Using PBL to deliver course in Digital Electronics

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    Advances in Engineering Education

    Using PBL to deliver course in Digital Electronics

    ArchAnA MAntri

    caa ise of Egeeg ad teoogy

    Paaa, Pjab, ida

    Dr. Sunil Dutt

    naoa ise of tea teaes tag ise

    cadga, ida

    Dr. J.P. GuPtA

    Jaypee ise of ifomao teoogy uvesy

    noda, ua Pades, idaDr. MADhu chitkArA

    caa ise of Egeeg ad teoogy

    Paaa, Pjab, ida

    ABSTRACT

    Pblem Baed Leai (PBL) ha pe t be a hihly ucceful pedaical mdel i may

    educatial eld, althuh it i cmpaatiely ucmm i techical educati. It e beyd

    the typical teachi methdly by pmti tudet iteacti. Thi pape peet a PBLtial applied t a udeaduate Diital Electic cue i the Electic ad Cmmuicati

    Eieei (ECE) pam at Chitkaa Ititute f Eieei ad Techly, afliated with

    Pujab Techical Uieity (PTU), Idia. Al icluded i thi pape i the appach t dei

    quaipeeded pblem f the PBL tial i thebaic Diital Electic cue ad it de-

    liey. It al iclude the cmpai f the eult f the PBL ad taditial pedaie.

    I. INTRODUCTION

    caa ise of Egeeg ad teoogy (ciEt) s afaed w Pjab tea uve-

    sy (Ptu), Jaada, ida. te Boad of Sdes (BoS)a g eve ommee of aademas a

    e vesy devses ad dedes e sdy seme (m), syab ad e boad evaao

    saegy fo e udegadae pogam EcE. A oo a e seme of s egeeg pogam

    a e ofa webse of Ptu sows a e appoa s vey adoa, w a aef sg of

    objeves ad ams of ea ose e m fo e ee/ oa ad paa os. i

    aso ess ad deas e boad evaao saegy of e EcE pogam. i s a evome

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    wee e oy meod o mpa ea edao s adoalee, toa ad Paa

    (l/t/P) ad wee e afag vesy desbes e appoa o devey, s amos mpos-

    sbe o ode ay oe pedagogy, wo povg e sefess of e ew appoa. i a

    effo o faae e paadgm sf, e aos aed a sees of effos, o ode PBl fo e

    oses degadae pogam of Eeos ad commao Egeeg (EcE), a ciEt.

    te s of ese effos was e ose Aaog Eeos. Eoaged by e sess of

    s a, e ess aeved [1, 2], ad by e sess of PBl oe sma oses esewee

    e wod [35], aoe PBl ose was desged ad deveed fo e ose of Dga Eeo-

    s (DE). ts pape desbes e syabs of e Dga Eeos oses, ss e exampes of

    e qas-ope-eded pobems desged fo e ose, devey of e ose, e ompaso of

    ess of bo of e pedagoges ad e feedba, gve by e sdes sppo of PBl.

    II. SYLLABUS OF DIGITAL ELECTRONICS

    As pesbed by e afag uvesye syabs of Dga Eeos (DE) e de-

    gadae pogam of Eeos ad commao Egeeg oves e foowg ops:

    a. nmbe Sysem ad Bay code

    b. Mmzao of og fo

    . combaoa log cs

    d. Seqea cs

    e. D/A ad A/D covees

    f. Semodo Memoes

    g. log Fames.

    III. FORmATION OF ThE TwO ThREADS

    i ode o oas e pedagoges ad ess, e ass of seod yea EcE (69 sdes) was

    dvded o wo eadste PBl ead ad e tadoa ead.

    (a) te fomao of e tadoa ead was qe adoa w e sdes sg e

    assoom ows, fag e eae. te demaao of lee, toa ad Paa asses was

    qe ea. te eae gave ee ee asses, made e sdes pae osed eded

    pobems oa asses ad made e sdes do expemes e paa asses, a

    ypa aboaoy se p.

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    (b) te sdes PBl ead wee s ased o fom e gops w a mmm fo ad max-

    mm ve sdes ea gop. te ass ad a abes, w as aod em ad a sbbe

    boad paed e ee. te se-p s faaed eao ad dssso amog gops

    [16, 17]. A sma bay was aso b e assoom. te sdes wee fee o se e iee o

    e apops ad sea fo ay daa ad fomao eqed. tey od se smao sofwae

    ad aboaoy eqpme e ass sef fo aevg ay paa eag objeves.

