A digital signal processing teaching methodology using concept-mapping techniques

422 IEEE TRANSACTIONS ON EDUCATION, VOL. 48, NO. 3, AUGUST 2005 A Digi al Signal P ocessing Teaching Me hodology Using Concep -Mapping Techniques M. R. Ma ínez-To es, F. J. Ba e o Ga cía, Senio Membe , IEEE, S. L. To al Ma ín, Membe , IEEE, and S. Galla do Vázquez Abs ac —The main goal o his s udy is o de elop a scien i ic me hod o designing a eaching me hodology used in a basic digi al signal p ocessing (DSP) cou se. The p oposed me hod is based on concep -mapping echniques, which applies mul i a ia e s a is ic analysis o summa ize he expe ience and knowledge o eache s in ol ed in basic DSP eaching. As a esul , a se o eaching me hodologies is ob ained. This esul , as well as o he in o ma ion ob ained ela ed o he ela i e impo ance o he concep s o be co e ed, has been used o p og am he cou se. Mo eo e , di e en eaching ools ha e been de eloped o imple- men he p oposed eaching me hodology. Finally, he eliabili y o he me hod has been compa ed wi h simila s udies o alida e he p oposed me hodology. Index Te ms—Compu e -based educa ional ools, concep map- ping, digi al signal p ocessing (DSP), educa ional echnology, elec- ical enginee ing. I. INTRODUCTION IN ecen yea s, he e ha e been d ama ic changes in engi- nee ing educa ion, especially in elec ical and compu e en- ginee ing (ECE) educa ion, bo h in e ms o cu iculum con- en (wha is augh ) and deli e y o ma e ial (how i is augh ) [1]–[5]. On he one hand, emphasis in he elec ical enginee ing ield has shi ed signi ican ly o he design o digi al sys ems. A shi has been made om emphasizing con inuous- ime-linea ime-in a ian sys ems o disc e e- ime-linea ime-in a ian sys ems. Because o his emphasis on disc e e- ime sys ems, he use o digi al sys em p ocessing (DSP), eal- ime implemen ed using digi al signal p ocesso s (DSP de ices), is becoming mo e widesp ead. The highe educa ional ins i u ion commonly inco po a es eal- ime DSP cou ses a he sophomo e educa- ional le el. These cou ses usually p esen DSP undamen als and heo y—implemen a ion o disc e e- ime sys ems, DSP de- ice s uc u e and p og amming, ini e wo d leng h e ec s, as Fou ie ans o m (FFT) algo i hms, ini e impulse esponse (FIR) and in ini e impulse esponse (IIR) design, mul i a e DSP, powe spec um es ima ion, linea p edic ion, and op imal il e ing, e c.—along wi h a labo a o y componen ha uses e alua ion boa ds, including a DSP de ice. On he o he hand, echnology is e e ywhe e, bu does i ha e a place in he class oom? Since he ea ly days o com- pu e s, lea ning h ough compu e -media ed en i onmen s Manusc ip ecei ed Ap il 11, 2004; e ised Janua y 25, 2005. The au ho s a e wi h he Depa men o Business Adminis a ion and Ma - ke ing and he Depa men o Elec onic Enginee ing, Uni e si y o Se ille, 41092 Se ille, Spain. Digi al Objec Iden i ie 10.1109/TE.2005.849737 (hype media ools, web-based educa ional suppo , simula- ion en i onmen s, e c.) has d ama ically inc eased [6]–[8]. Howe e , he e a e con lic ing claims abou hese lea ning en i onmen s. Some esea che s s a e he alidi y, e en he necessi y, o hese educa ional ools, al hough o he au ho s a e mo e scep ical abou hem. Fo ins ance, a emendous inc ease in he use o compu e simula ion has been no ed, some imes e en eplacing ha dwa e-based labo a o y cou ses, causing s uden s o miss ou on he lea ning ha can only ake place in a adi ional labo a o y. Compu e -based educa ional se ings seem o ha e been implemen ed wi hou any scien i ic c i e ia o , wha is wo se, wi hou any eal necessi y. Ne e heless, he pedagogical alue o compu e -based educa ional ools has been demons a ed in pa icula si ua ions. This s udy demons a es ha he simul aneous in eg a ion o adi ional and compu e -based educa ional echniques