Assessing Student Conceptual Understanding of Force and Motion with Model Analysis

Transcription

1 CMU. J. Nat. Sci. (008) Vol. 7() 07 Assessig Studet Coceptual Uderstadig of Force ad Motio with Model Aalysis Porrat Wattaaasiwich * Departmet of Physics, Faculty of Sciece, Chiag Mai Uiversity, Chiag Mai 5000, Thailad *Correspodig author. porratw@chiagmai.ac.th ABSTRACT This study aims to assess studet coceptual model of uderstadig about force ad motio by employig a ew aalysis method, called model aalysis. This method was established from qualitative researches i order to qualitatively represet a framewor of studet uderstadig. With model aalysis, we ca obtai studets alterative owledge ad the probabilities for studets to use such owledge i a rage of equivalet cotexts. The model aalysis cosists of two algorithms cocetratio factor ad model estimatio. This paper oly presets results from usig the model estimatio algorithm. I order to use the model aalysis efficietly, the data must be collected from a well-desiged multiple-choice test. The Force ad Motio Coceptual Evaluatio (FMCE), the most well-ow test for probig mechaics coceptual uderstadig was admiistered to 746 egieerig freshme taig a itroductory physics with calculus at Chiag Mai Uiversity. Oly 545 complete studet resposes were aalyzed by the model aalysis. The class model desity matrices for both pre/post scores were costructed. I order to determie characteristics of the pre/post class, eigevalue decompositio was used to aalyze both matrices. Each matrix had a large eigevalue (> 0.65), idicatig the domiat features of the sigle-studet model vectors. This model eigevectors well represeted the overall model structure of pre/post class. The the pre/post class model states were characterized by a class model poit o a model plot. Both pre/post poits were located i the icorrect model regio, so both pre/post class states were still i a miscoceptio state. However, there was a small shift of post-class model poit towards the correct model, idicatig a small improvemet of overall uderstadig. Key words: Model Aalysis, FMCE, Coceptual Uderstadig, Force ad Motio INTRODUCTION Over three decades, results from physics educatio research (PER) idicate that most studets come to a physics classroom with miscoceptios, origiatig

2 08 CMU. J. Nat. Sci. (008) Vol. 7() from their misiterpretatios of everyday s experiece ad previous istructio (McDermott ad Redish, 999). These miscoceptios affect how studets respod to istructio, so physics istructors should acquire studet prior uderstadigs i order to desig more-effective teachig methods. I PER, free-respose questios, iterviews ad multiple-choice questios are ofte used to probe studet uderstadigs. I a large-scale settig, multiple-choice test is the easiest to aalyze ad the cheapest to coduct, but there is a lac of efficiet methods to aalyze studet resposes. May physics educatio researchers have developed various multiplechoice coceptual tests to detect studet miscoceptios such as Force Cocept Ivetory (FCI) (Hestees et al., 99) ad Force ad Motio Coceptual Evaluatio (FMCE) (Thorto ad Sooloff, 998). May studies employed these istrumets to measure studet uderstadig, however, the results from these istrumets ted to be used to obtai overall scores ad average pre/post gais (Hae, 998; Huffma, 998; Saviaie ad Philip, 00; Boham et al., 00). The typical aalysis of the multiple-choice tests ot oly fails to provide iformatio about studets miscoceptios but also igores studets wrog aswers cotaiig a large amout of valuable iformatio. Thus, the model aalysis was developed to extract iformatio about models of studet uderstadig from their resposes to multiple-choice test (Bao ad Redish, 006). This method is most effective i detectig well-defied miscoceptios. These miscoceptios were documeted from qualitative researches that studets ofte eter a classroom with a few umber of strog aïve coceptios. These miscoceptios are ofte i coflict with or ecourage misiterpretatios of the expert view. Oe of the welldefied miscoceptios is about force ad motio. Therefore, this study aims to ivestigate studets coceptios of force ad motio by usig the model aalysis. METHODOLOGY Settigs The data were collected durig the first semester of academic year 006. The FMCE pre- ad post-tests were give to studets taig physics for egieerig ad agro-idustrial studets I (PHYS0705) o the first ad the last day of class. Studets were give 45 miutes to complete the FMCE. There were 746 studets taig both pre- ad post-test. After disregardig icomplete resposes, oly data from 545 studets were aalyzed by the model aalysis. Istrumet The FMCE was developed by Thorto ad Sooloff (998). Sice the it has become oe of the most popular istrumets used to probe studet uderstadig of Newtoia mechaics. This test cosists of 47 multiple-choice sigle-respose items ad oe ope-eded questio. FMCE items ca be categorized ito five clusters of basic mechaics cocepts velocity, acceleratio, Newto s first ad secod laws, Newto s third law ad eergy. For each item of FMCE, if studets