    () te expeme was s oded w e ead ao esef as e faao. te same

    expeme was epeaed e ex yea w a fes ba of 68 sdes, w e same se of

    tea Pobems (tPs) b w a dffee seo eae as faao.

    IV. TEAChING PEDAGOGY

    (a) te eag pedagogy fo e tadoa ead oed o be adoa sg lee,

    toa ad Paa asses, w e eae as Sage o Sage [6]. te eae made e lee

    pa ad lab Paa o wse, ee wse, ab wse sede, fo devey of e woe syabs,

    g fom owedge eve o e appao eve. Se aso deveed e ose aodae o

    e same. te qas-ope-eded-pobems, as gve seo Vi, wee aged o moe osed-

    eded-oes ad gve o e adoa gop fo pae, e oa asses. tese pobems

    wee addo o may oe aaya qesos, w e sdes paed oa asses.

    te ee ad oa sessos wee eaed ogo e semese. te oe devey

    e lee asses was oe wayfom eae o sdes. howeve e sdes wee aowed o

    wo gops, pae aaya pobems ad dsss e sses toa asses. te pae

    sesso fo a paa op was aways afe e oep was deveed ad desood by e

    sdes e lee asses. te paa sessos e lab asses ad objeves, aga, dee-

    med by e pesbed sdy seme ad syabs of e afag uvesy ad e eae. A

    a, ee was a ea demaao e lee, toa ad lab asses ems of e devey

    of oe, wa e sdes pefomed ad e leag Objeves.

    (b) Fo e PBl ead, ee was o sed pa ems of devey of oe. howeve e

    eaeee, emed Faao - pepaed a ompee se of tea nodes ad leag Obje-

    ves. A few exampes of tea nodes ad leag Objeves, eaed o e sbje ae:

    Technical Nodes:

    l Pepae abe of a Dempexe ad Mpexe.l iepe e abe of a Mpexe ad we e ageba eqao epeseg s

    ombaoa .

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    Learning Objectives:

    l Sdes sod be abe o eogze e of a Dempexe ad pepae s abe.l Sod be abe o se Deode as Dempexe ad ve vesa.l Sod be abe o we e of a Dempexe ad a Mpexe ad se as a ompee

    se.

    te faao desged opeeded tea Pobems (tPs) ad go em aeaed by a

    gop of seo eaes. We desgg tPs, ae was ae a e sope was boad eog so

    a e sdes od aeve a e tea nodes ad leag Objeves e oepa,

    we aempg o sove em.

    Sdes gapped w ese fzzy tea Pobemsoe a a me, as gve e seo Vi

    beow ad ed o desad e sope, sses ad oeps semmg fom o ee e tP

    befoe aempg o defy e eag pos a wod gde em owads e fomao of

    a evea espose [8] ( e fom of a eoy, ypoess, soo o agme).

    tee was o demaao of lee, toa o Paa asses ad e oa me avaabe

    fo e ose was dvded o sevea wo o PBl-sessos. te sdes deveoped a de-

    sadg ad aso fod e soo o e tP we avesg e oepa spae, oveg e

    ea odes ad aso eaed o wo eams. te oe of e eae was aged fom e

    oe-devey-ma o a faao. te sdes woed o e tea Pobems, yg o

    d o oe of e may possbe soos, deemg ad aevg e ow eoea ad

    paa leag Objeves. te eae emaed ad woed as gde-by-sde, y ag

    p e oe of a faao. Se aefy mooed ea ad evey sep of e gops ad emaed

    awae of e pogess made by e gops. A mes, we e faao fe a a e sdes

    eoeed e same d of boee, e faao ee deveed a sed ee o

    aed po a e sdes o pefom e same expeme, so a ey od poeed fe.

    Moode sofwae was sed fo oe sbmsso of assgmes ad peseaos fo bo e

    eads ad aso o exed e dssso amog sdes eve beyod e assoom.

    V. TImE ALLOTmENT AND EVALUATION PARAmETERS

    te oa os pe wee, aoed o e sbje of Dga Eeos (DE), wee xed ad was

    pededed by e vesy, e me aomes fo e PBl ead ad e tadoa ead

    wee made paae as gve tabe 1. i e PBl sessos, e demaao of ee, oa ad

    paa was emoved ad e sdes o oy deded e saegy, b aso maaged e

    me o aeve e eoea ad paa leag Objeves.