can subs an ially imp o e he eaching and lea ning p ocess. The need o e ise he eaching me hodology o enginee ing has o en been discussed. Al hough many enhancemen e- o ma ions ha e been pu in o p ac ice o e he yea s, no much a en ion has been paid o scien i ic analysis o im- p o ing he eaching p ocess. The educa ional p ocess has been e alua ed and, a mos , empi ically imp o ed. This pape p esen s he applica ion o a scien i ic me hod, based on con- cep -mapping echniques, o design a eaching model o a DSP cou se, included in he elec onic enginee ing cu iculum a he Uni e si y o Se ille, Se ille, Spain. The concep -mapping echnique has some imes been used o eaching e alua ion [9], bu i can also be used o eaching planning [10], as is p oposed he e. F om he concep -mapping analysis, di e en eaching me hods (clus e s) ha e been es ablished e i ying many o he imp o emen s ha ha e been ecen ly de eloped o e o m enginee ing educa ion—ac i e o coope a i e lea ning, echnology enhancemen , jus -in- ime lea ning, and cu iculum in eg a ion. This pape is o ganized as ollows. Fi s , he concep -map- ping echnique is p esen ed in Sec ion II. Then, in Sec ion III, he subjec , based on he s udy o a mode n DSP de ice and i s applica ions, is desc ibed, and he concep -mapping echnique is used o de elop he concep ual amewo k ha guides he educa- ional p ocess. A e wa ds, in Sec ion IV, he eaching me hod- ology ob ained is analyzed. Finally, he conclusions a e d awn. II. CONCEPT-MAPPING OVERVIEW A concep map is a o m o s uc u ed concep ualiza ion ha can be used by g oups o de elop he concep ual amewo k o guide an e alua ion, an exe cise, a plan, e c. [10], [11]. To 0018-9359/$20.00 © 2005 IEEE MARTÍNEZ-TORRES e al.: DSP TEACHING METHODOLOGY USING CONCEPT-MAPPING TECHNIQUES 423 de elop he concep map, a p ocedu e ha used quan i a i e and quali a i e ea u es was applied. A he s a , he pa ici- pan s gene a ed in o ma ion h ough b ains o ming. As pa o he p ocess, he da a was s uc u ed, quan i ied, and analyzed using s a is ical me hods ha include a mul idimensional scale and clus e s analysis. Concep -mapping shows he main ca e- go ies o ma hema ically de e mined ideas de i ed om he pa - icipan s’inpu . Each subse o ideas is ep esen ed on he map in clus e o m. Those clus e s ha a e closes o each o he a e said o be mo e di ec ly linked. The maps ep esen he opinion o he pa icipan s. The ollowing p ocedu e o de elop he concep map is laid ou in he ollowing phases [12]: 1) selec ing and p epa ing he pa icipan s; 2) b ains o ming i ems (concep s) ha deal wi h he opic ma e ; 3) s uc u ing and a ing hose i ems; 4) ep esen ing hose i ems on a concep map (using a mul i- dimensional scale and clus e s analysis); 5) in e p e ing he maps. III. APPLICATION TO DSP TEACHING The concep -mapping echnique has been applied o ob- ain he eaching me hodologies ha a e bes sui ed o an unde g adua e in e media e DSP subjec a he Uni e si y o Se ille. This subjec ocuses on he design o ad anced em- bedded digi al sys ems, DSP de ices, and hei applica ions. Special a en ion is paid o mic op ocesso a chi ec u e and unc ionali y and o p ac ical applica ions ela ed o digi al signal p ocessing algo i hms. The Texas Ins umen s C3X amily has been selec ed as he DSP de ice a chi ec u e ha can ully accomplish he objec i es o he subjec . Thein e nal s uc u e o C3X amily is used o ex- plain complex embedded sys ems and hei u ili y in DSP a ea. The TMS320C3X amily is a 32-b loa ing poin , gen- e al-pu pose, digi al signal p ocesso gene a ion om Texas Ins umen s (TI).1The amily a chi ec u e ea u es p esen a cen al p ocessing module ha is common o all amily mem- be s and has been designed o execu e commonly used DSP benchma ks in minimum ime o single-mul iplie a chi ec- u e. The in e nal buses