3 CMU. J. Nat. Sci. (008) Vol. 7() 09 thi that oe of the choice is correct, they ca choose to aswer choice J. The Thai versio of FMCE traslated by Physics Educatio Networ of Thailad (PENThai) was used to collect data. TRADITIONAL ANALYSIS The traditioal ad typical quatitative aalysis of multiple-choice test was used i order to compare the results with the oe usig model aalysis. Studet resposes were iput ito a excel template desiged by Wittma (00), the the percetage of studets correct resposes o pre-ad post-test were plotted accordig to differet clusters ad overall scores, as show i Figure. The percetage gai is calculated as follows: % Gai % post % pre (00 % pre) () Figure : Percetage of Pre/Post FMCE scores categorized ito overall ad five cocept clusters. From Figure, Newto s st ad d laws cluster has the lowest percet correctio i both pre/post test scores. Therefore, usig the model aalysis should provide useful results of studet s uderstadig model i this topic. MODEL ANALYSIS The model aalysis cosists of two algorithms cocetratio factor ad model estimatio. The cocetratio factor shows a distributio of studet resposes, whether they are clustered o certai choices or scattered amog all choices. The model estimatio is a quatitative evaluatio of studet models of uderstadigs derived from a umerical aalysis of studet resposes o multiple-choice tests. Sice the cocetratio factor of studet resposes o FMCE

4 0 CMU. J. Nat. Sci. (008) Vol. 7() has already bee reported (Wattaaasiwich, 006), this paper oly presets the result from usig the model estimatio algorithm. Theoretical Framewor: Studet Model State It is a cotiuig effort amog educatioal researchers to loo for ew ways to uderstad studet learig process. However, learig is a complicated process, so it could ot be measured directly. We ca oly model studet ways of thiig ad further improve our uderstadig of studet learig. From physics teachig experieces, studets are ot cosistet i solvig problems ad sometimes eve use cotradictory ideas to aswer similar questios. I may cases whe a similar cocept is preseted uder differet physical cotexts, studets may have difficulties i idetifyig the correct physics. They ted to use pieces of owledge that are iduced by the surface features of the specific cotexts. Therefore, studets seem to fuctio as if they hold a mixture of differet models (a correct oe ad icorrect oes) without owig the appropriate situatio i which to apply them. From results of cogitive research, it may be of great iterest to cosider the studet as always beig i a cosistet metal state. For studets to reach a complete expert model, they eed to go through a process of coceptual chage, as show i Figure. The mixed state is regarded as a importat trasitioal stage for a studet to reach a complete favorable coceptual chage i learig physics. Hece, measuremets of such mixed states have importat values i assessmet ad istructio (Bao ad Redish, 006). Studets i this mixed model state (sometimes referred to as a hybrid model) ofte combie certai parts of the ew owledge ad parts of their existig owledge. It is a solutio of recociliatio to produce a locallycosistet model for two types of owledge which are otherwise cotradictory. Figure : A process of model developmet leadig to a coceptual chage. Whe studets aswer a particular physics questio, the cotext of that questio triggers them to apply a certai model. The process of model activatio is complicated, so we caot measure studets model states directly. Bao ad Redish