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    te seeo of sdes fo e PBl ead was y adom. Se e PBl ass od o

    sppo a age sze, e mbe was med o 25. howeve, afe e a ae, some sdes

    ef e ass ad ejoed e adoa gop ad e PBl ead was w 18 sdes e

    s expeme ad w 21 sdes e ex ba.

    te evaao ea of bo e eads wee maed as gve tabe 2:

    Table 1. Time Allotment for PBL and Traditional threads.

    Table 2. Evaluation Parameters of Traditional and PBL Groups.

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    te exea eoy pape s se by e uvesy ad s a ombao of sbjeve ad obje-

    ve ype qesos. te qesos ae opoaed, s a a e eves of Booms taxoomy

    ae esed e pape.

    Oe e eag pedagogy ad me dsbo wee paaeed fo bo e eads, e

    ose was deveed o bo e gops, by e same eae.

    VI. ThE TEChNICAL PROBLEmS (TP) DESIGNED FOR PBL ThREAD

    te Qas-ope-eded tea Pobems (tPs) e PBl ead wee e sag pos

    of e devey of e ose ad ee owedge oso. tese tPs wee aefy

    famed dssso w seo eaes of e depame. We g saes fo eva-

    ao fo PBl, s fod a say, e evaao saegy fo PBl s qe dffee fom

    a of e adoa paes. B s ase, se e oe famewo of evaao was

    a of e uvesy ad od o be aged, e tea Pobems famed s ev-

    ome, od o be y ope-eded. howeve, ey wee boad eog so as o de

    g e sdes mds ad we aempg e tPs, ey wee abe o avese ad

    ove e eeva poos of e syabs. Some tea Pobems fom e woe se ae

    sed beow:

    TP 1:

    A eeo eepoe exage s beg poweed by a oma powe sppy. howeve,

    oog a e ay of e exage, a powe bap geeao s aso saed, w

    a sppy powe ase of powe fae. A aam s o be desged. tee w be wo

    lEDs (oe gee ad e oe ed) o e fo pae of e exage, s a e gee lED

    gows we powe sppy s avaabe. i ase of fae of powe sppy, e exage daws s

    powe fom a geeao, ad s ase, e gee lED goes OFF ad e rED lED gows. i

    ase, e geeao aso goes dow, bo gee lED ad ed lED go OFF ad a bzze sas

    gg dag a ee s a majo fae. Desg s oo fo bo e lEDs ad

    e bzze.

    l Dee depede ad depeda vaabes (a), (b) ad () above.l Deveop a maemaa expesso fo above ses of saemes.l tabae e above ses of saemes symboay by sg vaabes deed above, weeve

    eqed.

    l Sow e above ses of saemes poay.l Vefy yo ess paay.

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    TP 2:

    te ame ad log u of a ompe pefoms e ame ad og opeaos fo

    e poesso. i s Alu a s o be desged, wee wo 4-b bay mbes ae o be

    sbaed sg wos ompeme. Desg a ombaoa fo e same.

    TP 3:

    Yo ae epog fo dy yo s eve assgme as gadae aee e desg depa-

    me of a eeos m. te foowg pobem as bee gve o yo:

    A poo of e aseve eeos of e exage s deped e fom of bo dagam

    as gve Fge 1.

    Bo e exages ae fo 2 ses. Depedg o seeo es yo ave o desg ad es

    e mpexe ad dempexe s e exage. Yo ave o d o e ommeay

    avaabe ics fom a eas ee vedos ad pepae a BOM (B of Maea). Yo boss as gve

    yo a me m of fo os o desg e same ad sbm e soo we fom.

    te daa avaabe fom ses ae aaog fom.

    TP 4:

    (A) i a ompe, e ea poessg (cPu) wos as e ba. i o oy does e

    aaos ad oga opeaos b aso aes ae of p ad op opeaos. i s a

    geeazed opeao, ee ae eg deves a s poesso s adg. te abao s

    gve beow tabe 3:

    te poesso as a 6-b addess bs. Devse o a meod o geeae e po mbe of ea

    i/O deves oe a a me, ad sed/eeve e daa.