and special DSP ins uc ion se o he TMS320C3x ha e he speed and lexibili y o execu e up o 150 MFLOPS (million loa ing-poin ope a ions pe second). I op imizes speed by implemen ing unc ions in ha dwa e ha o he p ocesso s implemen h ough so wa e o mic ocode. This ha dwa e-in ensi e app oach p o ides pe o mance p e- iously una ailable on a single chip. This DSP can pe o m pa allel mul iplica ions and a i hme ic logic uni (ALU) op- e a ions on in ege o loa ing-poin da a in a single cycle. Each p ocesso also possesses a gene al-pu pose egis e ile, a p og am CACHE, dedica ed auxilia y egis e a i hme ic uni s (ARAUs), in e nal dual-access memo ies, one di ec memo y access (DMA) channel suppo ing concu en inpu –ou pu (I/O), and a sho machine-cycle ime. High pe o mance and ease o use a e esul s o hese ea u es. Gene al-pu pose 1The Texas Ins umen s websi e is a h p://www. i.com applica ions a e enhanced g ea ly by he la ge add ess space, mul ip ocesso in e ace, in e nally and ex e nally gene a ed wai s a es, wo ex e nal in e ace po s, wo ime s, se ial po s, and a mul iple-in e up s uc u e. Mo eo e , his en i onmen suppo s a wide a ie y o sys em applica ions, om hos p o- cesso o dedica ed cop ocesso , including high-le el language (implemen ed h ough i s egis e -based a chi ec u e, la ge add ess space, powe ul add essing modes, lexible ins uc ion se , and well suppo ed, loa ing-poin a i hme ic). The gene al p ocedu e o concep -mapping de elopmen , ou lined in he ollowing subsec ions, is based on he i e s ages ha we e desc ibed in Sec ion II. A. Selec ion and P epa a ion o he Pa icipan s One o he mos impo an asks in de eloping a concep map is deciding who will pa icipa e in he p ocess. Expe imen s demons a e ha concep ualiza ion is be e when he p ocess includes a wide ange o expe people. A b oad, he e ogeneous pa icipa ion helps o ensu e ha he di e en poin s o iew will be conside ed, hus encou aging “cons uc ing” he igh concep ual amewo k. Fo his s udy, eache s wi h con as ing wo k expe iences in DSP eaching, pa icula ly wi h he amily TMS320C3X, ha e been selec ed. A o al o 14 eache s pa icipa ed, all o whom had bo h eaching and DSP applica ion de elopmen expe ience. This numbe o people is wi hin he adequa e limi s, be ween en and 20 [10]. B. B ains o ming The nex s age consis ed o es ablishing a lis o i ems ela ed o he eaching o he p oposed cou se. Using he b ains o ming echnique, he wo k g oup iden i ied a lis o 82 i ems, shown in Table I. C. S uc u ing and Ra ing he I ems When a se o i ems ha desc ibes he concep ual domain o he gi en opic is es ablished, one mus p o ide in o ma- ion abou how hey a e in e ela ed and measu ed in ela ion o he opic. Bo h asks make up he s age o i em s uc u ing h oughou he concep -mapping de elopmen p ocess. The i s ask o he wo king g oup consis ed o classi ying he 82 i ems in se e al g oups based on hei a ini y wi h e- spec o some common eaching me hodology. Each o he pa - icipan s applies his o he pe sonal expe ience o de ine he numbe o g oups and he eaching me hodology. A simila i y ma ix, de ined as wi h 82, is ob ained as ollows: he alue o he elemen is equal o 1 i he h and he h i ems a e g ouped oge he and is equal o 0 o he wise. The o al simila i y ma ix, de ined as , is ob ained as he addi ion o all he simila i y ma ixes. The second ask in ol ed a ing each i em acco ding o i s con ibu ion o he goals o he cou se. The i ems hen had o be en e ed on he sco ing able in Like scale o m, wi h a ange o 1 o 5, conside ing ha “li le con ibu ion,” “a lo o con ibu ion,”and he numbe s in be ween e e ed o in e - media e con ibu ions. A “ze o-con ibu ion”sco e was no pos- sible, since he b ains o ming s age speci ically asked o hose 424 IEEE TRANSACTIONS ON EDUCATION, VOL. 48, NO. 3, AUGUST 2005 TABLE I LIST OF