Personalized Content Sequencing Based on Choquet Fuzzy Integral and Item Response Theory

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1 0 Iteratoal Coferece o Educato Techology ad Computer (ICETC 0 Persoalzed Cotet Sequecg Based o Choquet Fuzzy Itegral ad Item Respose Theory Ahmad Karda, Roya Hosse Departmet of Computer Egeerg ad IT Amrabr Uversty of Techology Tehra, Ira e-mal: {aaarda, hosseec}@autacr Abstract Persoalzato of learg path s a mportat research ssue curret E-learg systems because learers dffer from varous aspects such as owledge level, eperece, ad ablty Therefore, most persoalzed systems focus o learer prefereces, ad browsg behavor for provdg adaptve learg path gudace However, these systems usually eglect to cosder the depedece amog the learg cocept dffculty ad the learer model Geerally, a learg cocept has vared dffculty for learers wth dfferet levels of owledge Cosdered the mportace of learg path wth learg cocepts dffculty that are hghly matched to the learer s owledge ad ablty, ths paper proposes a system based o Choquet Fuzzy Itegral ad Item Respose Theory Ths system recommeds approprate learg cotets to learer durg the learg process Keywords-E-learg; dffculty level; Choquet fuzzy tegral; learg path; Item respose theory I INTRODUCTION Epoetal growth of Iteret as well as recet advaces of Iformato Techology educatoal cotet, have strog mpact o educatoal process Oe of the aspects of educato that has bee greatly flueced s learg I ths regard, Iformato ad Commucato Techologes (ICTs provde opportutes to use ew ad effcet educatoal tools ad methods that support learers durg the learg process Computer-Based Trag (CBT s ow as a practcal tool the learg process E-Learg s the advaced form of CBT ad s capable of ehacg both the effectveess ad effcecy of learg [] However, the developmet of Web-Based tutorg systems has created a great deal of hypermeda learg sessos Cosequetally, learers are uable to lear very effcetly due to formato overload ad dsoretatos [] O the other had, as log as the users dffer o ther goals, owledge level, ad terest, t s ot effectve to provde a fed sequece of learg cotets for all learers Hece, persoalzed currculum sequecg s ecessary for adaptve learer support Web-Based tutorg systems [3] Accordg to [4] currculum sequecg s a mportat elemet of persoalzed learg; t provdes each learer the most sutable dvdually plaed sequece of cocepts to lear ad cotets to wor wth So far, dfferet systems were proposed for supportg learers through ther learg process Eamples of such systems clude systems that support learer by provdg persoalzed sequece of eercses, or problems Most of the persoalzed tutorg systems cosder learer owledge, ablty, ad prefereces for provdg adaptve ad persoalzed cotet sequecg But they stll gore the depedece amog the dffculty level of learg cocepts ad the learer s owledge To llustrate t more, a learg cocept may have dfferet dffculty for learers wth dfferet owledge level ad ablty Dyamc problem dffculty s obvously better matched to the leaer s owledge level, ad hece ca ease the compreheso of learg cocepts The related wor [5] calculates problem dffculty wth regards to the learer model ad recommeds sutable problems to the learer Epermetal results of [5] cofrm that dyamc problem dffculty performs well for a wde rage of learers, whereas statc problem complety performs well for studets of termedate ablty, but rather badly for begers ad advaced learers The ma drawbac of the proposed method [5] s the use of costrat based modelg for calculato of problem dffculty Accordg to [6] ths model requres a huge set of costrats to be defed ad ths adds to ts complety Moreover, t s ot always possble to defe costrat for some owledge domas To costruct a learg path wth learg cocepts dffcultes that are hghly matched to the learer s owledge ad ablty, ths research presets a Web-Based