5 CMU. J. Nat. Sci. (008) Vol. 7() (006) proposed that the probability of activatig model state could be obtaied by aalyzig studets resposes to a well-desiged istrumet. I other words, the process of model activatio could be treated as a process of quatum measuremet. Accordigly, the metal state of the studet ca be represeted with respect to a set of commo models i a liear vector space, referred to as the model space. Each commo model is associated with a elemet of a orthoormal basis, e as show i Figure. This supports the fact that differet metal models ca have similar features. Bao ad Redish (006) idicated that studies i eurosciece about eural etwors stimulated the ideas of usig this represetatio. e e e Figure : A model space cosistig of three orthogoal model vectors e, e ad e. Costruct Studet Model State I order to costruct studet model state, studet resposes from a welldesiged multiple-choice test are required. The well-desiged istrumet has to be developed so that the choices of the questio are desiged to probe the differet commo studet models. These models have bee revealed from qualitative physics educatio research. There are commo models of force ad motio foud from PER ad a ull model refers to other ideas or icomplete aswers: Model : It is ecessary to have a force to maitai motio ad there is o such thig as a force i the directio of motio. (Correct) Model : A force is eeded to maitai motio. This model also icludes the ideas that there is always a force i the directio of motio ad that the force is directly related to the velocity of motio. (Icorrect) Model : Null model I the FMCE, four questios (questios, 5, ad ) are associated with Newto s first ad secod law. Whe aalyzig each questio, we ca idetify distracters associatig with a particular model, as show i Table.

6 CMU. J. Nat. Sci. (008) Vol. 7() Table : Distracters of force-motio questios with a specific model. Questio Model Model Model The th studet D B Others A 5 D B Others B A G Others G A D Others A The last colum represets choices that a arbitrary th studet might aswer for each questio. From this studet s aswers, we ca costruct the th studet s model state or u, as i (), where m is umber of questios associated with the specific cocept, ad,, are umbers of choices correspodig with Model, Model ad Model, respectively (Bao ad Redish, 006). () Costruct Class Model Desity Matrix After costructig the th studet s model state, his model desity matrix ca be determied as below: () The each studet s model desity matrix is summed up to get a class model desity matrix as i (4), where is total umber of studets i the class. (4) After calculatig the class model desity matrix for both pre- ad post-test, eigevalues ad eigevectors for both matrices were calculated by usig MATLAB program, as show i Table. u m u T m u u D N D N D

7 CMU. J. Nat. Sci. (008) Vol. 7() Class model desity matrix Pre Table : The pre/post class model desity matrix, their eigevalues ad their eigevectors. Post Eigevalues Eigevectors The characteristic of models that studets i the class used ca be obtaied by aalyzig these matrices. Both the similarity of idividual studet s model vectors ad the umber of studets with similar model vectors ifluece the eigevalue, especially if the class model desity matrix has a domiat ad large eigevalue (> 0.65). This implies that most studets i the class have similar model vectors, referred to as a primary vector (Bao ad Redish, 006). From Table, both pre/post matrices have domiat eigevalues, so both classes have primary vectors which give a good evaluatio of the model structure of both classes. Bao ad Redish (006) suggested to use a model plot to further aalyze the primary vector. Model Plot The model plot is for represetig the class model state with respect to commo models. The model plot, i this case, is a two-dimesioal graph because there are two commo models used i aswerig the force ad motio questios. The class model states or eigevectors with domiat eigevalues ca be represeted as a class model poit o the model plot with a coordiate (P, P ). From Table, vertical ad horizotal compoets for pre/post class model poit are calculated ad plotted o the model plot as show i Figure 4. Table : The pre/post domiat eigevalues, class model eigevectors ad vertical/ horizotal compoets for the class model poit. Pre- Post- Eigevalues Eigevectors Model Poit A vertical compoet P =(0.8) (-0.8) =0.0 P =(0.79) (-0.) =0.0 A horizotal compoet P =(0.8) (-0.9) =0.56 P =(0.79) (-0.9) =0.5