IDENTIFIED ITEMS i ems ha con ibu ed o ob aining he cou se goals. The e o e, o a g ea e o lesse ex en , all he i ems had some con ibu ion. D. Rep esen ing he I ems in a Concep -Map Fo m Fu he mo e, a double analysis was pe o med using in o ma- ion abou he ollowing s a is ical analysis: a mul idimensional scale and a clus e analysis. To comple e his double analysis, MATLAB was used. Mul idimensional scaling is a ma hema ical ool ha uses p oximi ies be ween objec s, subjec s, o s imuli o p oduce a spa ial ep esen a ion o hese i ems. The p oximi ies a e de ined as any se o numbe s ha exp esses he amoun o simila i y o dissimila i y be ween pai s o objec s, subjec s, o s imuli. The objec o a mul idimensional scale is o ind he coo di- na es o he poin s in -dimensional space so ha he e is a solid ag eemen be ween he obse ed p oximi ies and he in e poin dis ances [13]. In concep mapping, his mul idimensional scale se s up a poin map ha ep esen s he se o decla a ions made du ing he b ains o ming session. I is based on he esul s o he simila i y ma ix o he classi ied ask. The mos common app oach used o de e mine he coo dina es o he objec s is an i e a i e p ocess, commonly e e ed o as he Shepa d–K uskal algo i hm [13]. The mul idimensional scale gi es he analys a speci ic numbe o dimensions ha ep esen he se o poin s. I a one-dimensional (1-D) solu ion is equi ed, all he poin s will o m one line. A wo-dimensional (2-D) solu ion will place he MARTÍNEZ-TORRES e al.: DSP TEACHING METHODOLOGY USING CONCEPT-MAPPING TECHNIQUES 425 Fig. 1. Poin map ob ained om mul idimensional scaling. se o poin s on a plane. The analys would be able o use hese dimensions. On he o he hand, in e p e a ion o solu ions wi h mo e han h ee dimensions is di icul . The e o e, when using concep maps, one should use 2-D g aphs. In his case, he di e en i ems we e dis ibu ed on a 2-D plane, s a ing om he simila i y ma ix, in such a way ha he dis ance be ween he di e en i ems is in e sely p opo ional o hei a ini y. Tha is, hose i ems si ua ed close o each o he a e concep ually mo e closely ela ed han hose ha a e placed u he om he plane. By ep esen ing he in o ma ion in a 2-D space, he loss o in o ma ion o ob ain a less complica ed in e - p e a ion o he in o ma ion is accep ed. The clus e analysis o ganizes he in o ma ion coming om he mul idimensional scale, no om he simila i y ma ix [14]. Wa d’s algo i hm was used o he clus e analysis since i o e s mo e sensi i e solu ions and can be be e in e p e ed han o he es ima es [15]. A i s , he clus e analysis conside s each i em as i s own clus e , hus ob aining a solu ion o clus e s, in his case 82, co esponding o he numbe o iden i ied i ems. Fo each le el o analysis, Wa d’s algo i hm combines wo clus e s un il inally all he i ems a e combined in o jus one clus e . De e mina ion o he numbe o clus e s o be used in he inal solu ion is im- po an . Subsequen ly, disc e ion is equi ed when examining he di e en ypes o possible clus e solu ions o decide which ones make sense. As a ule use o he numbe o clus e s ha e s by excess, a he han by de ec , is no mal; in o he wo ds, a la ge numbe o clus e s is p e e ed o ha ing a clus e con- aining he e ogeneous concep s. Once he mul idimensional scale and he clus e analysis a e ca ied ou , a poin map and a clus e map a e o med. The inal analysis equi es an a e age sco e o each pa icipan o each i em and o each clus e , o ming a poin - a ing map and a clus e - a ing map. E. In e p e a ion o Maps In o de o in e p e he maps, a inal wo kg oup was o ga- nized. Gene ally, he esul s de i ed om he clus e analysis a e mo e di icul o in e p e han hose om he mul idimensional scale. The clus e analysis is seen as an indica o . A imes, one would like o “ isually a ange” he clus e s in o sensi i e pa s so ha he