tutorg systems based o Choquet Fuzzy Itegral ad Item Respose Theory Cocept dffculty s calculated by usg the formato provded the learer model ad the owledge doma The, approprate cotets matched wth the learer s ablty are recommeded to hm/her by usg Item Respose Theory So, the orgazato of ths paper s as follows: The followg secto presets the archtecture of the proposed systems Secto 3 proposes a methodology for cotet sequecg Fally, secto 4 provdes a cocluso for ths wor II SYSTEM ARCHITECTURE Ths secto presets the archtecture of the system for learg cotet sequecg based o Choquet Fuzzy Itegral ad Item Respose Theory As t s show Fg, / 0 IACSIT V-34

2 0 Iteratoal Coferece o Educato Techology ad Computer (ICETC 0 ths system cossts of fve major uts as well as four major databases The fve major uts are: Learer Iterface Ut, Dyamc Cocept Dffculty Calculato (DCDC Ut, Feedbac Ut, Cotet Recommedato Ut, ad Learg Cotet Repostory The four major databases are: Kowledge Doma, Learer Accout, Cocept Dffculty, ad Learer Model The Learer Iterface Ut provdes a learg terface for learers to teract wth the Feedbac Ut ad the Cotet Recommedato Ut DCDC Ut dyamcally calculates cocept dffculty based o the formato the learer model ad the owledge doma The Feedbac Ut ams to collect learer eplct feedbac formato from the Learer Iterface Ut ad stores t the Learer Model Cotet Recommedato Ut s charge of recommedg sutable cotets to learer based o the learer s ablty ad dffculty of learg cocepts by usg Item Respose Theory To ths ed, ths ut uses the values of dffculty level of cocepts that are calculated by the DCDC Ut Learg Cotet Repostory cossts of learg cotets whch are preseted to the learer durg the learg process Each cotet s desged to covey a certa cocept of the owledge doma Also, ths repostory cotas test tems A test s desged for each cotet to evaluate the uderstadg degree of a learer Havg fshed readg a cocept, the learer must aswer the correspodg test tem The umbers o the arrows Fg show the steps related to data flow wth the system These steps are as follows: Step The learer logs the system by provdg hs/her user accout formato Step The user log formato s compared to the formato the Learer Accout Step 3 If the formato s vald, the the user selects the Sub-doma to be leared from the system home page ad step 4 s followed Otherwse, the learer should try loggg the system utl he/she s authetcated Step 4 The system searches ad selects the set of cocepts that are related to the Learer-Selected Subdoma The cocepts that the learer has already leared are removed from ths set Cocept Dffculty Learg Cotet Repostory Kowledge Doma 5 Cotet Recommedato Ut 8 4 Dyamc Cocept Dffculty Calculato (DCDC Ut Learer Model Feedbac Ut Fgure The system archtecture Learer Accout Learer Iterface Ut 4 / 3 The learer s cosdered to lear a cocept f he/she aswers ts correspodg test tem correctly The fal set servers as oe of the puts of the DCDC Ut Step 5 The learer formato s the other put that s used by the DCDC Ut DCDC Process: Usg the puts provded by Step 4 ad Step 5, ths process calculates the cocept dffculty by usg Choquet Fuzzy Itegral whch s dscussed detal secto 3 Step 6 After the DCDC process s fshed, the dffculty level of each cocept s temporarly stored the Cocept Dffculty Step 7 The formato of the Cocept Dffculty serves as oe of the puts of the Cotet Recommedato Ut Step 8 The formato the learer model s the other put that s used by the Cotet Recommedato Ut Step 9 The formato the Learg Cotet Repostory serves as the thrd put of the Cotet Recommedato Ut Cotet Recommedato Process: Usg the formato provded by Step 7, Step 8, ad Step 9, ths ut selects ad ras sutable learg cotets for learer based o Item Respose Theory whch s dscussed detal secto 33 Step 0 The lst of recommeded cotets s trasferred to the Learer Iterface Ut Step The Learer Iterface Ut presets the