    Figure 1. Block diagram of the transceiver at an electronic exchange.

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    (B) Befoe asmg aaog daa sg dga bs, e same s oveed o dga bs ad

    eoded oo. Fo odg e daa, may odg semes exs. Oe of e eo deeg odes

    s a eve pay ode, w yo ave sded eae. A e eeve, dga b seams ae beg

    eeved. tey ae s passed og a 8-b sea o paae ovee. Befoe feedg em o

    sbseqe poessg , e pay s o be eed a eo deeo. Desg e deeo

    o pefom e desbed opeao.

    VII. FACILITATING ThE PBL ThREAD, CONTRAST OF RESULTS

    twey-oe sdes, wo eoed fo e PBl ead, wee ased o fame e gops. tey

    wee gve odoy peseaos o oaboave eag, ode o pepae em fo e

    ew eag expeee. tea-Pobem i was gve as e sag po of e PBl ass. te

    eams wee e ased o fame e leag Objeves o e ow. te sdes od dede

    oy some of e leag Objeves vey vagey (ey wee eve awae of a e sses voved

    sovg a pobem) [7]. te faao, e, sppemeed e leag Objeves by addg

    e emag oes, so as o mae a ompee se. havg a ompee se of leag Objeves

    was a vey mpoa sep o deeme e deo of wo. tese leag Objeves, ,

    wee mpoa dvg foes ad aed as gges owads e desed oome(s), we wog

    owads e soo. A mes, e leag Objeves go added de ose, we e sea

    fo fomao was s ogog. te gop membes e dsbed vaos ass amog em-

    seves; e.g., sea fo fomao fom vaos esoes, ompe e daa, do aaos, pefom

    expemes ad ay we p e wo doe ad pepae peseao. te gop membes wee

    eoaged o oae e above ass amog emseves fo ea tea Pobem a ad. Fo

    ea tea Pobem, e gop membes wee ased o ee a eam eade, wo wod seame

    gs ad mae eessay desos o wo dsbo. te gop membes wee aso eoaged

    Table 3. Devices to be connected to the CPU and the port numbers.

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    o dsss e sses, dede e ow eoea, paa ad sofwae ams ad expoe og

    e ow eag ad msaes. ts was doe by oos moog ad sg em o

    eod ea eeva dg, ay msaes ommed ad e oeve ao ae. Oe ey

    ad eaed e soo, ey wee aso ased o fame sma d of pobems ad defy ap-

    pao aeas. A a, ey wee gded ad oeed by e wadeg faao wo wod

    opmze e me ad eag ad aso eped em o daw osos so as o d e desed

    soo. leag oo pae as e sdes eoeed sesses ad faes we expog.

    te faao empaszed o s expoao voyage as m as eag e oe soo.

    te Despve ad e AnOVA abes ae sow tabes 47. tabes 4 ad 5 sow moe spe-

    ay e s expeme we e ao esef was e faao. tabes 6 ad 7 sow e

    same ess w oa mbe of sdes as 131 ad as e Despves ad AnOVA vaes fo

    bo baes ae ogee. te p-vaes ae ose o 0 a e ases (tabes 5 ad 7). te ge

    vaes of Mea PBl gops ad smae vaes of Sadad devaos, exep ase of ow-

    edge_es_soe_exea (tabes 4 ad 6), ae dave of e bee ess obaed ase of

    PBl eads as ompaed o ose tadoa teads. te sx oes e daa, w pea

    o sdes wo faed e oa_owedge_es_soe, ave bee exded fom e aayss.

    Table 4. Descriptive of PBL and Traditional group for their Knowledge and Skill Scores.

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    Table 5. ANOVA table showing p-values of various types of evaluation.

    Table 6. Descriptives of PBL and Traditional scores of both the sets, with different

    facilitators.