8 4 CMU. J. Nat. Sci. (008) Vol. 7() Model Regio Mixed Model Regio Post-class model poit Model Regio (a) (b) Figure 4: (a) Meaig of some regios i the model plot. (b) Model plot comparig betwee pre- ad post-class model poits. From the model plot i Figure 4 (b), the post-class model poit is located i the Model regio. This idicates that most studets i the class still had a miscoceptio about force ad motio. Due to the model aalysis, the characteristics of this miscoceptio are ow, so a istructor ca use this iformatio to improve teachig of this class. A small shift of post-class model poit towards the correct model idicates a small improvemet of overall class uderstadig i this topic. CONCLUSION I this paper, the author used the model aalysis to aalyze quatitative data i order to obtai a qualitative result of studet coceptual uderstadig of force ad motio. This method is useful i aalyzig studet s owledge states i large classes with well-desiged multiple-choice questios. With the measuremet data from FMCE, a sigle-studet model state ca be created. This state represets studet probabilities i applyig the differet commo models. The the idividual studet model states are summed up over the class to create the class model desity matrix. Usig the eigevalue decompositio, the eigevalues ad eigevectors of the desity matrix are obtaied, ad these give iformatio about the state of the class s owledge. The class model poit is obtaied ad plotted o the model plot. This is helpful i providig clear iformatio about class model state. From the result of this study, oly small progress i uderstadig was foud by comparig the pre/ post class model poits. However, the class model state was still i a miscoceptio regio eve after a proper istructio. This iformatio is extremely helpful i otifyig the istructor ad ca be used to improve a future istructio.

9 CMU. J. Nat. Sci. (008) Vol. 7() 5 ACKNOWLEDGEMENTS The author would lie to acowledge the Faculty of Sciece, Chiag Mai Uiversity, Thailad Research Fud (TRF) ad the Commissio o Higher Educatio (CHE) for fiacial support. The author also would lie to tha the PENThai team for providig the Thai versio of FMCE. REFERENCES Bao, L., ad E.F. Redish. 00. Cocetratio aalysis: A quatitative assessmet of studet states. America Joural of Physics 69(7): S45-S5. Bao, L., ad E.F. Redish Model aalysis: Represetig ad assessig the dyamics of studet learig. Physical Review Special Topics-Physics Educatio Research : -6. Boham, S., D.L. Deardorff, ad R.J. Beicher. 00. Compariso of studet performace usig web ad paper-based homewor i college-level physics. Joural of Research i Sciece Teachig 40(0): Hae, R.R Iteractive-egagemet versus traditioal methods: A six-thousad-studet survey of mechaics test data for itroductory physics courses. America Joural of Physics 66(): Hammer, D More tha miscoceptios: Multiple perspectives o studet owledge ad reasoig, ad a appropriate role for educatio research. America Joural of Physics 64(0): 6-5. Hesteses, D., M. Wells, ad G. Swachammer. 99. Force cocept ivetory. Physics Teacher 0: Huffma, D Effect of explicit problem solvig istructio o high school studets problem-solvig performace ad coceptual uderstadig of physics. Joural of Research i Sciece Teachig 4(6): McDermott, L.C., ad E.F. Redish Resources Letter PER-0: Physics Educatio Research. America Joural of Physics 67(9): Saviaie, A., ad S. Philip. 00. The force cocept ivetory: a tool for moitorig studet learig. Physics Educatio 7: Thorto, R.K., ad D.R. Sooloff Assessig studet learig of Newto s laws: The force ad motio coceptual evaluatio ad the evaluatio of active learig laboratory ad lecture curricula. America Joural of Physics 66(4): 8-5. Wattaaasiwich, P Ivestigatio of studet uderstadig of force ad motio by usig cocetratio aalysis. Proceedigs of The d Cogress o Sciece ad Techology of Thailad, 0- Oct 006. Quee Siriit Natioal Covetio Ceter, Bago. Wittma, M. 00. Force cluster calculatio template (00.) [Excel Template]. I E.F. Redish (ed) Teachig Physics with the Physics Suite CD. Wiley, New Yor.

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