recommeded cotets to learer Step After the learer fshes readg certa cotet, ts correspodg test tem s preseted to learer to evaluate hs/her uderratg degree Ths ut receves the learer s resposes to the tests Step 3 The Leaer Iterface Ut seds the receved Feedbac to the Feedbac Ut for updatg the formato the learer model ad recommedg sutable cotets to learer Step 4 The Feedbac Ut updates the formato the learer model based o the receved feedbac Step 5 To recommed learg cotet based o the learer feedbac, cocept dffculty level s calculated aga for the cocepts that have ot bee leared by the learer yet Steps 4 to Step 5 are repeated utl the learer lears all the cocepts the selected Sub-doma III METHODOLOGY Ths secto presets the proposed method for learg path costructo The followg subsectos frst troduce the fluetal parameters o calculatg learg cocept dffculty The Choquet Fuzzy Itegral s used to calculate the dffculty of learg cocepts Fally, regardg the dffculty of cocepts, a method based o Item Respose Theory s preseted to recommed sutable cotets to learer V-35

3 0 Iteratoal Coferece o Educato Techology ad Computer (ICETC 0 A Parameters Dyamc calculato of dffculty level for a cocept reles o the formato the learer model ad the owledge doma Therefore, both the learer ad the doma model are two fluetal elemets determg the learg cocept dffculty The learer model cossts of two parts, amely the learer s owledge model ad the learer s behavoral model The former models the learer s owledge cocepts of the owledge doma ad the latter models the learer s behavor ad more specfcally the umber of tme the learer studes each cocept of the owledge doma The detals of these parameters are as follows: Doma Model: The doma model cossts of the cocepts as well as the relatos betwee them I ths paper, the cocept that the dffculty level s calculated for t s called the Ma Cocept Sematc relatoshp betwee the Ma cocept ad other cocepts of the certa owledge doma ca be descrbed two forms: - Prerequste Cocepts that are ecessary to perceve the Ma Cocept, ad - Related Cocepts that are related to the ma cocept ad are part of the same Sub-doma Learer Behavoral Model: Ths model stores the formato about the learer s actvty, e the umber of tmes the certa cocept s studed by the learer Hece, the learer actvty the Ma Cocept, ts Prerequste Cocepts, ad ts Related Cocepts s mportat determg the dffculty level of the Ma Cocept Leaer Kowledge Model: The learer s wrog aswer to the tests related to the Ma cocept, ts Prerequste Cocepts, ad ts Related Cocepts mples the learer Kowledge the cocepts of the owledge doma B Cocept Dffculty Calculato Usg Choquet Fuzzy Itegral The Choquet Fuzzy Itegral s a operator that s used for the aggregato of the terdepedet parameters based o the fuzzy measure Accordg to [7] sutablty of ths tegral s proved for the Real-Tme applcatos Therefore, Choquet Fuzzy Itegral ca mprove the respose tme of a E-learg system I ths paper, Choquet Fuzzy Itegral s used to aggregate the fluetal parameters o cocept dffculty The defto of Choquet Fuzzy Itegral s as follows: Defto: Choquet Fuzzy Itegral s a tegral that uses fuzzy measure to aggregate the set of put parameters Accordg to [8] t s defed as (: g X E ( h = h( g( = [ h( h( ( = ] g( A where h( h( h( ad h ( 0 = 0 The varables that are used ( are as follows: Number of the put parameters I ths paper, = 3 X The set of put parameters of the Choquet Fuzzy Itegral Ths set s show as X = {,,, } Represets the umber of the relatos betwee the Ma Cocept, ts Prerequste Cocepts, ad ts Related Cocepts Represets learer s wrog aswers to the test tems related to the Ma Cocept, ts Prerequste Cocepts, ad ts Related Cocepts 3 Represets the umber of the learer s study actvty the Ma Cocept, ts Prerequste Cocepts, ad ts Related Cocepts h The fucto that determes the value of the put varables For eample, h ( s