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    i ode o gage e desg ad syess ss of e sdes, a sma poje was gve o a

    e sdes e ass a e ed of e em. te sdes wee gve wo sepaae wed dg-

    a s o bead boads, w a sge fa oded ea . te s gve wee

    hexadema o Seve Segme deode ad a tee-b Asyoos coe.

    te assessme poede of e s es ded dawg e by ag e oe-

    os, defy e , mag e abe/sae abe, dg o e fas, efyg em

    ad mag e s wo. A of e ompoes, ae ogee ad e mey ompeo of

    e s es wee gaded o a sae of A11 o D. We PBl sdes wee aowed o wo e

    gops, e sdes of e tadoa ead wee aso ased o oose e eammaes ad mae

    e gops. A of em wee eqed o d a woabe soo o e poje a spa of fo

    os. A eam of fo seo fay membes was e ased o evaae e pojes o a pedeed

    saegy. ress sowed a fo of e ve gops fom e PBl ead wee gaded A11, we

    oe gop was gaded B1. O e oay, oy wo gops of e tadoa ead od be gaded

    A1, e es wee gaded beow B. ts es was a ea dao of bee ss aqed by e

    PBl sdes, bo ems of wog gops ad paa owedge ad aby.

    A qesoae, sow tabe 8, was aed o a e sdes e ass; tabe 8 aso

    gves e smmazed ess.

    Table 7. ANOVA table showing p-values for both the batches taken together.

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    VIII. CONCLUSION

    May saes of sg PBl sg ad meda seam ae ed [1215] e eae, b

    oe ds vey few saes of sg e PBl appoa e wodwde egeeg m

    eae [35, 911] ad oe no ida. Eve e pedagogy of eag ad e evaao s

    deded by e uvesy. ts eaves vey e oom o empoy PBl vaos oses. By ag

    p s sees of effos fo vaos oses e de gadae Eeos ad commao

    Egeeg pogam, a qe way of egag PBl w e evaao saegy of uvesy,

    as bee aed, mpemeed ad evaaed.

    Aayss of e owedge es oded o e sdes by way of ed semese exams ad

    ea we eoy papes sowed a e cass Mea was 64%. i aso sowed a we e

    PBl sdes soed m bee e ea ompoe of e owedge es, ee was o

    majo dffeee e exea ompoe, w e saes sgy g favo of e PBl s-

    des. howeve, a emaabe dffeee was oed e s es ad espose o e ade

    svey qesoae (tabe 4). te paa ss aqed by e sdes of PBl ead wee moe

    a ose aqed by e sdes tadoa ead, as s ea fom e es of e s es

    Table 8. Questionnaire and the student responses.

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    oded a e ed of e semese. i was obseved a e sdes voay spe moe

    me e PBl ass a ee tadoa ead oepas. ts fa a ave moe a oe

    feee. if ae efeee o e sgy bee owedge es soes, s a mea a e

    sdes PBl ad o sped moe me e ass o ave a bee owedge soe. O e oe

    ad moe me spe e PBl ass a be abed o geae movaoa eve of e sdes

    PBl. te espose o qeso 2 tabe 4 (Fge 2b) eay sows a bee desadg eve

    fo e PBl ead. te espose o qeso 4 (Fge 2d) eeded a e moe qesog fom e

    sdes as o wy e PBl sdes wee o as ode of pefomg we e exams. howeve,

    o sasfaoy expaao od be obaed fom e sdes. if e esposes o qesos 3

    (Fge 2), qeso 6 (Fge 2f) ad qeso 7 (Fge 2g) tabe 6, ae ay dao of e po-

    dvy ems of leag Objeves, e sae deey s favo of PBl. te opyg abs

    Figure 2(a). Response to the questionWhat was your satisfaction level with the tutor of

    Digital Electronics?

    Figure 2(b). Response to the questionHow condent are you that you would be able

    to extrapolate the theoretical concepts and analytical skills learnt in DE to other subjects in

    higher classes?

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    Figure 2(c). Response to the questionOn an average how much time of the class did

    you use effectively?

    Figure 2(d). Response to the questionAre you condent of performing well in the

    external exams?

    Figure 2(e). Response to the questionDid you copy the assignments? (on a scale of

    1 to 5)

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    of e sdes fo assgmes, oweve, wee ompaabe bo PBl ad tadoa eads. A

    a, w wo expemes doeoe Aaog Eeos [1] ad e oe Dga Eeos,

    og e sampe szes wee sma, ad w eoagg ess obaed bo e expemes,

    s eommeded a PBl be sed o wde bass. howeve befoe dedg o sw ove fom

    e adoa meodoogy o PBl, moe sses e fay ag adg PBl asses, ad

    e os fao, se e PBl ass ao ade age mbes, eed o be soed o s.

