">

...

</itemfeedback>

<itemfeedback ident="fb12">

...

</itemfeedback>

</item>

<item ident="2">

........

</item>

<item ident="1.1">

......

<resprocessing>

<respcondition>



<jump linkrefid="1"/>

</respcondition>

<respcondition continue="No">



</respcondition>

</resprocessing>

<itemfeedback ident="fb111">...</itemfeedback>

<itemfeedback ident="fb112">...</itemfeedback>

</item>

Example

Dynamical generation of variables


Numerical values data is part of text, normally inside <section><flow_mat><material>(<mattext>|<matemtext>)<item><presentation><material>(<mattext>|<matemtext>)

Numerical results are inside <conditionvar>

Tags can be redefined to include a PI instruction that, at code level, replaces its value by the value’s value previously defined

A whole set of tags to define the variables should have to be introduced into QTI specification

The processing code should be able to work out everything

Example<mattext>A car runs at <?replace v?> km/h. What distance will it travel in <?replace t?> minutes?</mattext>

This is what should be done, but

Dynamical generation of variables at run time


Example<mattext><fix>A car runs at </fix> <var>v</var> <fix>km/h. What distance will it travel in</fix><var>t</var> <fix>minutes?</fix></mattext>

v = 65 t = 50v = 90 t = 40

<mattext>A car runs at 65 km/h. What distance will it travel in 50 minutes?</mattext>

• The result is a normal QTI instance able to be understood by any QTI aware code

• The data file can be hand defined or computed by any code in any language

• The sampling and text processing is very simple

• The data file can be defined and stored or generated on the fly

Schema for the dynamical generation of variables


Example for the dynamical generation of variables


<var_gen> <option name="car" weight="5"> <var_text name="text"> A car runs at </var_text> <var_text name="speed_unit"> km/h </var_text> <var_text name="time"> minutes </var_text> <var_num_single name = "v" type = "int"> <random> <interval> <value> <cte>70</cte> </value> <value> <cte>95</cte> </value> </interval> </random> <presentation type="int"> <digits>2</digits> </presentation> </var_num_single> <var_num_single name = "t" type = "int"> <list> 40,45,50,55,65 </list> </var_num_single> <presentation type="int"> <digits>2</digits> </presentation> <var_cal name="v_ana" type = "float"> <?eval $v_ana=$v?> </var_cal> <var_cal name="t_ana" type = "float"> <?eval $t_ana=$t/60?> </var_cal> </option> <option name="plane" weight="3"> <var_text name="text"> A plane flights at </var_text> <var_text name="speed_unit"> miles/h </var_text> <var_text name="time"> minutes </var_text> <var_num_single name = "v" type = "int"> <random> <interval> <value> <cte>500</cte> </value> <value> <cte>600</cte> </value> </interval> </random>

<presentation type="int"> <digits>3</digits> </presentation> </var_num_single> <var_num_single name = "t" type = "int"> <list> 55,65,85</list> </var_num_single> <presentation type="int"> <digits>2</digits> </presentation><var_cal name="v_ana" type = "float"> <?eval $v_ana=1.6093*$v?> </var_cal> <var_cal name="t_ana" type = "float"> <?eval $t_ana=$t/60?> </var_cal> </option> <option name="snail" weight="2"> <var_text name="text"> A snail creeps at </var_text> <var_text name="speed_unit"> cm/minute </var_text> <var_text name="time"> hours </var_text> <var_num_single name = "v" type = "int" > <random> <interval> <value> <cte>9</cte> </value> <value> <cte>18</cte> </value> </interval> </random> <presentation type="int"> <digits>2</digits> </presentation> </var_num_single> <var_num_single name = "t" type = "float"> <list> 0.6, 0.8, 1.2 </list> </var_num_single> <presentation type="dec"> <digits>2</digits><dec>1</dec> </presentation>

<var_cal name="v_ana" type = "float"> <?eval $v_ana=6*$v/10000?> </var_cal> <var_cal name="t_ana" type = "float"> <?eval $t_ana=$t?> </var_cal> </option></var_gen><var_com> <var_cal name="dis_correct" type = "float"> <?eval $dis_correct=$v_ana*$t_ana?> </var_cal> <var_cal name="dis_wrong1" type = "float"> <?eval $dis_wrong1=$v_ana*$t?> </var_cal> <var_cal name="dis_wrong2" type = "float"> <?eval $dis_wrong2=$v*$t_ana?> </var_cal> <var_cal name="dis_wrong3" type = "float"> <?eval $dis_wrong3=$v*$t?> </var_cal></var_com>

Development


• A group of 8 physics’ professors are preparing 8*7 (?) problems in 8 different areas

• A PHP code is being adapted to read the XML instance

• A XML file with all(?) units is being built

• A script to run math expressions with Mathematica is planned

SupportThis work is funded by a grant from the Catalan Goverment MQD2002

THANK YOU FOR YOUR ATTENTION!!

Standardization of physics exercises Dynamical generation of data J. Parellada Facultat de Física...

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