the value of g The λ-fuzzy measure whch s defed as g : P( X [0,] such that: g( φ = 0, g( X = ( If A, B P( X ad A B, the g( A g( ( 3 If A, B X, A B = φ, the g( A = g( A + g( + λg( A g( ( 4 for some fed λ > The value of λ s foud from the equato g ( X = that s equvalet to solve (5: g ( X = ( ( + λg, λ 0 λ λ = ( 5 A Ths varable represets the set of put parameters the form of A = {, +,, } g A Ths value s recursvely calculated by (6 ad (7: ( g ( A = g({ } = g (6 g( A = g + g( A + + λ gg( A +, < (7 To calculate the dffculty level of the cocepts the owledge doma the followg steps should be followed: Step The cocept dffculty s calculated by usg ( h ( s the sum of Prerequste ad Related Cocepts of the Ma Cocept; h( s the learer s wrog aswers to test tems related to Ma Cocept, ts Prerequste Cocepts, ad ts Related Cocepts; h( 3 s the learer s study actvty the Ma Cocept, ts Prerequste Cocepts, ad ts Related Cocepts V-36

4 0 Iteratoal Coferece o Educato Techology ad Computer (ICETC 0 Step Accordg to the assumpto of (, the values of h are sorted ascedgly such that ( h h( h( ( Step 3 The value of the fuzzy measure s calculated for each of the three put parameters Ths research uses the fucto troduced [9] whch calculates the fuzzy measure values as (8: g = =,, 3 ( 8 + d( h, h 0 g represets the fuzzy measure value of d( h, h0 s the Eucldea dstace betwee h ( ad h 0 h 0 s a optoal value from whch the dstace of all h ( s calculated I ths research, t s assumed that h 0 = 0 Step 4 The value of λ s calculated by usg (5 Step 5 The value of g( A, g( A, ad g( A 3 s calculated accordg to the value of λ usg (6 ad (7 Step 6 To calculate the dffculty of the Ma Cocept, the values of h ad g are used ( ( C Cotet Recommedato The proposed system recommeds approprate cotets to the learer by estmatg learer s ablty ad rag the cotets accordgly Item Respose Theory (IRT evaluates the ablty of leaer ad recommeds sutable cotet to hm/her The goal of IRT s to estmate Fgure A typcal Item Characterstc Curve the learer s ablty wth regards to hs/her dchotomous aswers to test tems The IRT model llustrates the relatoshp betwee learer s aswer ad a test tem through the Item Characterstc Curve (ICC As show Fg ths curve s S-shaped The horzotal as represets the ablty of learer a lmted rage ad the vertcal as represets the probablty that the learer wth certa ablty ca aswer the test correctly [0] The Item Characterstc Curve s recogzed wth the cumulatve form of the logstc fucto Ths paper uses the oe-parameter logstc model (PL or Rasch model to estmate the ablty of the learer Accordg to [0] the formula of PL s defed as (9: P ( = ( 9 + ep( D( b where P ( represets the probablty of a correct aswer to a test tem, b s the dffculty of the th cocept whch, ths paper, s calculated by the DCDC Ut, ad D s a costat 70 Sce each cotet coveys certa cocept, both the cocept ad ts correspodg cotet wll have the same dffculty level Ths paper estmate learer s ablty by usg Bayesa estmato The Hermte-Gauss quadrature [] s used to appromate the ablty of the learer as (0: where q = q L( u, u,, u A( L( u, u,, u A( (0 s oe of q equdstat quadrature pots A s comprsed betwee the lmted rage of ablty ( the weght assocated to each of the quadrature pots accordg to a ormal probablty dstrbuto wth mea zero ad varace oe L( u, u,, u s the lelhood of the aswers patter after the admstrato of tems I (0, the lelhood fucto L( u, u,, u s calculated as (: = u u, u,, u P ( Q ( = L( u ( As (9, P ( represets the probablty that learer aswers the th test tem correctly Q ( represets the probablty that learer caot gve a correct aswer to the th test tem ad s calculated as Q ( = P ( u s the result of the learer aswer to the test tem ad s for correct aswer ad 0 for the correct aswer to tem The proposed system uses the feedbacs from the leaer for estmato of hs/her ablty If learer gves correct aswers to the test tems, the hs/her ablty wll be creased usg the formula metoed (0; otherwse, learer s ablty wll be decreased Havg estmated the learer s ablty, the Cotet Recommedato Ut selects ad ras a seres of approprate learg cotets the Learg Cotet Repostory based o the value of the Item Iformato Fucto Ths value depeds o the matchg degree betwee the dffculty of the tem ad the learer s V-37