    REFERENCES

    [1] A. Ma, S. D, J.P. Gpa, ad M. caa, Desg ad Evaao of a PBl based cose Aaog Eeo-

    s, iEEE tasaos o Edao, vo. 51, o. 4, pp. 432438, nov 2008.

    [2] A. Ma, S. D, J.P. Gpa, ad M. caa, Desgg pobems fo pobem-based eag ose Aaog Ee-

    os: cogve ad pedagoga sses, Asaasa Joa of Egeeg Edao, vo. 14, o. 2, pp. 3342, 2008.

    Figure 2(f). Response to the questionDid you enjoy attending the classes of DE?

    Figure 2(g). Response to the questionRate your practical skills in DE (Assembling the

    circuits, wiring, troubleshooting, etc.)

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    ADvAnCEs In EngInEErIng EDUCATIon

    Ui PBL t delie cue i Diital Electic

    [3] D.l. Mase ad P.J. Gaba, A Mdspay coopeave Pobem-Based leag Appoa o Embedded

    Sysems Desg, iEEE tasaos o Edao, vo. 41, o. 2, May 1998.

    [4] A. Sege ad D.t. rove, Pobem based eag a odoy ompe egeeg ose, 32d foe,

    ASEE/iEEE Foes Edao ofeee, nov 69, 2002, p://www.wp.ed/news/cof/FiE2002/.

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    iEEE tasaos o Edao, vo. 49, o. 1, Feb 2006.

    [6] c.M. Aso, l.E. Beod, c. cossad, J. Sp, M.A. MDemo, ad S. Wess, Empoweme o lea

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    pp. 146, 2003.

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    [8] B. Wso ad P. coe, cogve teag Modes, hadboo of resea isoa teoogy, 1s ed.,

    pp. 601621, new Yo: Soas, 1996.

    [9] J.E. Geebeg, B. Dege, ad M.l. Gay, hads-o leag Bomeda Sga Poessg, iEEE Egeeg

    Mede ad Boogy Magaze, pp. 7179, J-Ag, 2003.

    [10] r.M. Fede, teag Egeeg a a resea uvesy: Pobems ad possbes, Edao Qma,

    15(1), pp. 4042, 2004.

    [11] W.E. Moz ad l.l. hsma, A oaboave appoa bomeda egeeg edao, iEEE ta. Bomed.

    Eg., vo. 22, pp. 124129, 1975.

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    pp. 422432, 1993.

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    [17] r.M. Fede ad r. Be, Effeve saeges fo oopeave eag, J. coop. coab. coege tea, vo. 10,

    pp. 6975, 2001.

    AUThORS

    Arcana mantri ods e M.te. degee (Dga commao) fom nit, Bopa, ida.

    Pesey wog as Deo Aadems a caa ise of Egeeg ad teoogy, se

    s psg e dooa esea Eeos ad commao Egeeg ad Edao

    teoogy. he aeas of ees de c teoy ad Aayss, Dga commao, ad

    Edao teoogy.

    http://www.wpi.edu/News/Conf/FIE2002/http://www.wpi.edu/News/Conf/FIE2002/
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    SPRING 2009 17

    ADvAnCEs In EngInEErIng EDUCATIon

    Ui PBL t delie cue i Diital Electic

    Sunil Dutt ods a P.D. Edao ad as pbsed may wos Psyoogy of Ad

    leag ad Pefomae Evaao. hs aeas of speazao de resea Meodoogy,

    Measeme ad Evaao, ad Edaoa Maageme.

    J.P. Gupta s a ams of Baaas hd uvesy. he s a posgadae Eeos ad

    commao Egeeg ad ods a Dooa degee compe Egeeg fom e u-

    vesy of Wesmse, lodo. Pesey e Ve caeo of Jaypee ise of ifomao

    teoogy uvesy, e s a aamed aadema ad a ex-pofesso of iit, rooee. he as

    gded may P.D. eses ad ed mpoa admsave posos mpoa goveme

    bodes, besdes beg voved may esea ad deveopmea aves.

    madu Citkara ods a Dooae Edao; e aeas of eess ae as vaed as Edao

    teoogy, Pe Maemas, Aee, ad Goveae. Beg smea bgg evo-

    oay ages e edaoa seao of e ego ad epe of rasa Vas raa

    Awad, by nEhEG, ida, se s ooed po as e Edao io e ego of Pjab, ida.

    Se s aso e Deo of caa Edaoa ts.