mul idimensional space could be in e p e ed mo e easily. The key is o main ain he in eg i y o he mul idimen- sional scale esul s by achie ing a solu ion ha will no allow he clus e s o o e lap. A consensus o he names gi en o he di e en clus e s mus be eached, using as a s a ing poin hose names gi en o he g oups by he pa icipan s. IV. CONCEPT-MAPPING APPLICATION RESULTS The poin map o Fig. 1 is he esul o mul idimensional scaling. Each numbe ep esen s an i em o Table I. The dis- ance be ween poin s is a measu e o a ini y. Close i ems a e mo e closely ela ed o each o he , while u he poin s show a high le el o dissimila i y. The esul an map is a (bidimen- sional) app oach o he dis ances ob ained om he sum o each pa icipan simila i y ma ix. Fig. 2 illus a es he a ing poin map, de i ed om he alue ha he pa icipan s assigned o each i em, ollowing he Like 1- o-5 scale. In he uppe le -hand co ne o he igu e, he co - espondence be ween laye s and nume ical Like alues a e shown. Once he bidimensional ep esen a ion o he 82 i ems is achie ed, he i ems mus be g ouped in homogeneous clus e s. These clus e s will de ine he esul ing eaching me hodologies. 426 IEEE TRANSACTIONS ON EDUCATION, VOL. 48, NO. 3, AUGUST 2005 Fig. 2. Ra ing poin map ob ained om mul idimensional scaling. Fig. 3. Clus e map. The esul o he clus e analysis is summa ized in Fig. 3. Acco ding o Wa ds’algo i hm, he i ems a e g ouped in en clus e s. The concu ing denomina ions o he en clus e s a e shown in Table II. Th ee g oups can be obse ed in he clus e map (Table II). The i s one is based on clus e s numbe s 1, 2, 3, 6, and 7. I includes clus e numbe 2, which implies a con en ional lec u e. Clus e s numbe s 3 and 7 ( heo e ical and p ac ical sel -lea ning MARTÍNEZ-TORRES e al.: DSP TEACHING METHODOLOGY USING CONCEPT-MAPPING TECHNIQUES 427 Fig. 4. Clus e a ing map. TABLE II CLUSTER ANALYSIS RESULTS using e e ence ma e ial) appea e y close o he second one. In hese cases, he lea ning p ocess calls o he ac i e pa ic- ipa ion o s uden s wi h adequa e e e ence ma e ial. Clus e 1 also belongs o his g oup. In his pa icula case, an o ien ed o guided lea ning using mul imedia eaching ools has been de- ined. This eaching me hodology conside s he ac i e pa ici- pa ion o s uden s in hei lea ning p ocess, in acco dance wi h he u u e Eu opean C edi s T ans e s Sys em (ECTS), [16], [17]. None heless, he eaching p ocess is no jus educed o con en ional classes. Fo ins ance, clus e 1 explici ly shows hose i ems o which one mus be ained using no el compu e - based eaching ools, such as mul imedia anima ions. Unde his clus e , i ems such as DSP special add essing modes, in e nal bus ope a ions, pipelining ope a ions, and con lic s o CACHE memo y, a e ound. These concep s a e e y di icul o explain using con en ional classes. Howe e , any mul imedia ool, in- cluding anima ions o show he associa ed dynamic da a low, is specially indica ed o he eaching p ocess. Finally, clus e 6 ies heo y and labo a o y wo k in he subjec oge he by means o labo a o y semina s on so wa e and ha dwa e ools o be used h oughou he cou se. The second g oup is based on clus e s 4, 5, and 9, ela ed o labo a o y wo k. In his case, a simula ion ool and a designe ki a e used in labo a o y classes o de elop p ac ical applica- ions. This clus e ela es o he p ac ical poin o iew o he heo e ical concep s desc ibed in clus e 1. The las g oup embodies clus e s numbe 8 and 10. I connec s he subjec o he eal and p o essional wo ld. To mee his goal, alks, con e ences, and deba es (clus e 8) and isi s o i ms wo king in he DSP and mic oelec onic design a eas (clus e 10) a e p oposed. The p incipal aim is o b ing he company pe spec i e close o he s uden s: making decisions, looking o solu ions, de eloping analysis skills, con ac ing he wo