5 0 Iteratoal Coferece o Educato Techology ad Computer (ICETC 0 ablty Cotets that ther test tem has hgher formato value are more approprate for the learer The Item formato fucto s defed as (: I ( = P ( Q ( ( where P ( ad b are the formato value ad the dffculty parameter of the th test tem respectvely As metoed prevously, the value of b s calculated by the DCDC Ut Hece, the Cotet Recommedato Ut ras the cotets accordg to the formato values of ther correspodg test tems Fally, ths ut recommeds the raed cotets to the learer IV CONCLUSION Ths research proposes a system to provde persoalzed learg path for the learer Choquet Fuzzy Itegral s used to dyamcally calculate the dffculty level of learg cocepts The the cotet sequecg s adapted to the learer s ablty by usg Item Respose Theory Choquet Fuzzy Itegral cosders both the formato the learer model ad the relatoshp betwee the cocepts of the owledge doma, ad hece s more precse tha the statc methods whch cosder equal cocept dffculty for all the learers wth dfferet levels of owledge Also, Choquet Fuzzy Itegral has less complety compared to the wor doe [5] due to the use of Costrat-Idepedet learer model Moreover, t ca be easly appled to dfferet owledge domas Usg both the Choquet Fuzzy Itegral ad Item Respose Theory, the preseted system ths paper provdes a persoalzed learg path for the learer such that the dffcultes of the cotets are hghly matched to hs/her owledge ad ablty Ths, tur, leads to a more effcet learg process Future wors ams to provde a prototype system ad evaluate ts effcecy through epermetal aalyss [5] A Mtrovc ad B Mart, "Evaluatg adaptve problem selecto," Lecture Notes Computer Scece, vol 337, pp 85 94, 004 [6] T WEI, "A tellget tutorg system for Tha wrtg usg costrat based modelg," Master of Scece, School of Computg, Natoal Uversty of Sgapore, 005 [7] J-I Sheh, H-H, Wu ad H-C, Lu, "Applyg a complety-based choquet tegral to evaluate studets performace," Epert Systems wth Applcatos, vol 36, pp , 009 [8] J-H Chag, "Aggregatg membershp values by a choquet-fuzzytegral based operator," Fuzzy Sets ad Systems, vol 4, pp , 000 [9] S Medasa, J, Km ad R, Krshapuram, "A overvew of membershp fucto geerato techques for patter recogto," Iteratoal Joural of Appromate Reasog, vol 9, pp 39 47, 999 [0] F Baer, "The bascs of tem respose theory," ERIC clearg house o assessmet ad evaluato, 00 [] J-G Blas ad G Raîche, "Some features of the samplg dstrbuto of the ablty estmate computerzed adaptve testg accordg to two stoppg rules," preseted at the th Iteratoal Objectve Measuremet Worshop, New Orleas, 00 ACKNOWLEDGEMENTS Ths paper s provded as a part of the research performed the Advaced E-learg Techologes Laboratory Amrabr Uversty of Techology ad s facally supported by Ira Telecommucato Research Ceter (ITRC Therefore, the authors would le to tha ths ceter for ts sgfcat help REFERENCES [] S Aleader, "E-Learg developmets ad epereces," Educato+Trag, vol 43, pp 40 48, 00 [] C-M Che, C-Y, Lu ad M-H, Chag, "Persoalzed currculum sequecg utlzg modfed tem respose theory for web-based structo," Epert Systems wth Applcatos, vol 30, pp , 006 [3] P Bruslovsy, "Adaptve ad tellget techologes for web-based educato," Küstlche Itellgez, vol 4, pp 9-5, 999 [4] F Zhu ad N Yao, "Otology-based learg actvty sequecg persoalzed educato system," Proc 009 Iteratoal Coferece o Iformato Techology ad Computer Scece, tcs, vol, pp85-88, do:009/itcs00964 V-38

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