king en i onmen , employing eal applica ions, e c. Fig. 4 depic s he clus e a ing map. The a ing equi alence is shown in he lowe le -hand co ne . Clus e s numbe 8, 9, and 10 a e p edominan e sus he o he s which ha e a simila weigh . To summa ize, clus e s ela ed o p ac ical applica ions and o e ing ex e nal ac i i ies a e a ed as p edominan . A. Reliabili y Analysis The adi ional heo y no mally applied o he eliabili y o social science esea ch does no co ec ly i on concep maps, since he assump ion is ha o each i em es ed he e is a co ec answe known in ad ance. The e o e, each indi idual is mea- su ed o he ques ion and ma ked only as co ec o inco ec . La e , he eliabili y o each es i em(s) o o he o al sco e is es ima ed. Howe e , wi h concep maps, one answe is no as- sumed o be co ec o inco ec . To measu e eliabili y, he da a 428 IEEE TRANSACTIONS ON EDUCATION, VOL. 48, NO. 3, AUGUST 2005 TABLE III DESCRIPTIVE STATISTICS FOR RELIABILITY ESTIMATES FOR 38 CONCEPT MAPPING PROJECTS ma ix s uc u e is in e ed (wi h espec o adi ional heo y) so ha he pe sons a e placed in columns, and he i ems (o pai s o i ems) a e placed in ows. The alue o eliabili y ocuses on consis ency ia he g oup o supposedly homogeneous pa ici- pan s. In ha espec , alking abou he eliabili y o he simi- la i y ma ix o he eliabili y o he map, bu no he eliabili y o he indi idual s a emen s, is help ul [18]. The key p oduc o he concep mapping p ocess is he 2-D map i sel ; consequen ly, he e o s made o e i y he eliabili y a e di ec ed owa d he cen al phases o analysis, de elopmen , and ep esen a ion. In he s udy published by T ochim [18], he eliabili y o con- cep mapping was es ed by six coe icien s ha could be easily es ima ed om he a ailable da a on any concep map p ojec . These coe icien s we e de ined and es ima ed o 38 concep map p ojec s. The esul s indica ed ha he concep -mapping p ocess could be conside ed eliable, acco ding o he s anda ds gene ally ecognized o accep able eliabili y le els. This s udy only conside ed he concep -mapping eliabili y. On hese concep maps, a es o de e mine whe he he elia- bili y le els we e wi hin he accep able eliabili y s anda ds was conduc ed. All o he eliabili y es ima o s e e ed o on he concep maps and used in T ochim’s eliabili y s udy we e calcula ed o his s udy, and hey we e compa ed wi h he esul s ob ained in T ochim’s esea ch (Table III). A high le el o eliabili y was ound wi hin hese concep maps. Fu he mo e, he indica- o s we e ound o be alid and wi hin he s anda ds shown by T ochim. The coe icien s de ined by T ochim a e as ollows. 1) Indi idual- o-Indi idual So Reliabili y :Co e- la es each pe son’s bina y so ma ix o each pai o indi iduals; i explains how he so s a e co ela ed o he di e en pa icipan s in he de elopmen o he concep map. This co ela ion is iden i ied by calcula ing he a e age o he co ela ions and by applying he Spea man–B own P ophecy o mula [19], as ollows: whe e co ela ion es ima ed om he da a; whe e is he o al sample size, and is he sample size on which is based; eliabili y es ima ed acco ding o he Spea men– B own P ophecy o mula. In his case, he eliabili y was shown o be 0.703, a alue ha is less han T ochim’s a e age alues, bu s ill ound o be wi hin he limi s; he minimum alue ob ained by T ochim was 0.670, as shown in Table III. The e o e, his alue is conside ed accep able. 2) Indi idual- o-To al Ma ix Reliabili y :This co - ela es each pe son’s bina y so ma ix , wi h he o al ma ix ; i de e mines how he so s ca ied ou by each pe son co ela e wi h all he so s. To ind he calcula ion, one mus ake he a e age o hese co ela ions and apply he Spea men–B own P ophecy o mula. The alue o he indi- idual o o al ma ix eliabili y is 0.918. This alue is close o he a e age alue, which indica es ha he eliabili y o his ype is alid on his map. 3) Indi idual- o-Map Reliabili y :This co ela es each pe son’s bina y so ma ix , wi h he Euclidean ma ix dis ances .To ind his calcula ion, one akes he a e age o hese co ela ions and applies he Spea men–B own P ophecy o mula. In his case, he alue was 0.882. This alue is highe han he a e age alue ound in T ochim’s esea ch. 4) A e age In e so Reliabili y :This calcula es he co ela ion among he sco es o each pai o pe sons. To ind he calcula ion, one akes he a e age o hese co ela ions and applies he Spea men–B own P ophecy o mula. This concep map showed he alue was 0.745, which demons a es ha he sco es ound on his concep map we e ela i ely eliable since his alue was close o he a e age o T ochim’s concep map. 5) Spli -Hal Reliabili ies ( and ): Di ide he se o so s om each p ojec in o wo hal es and calcula e concep maps o each g oup. The o al ma ices and a e co e- la ed, and hen he Spea men–B own P ophecy o mula is ap- plied o ob ain . The Euclidean dis ances we e co ela ed be ween all pai s o poin s on he wo maps and , and he Spea men–B own co ec ion was applied o achie e . The simila i y ma ix esul and he dis ance ma ix esul we e close o he a e age alues de ined by T ochim. The e o e, hese alues a e conside ed accep able. In sho , his concep map is eliable since he di e en elia- bili y indica o s showed alues wi hin he accep able limi s se by T ochim. V. CONCLUSION A scien i ic me hod o designing a eaching me hodology has been used o planning a basic digi al signal p ocessing (DSP) cou se. The p oposed me hod, based on concep -mapping ech- niques, has applied mul i a ia e s a is ic analysis o summa ize he expe ience and knowledge o eache s in ol ed in he educa- ional p ocess. Consis en ly, a se o en eaching me hodologies has been ob ained o p og amming he cou se. The eaching MARTÍNEZ-TORRES e al.: DSP TEACHING METHODOLOGY USING CONCEPT-MAPPING TECHNIQUES 429 me hodology has also been analyzed by calcula ing he elia- bili y es ima o s. Finally, i has been alida ed by compa ing he ob ained eliabili y es ima o s wi hin he T ochim’s limi s. REFERENCES [1] R. M. Felde , G. N. Felde , and J. 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He esea ch in e es s include in ellec ual capi al and knowledge managemen . F. J. Ba e o Ga cía(M’03–SM’05) was bo n in Se ille, Spain, in 1967. He ecei ed he elec ical enginee ing and Ph.D. deg ees om he Uni e si y o Se ille, Se ille, Spain, in 1992 and 1998, espec i ely. In 1992, he joined he Depa men o Elec onic Enginee ing a he Uni e si y o Se ille, whe e he is cu en ly a Full P o esso . His cu en in e es s include mic op ocesso and digi al signal p ocessing de ice sys ems, uzzy-logic-based sys em, con ol o elec ical d i es, and powe elec onics. S. L. To al Ma ín(M’01) was bo n in Raba , Mo occo, in 1972. He ecei ed he elec ical enginee ing and Ph.D. deg ees om he Uni e si y o Se ille, Se ille, Spain, in 1995 and 1999, espec i ely. He is cu en ly a Full P o esso in he Elec onic Enginee ing Depa men , Uni e si y o Se ille. His esea ch in e es s include mic op ocesso and dig- i al signal p ocessing de ice sys ems, s ochas ic p ocessing, and hei indus ial applica ions. S. Galla do Vázquez was bo n in Huel a, Spain, in 1978. He ecei ed he elecommunica ion enginee ing deg ee om he Uni e si y o Se ille, Se ille, Spain, in 2002. He is cu en ly wo king owa d he Ph.D. deg ee in elec onic enginee ing, signal p ocessing, and communica ions a he Uni e si y o Se ille, Se ille, Spain. In 2003, he joined he Depa men o Elec onic Enginee ing a he Uni e si y o Se ille as a Resea che on a esea ch p ojec aimed a powe elec onic con e sion con ol s a egies. His esea ch in e es s include digi al signal p ocessing de ice sys ems, in o ma ion and communica ion echnologies, and powe elec onics.