Is there a gap i iitial secodary mathematics teacher educatio i Spai compared to other coutries? Hay u vacío e la formació iicial del profesorado de matemáticas de Secudaria e España respecto a otros países? doi: 10.4438/1988-592X-RE-2015-372-317 Laura Muñiz-Rodríguez Pedro Aloso Velázquez Luis J. Rodríguez Muñiz uiversidad de oviedo Marti Valcke uiversitet get Abstract Iitial teacher educatio is a key factor i the teachig ad learig process. Previous studies o educatioal policies evidece some deficiecies i the quality of teacher traiig programs i Spai, both i primary educatio ad secodary educatio. I 2008, Spai participated, alog with 16 other coutries, i the Teacher Educatio ad Developmet Study i Mathematics (TEDS-M), a iteratioal comparative study which examied how differet coutries prepared their prospective teachers to teach mathematics i primary ad lowersecodary school. The Spaish participatio i the study was limited to future primary teachers; but, what is the situatio of iitial educatio for future secodary mathematics teachers i Spai? I this paper we preset a aalysis of iitial traiig programs for future mathematics teachers i secodary (1) This work has bee partially supported by Campus of Iteratioal Excellece of Uiversity of Oviedo. 106
educatio i Spai. First, we study the mai characteristics of iitial teacher traiig programs i other coutries: orgaizatio, structure, duratio, access requiremets, ad professioal stadards. Next, we aalyzed the Spaish situatio, startig with a brief historical review of the previous model, ad cotiuig with a detailed descriptio of the curret approach. The results show clear differeces whe comparig Spai with other coutries, ad idicate the eed of itroducig measures i order to overcome the curret deficiecies of teacher traiig programs ad cotribute to the improvemet of its quality. Key words: iitial teacher educatio, teacher traiig programs, secodary mathematics educatio, prospective mathematics teachers, secodary mathematics teacher competeces. Resume La formació iicial del profesorado es u factor clave e el proceso de eseñaza-apredizaje. Estudios previos sobre políticas educativas señala u problema de calidad e los programas de formació iicial docete e España, tato a ivel de Educació Primaria como de Educació Secudaria. E 2008, España participó, juto co otros 16 países, e el Teacher Educatio ad Developmet Study i Mathematics (TEDS-M), primer estudio iteracioal comparativo sobre el coocimieto adquirido por los futuros profesores de matemáticas e Educació Primaria y Educació Secudaria obligatoria al acabar su formació iicial. La participació española e el estudio quedó limitada a futuros maestros; pero cuál es la situació de la formació iicial para futuros profesores de matemáticas e Educació Secudaria e España? E este artículo presetamos u aálisis de los programas de formació iicial para futuros profesores de matemáticas e Educació Secudaria e España. E primer lugar, estudiamos las pricipales características de la formació iicial docete e otros países: orgaizació y estructura de las eseñazas, duració, requisitos de acceso, estádares profesioales, etre otras. A cotiuació, aalizamos la situació española, comezado co ua breve reseña histórica del modelo aterior, y cotiuado co ua descripció detallada del efoque actual. Los resultados demuestra claras diferecias cuado comparamos el caso de España co otros países, e idica la ecesidad de adoptar medidas que permita suplir las pricipales carecias de estos programas y cotribuya a la mejora de su calidad. Palabras clave: formació iicial docete, programas de formació iicial, educació matemática secudaria, futuros profesores de matemáticas, competecias del profesor de matemáticas e educació secudaria. 107
Itroductio All over the world, there is a growig cocer about mathematics educatio. At the same time, iitial teacher educatio has bee questioed due to the results from the atioal ad iteratioal assessmets such as PISA (Program for Iteratioal Studet Assessmet), TIMSS (Treds i Mathematics ad Sciece Studet) or PIRLS (Progress i Iteratioal Readig Literacy Study). I particular, iitial educatio for secodary mathematics teachers i Spai is a matter of cocer to educatioal authorities ad policy-makers. This focus o teacher educatio could arise because of evidece suggestig that Spaish teachers lack essetial kowledge for teachig mathematics due to the low quality of iitial educatio programs for secodary mathematics teachers. We ca illustrate this checkig that there is a lack of atioal teachig stadards ad geeral guidelies determiig what specific competeces, skills, cotets, ad assessmets procedures future mathematics teachers should acquire. While some Europea coutries, such as Uited Kigdom or Germay, provide cetral level regulatios, recommedatios ad guidelies for iitial teacher educatio programs, Spaish uiversities are very autoomous i determiig the cotet of their mathematics teacher educatio programs. Aother thory problem is that each istitutio is allowed to establish specific restrictios ad etry requiremets cadidates should fulfill i order to eter to a specific educatio master program, as it is explaied further ahead i the text. Cosequetly, future mathematics teachers cotet kowledge seems to be varied, heterogeeous, ad badly structured. Available research evidece ad theoretical frameworks give clear directios whe studyig teacher educatio ad its positio withi a educatioal system. For istace, some studies i the Europea framework highlight that iitial teacher educatio has sigificat ifluece o the learig process, emphasizig the close relatio betwee the quality of studets learig ad the quality of teacher educatio based o iitial ad cotiuous educatio programs. O the other had, metaaalysis studies poit at the weak relatioship betwee iitial teacher educatio ad the quality of studet learig. Furthermore, absece of practical preparatio i teacher educatio could have importat cosequeces, such as ovice teachers lackig the 108
copig skills ecessary to fulfill their teachig roles, ofte resultig i a theory-practice shock, ad/or high rates of attritio durig the first years of teachig. I this sese, prospective secodary teachers i Spai complai about the missig lik betwee theory ad practice. The mai goal of this article is to carry out a critical aalysis of iitial educatio programs for secodary mathematics teachers based o a iteratioal compariso i order to idetity its pricipal stregths ad weakesses ad suggest adequate measures to esure a high quality teacher educatio system. For our purpose, we first draw a iteratioal compariso of teacher traiig approaches for prospective secodary mathematics teachers, focused o orgaizatioal ad structural features such as duratio, structure, level of the degree awarded at the completio of the teacher traiig program, requiremets studets should fulfill i order to eter ito the program, ad existece of a professioal competecy framework for studet teachers. This iteratioal perspective is ext used to aalyze the Spaish cotext ad idetify crucial differeces that ca arise importat cosequeces i the Spaish teacher educatio system quality. Fially, we discuss possible prospective actios based o the results obtaied from the aalysis. A iteratioal view of iitial educatio programs for secodary teachers I may coutries, i order to become a teacher, cadidates are required to have successfully fialized a iitial teacher educatio program. However, teacher educatio programs vary cosiderably across atios. I this sectio, i order to idetify how coutries aroud the world prepare teachers to teach mathematics i secodary 2 school, we preset some descriptive data. The aalysis is based o comparisos of 14 coutries: Chile, Filad, Frace, Germay, Israel, Italy, Japa, Korea Republic, Norway, Polad, Spai, Turkey, Uited Kigdom ad Uited States. We opted for these coutries sice they ivolve diverse ad represetative educatioal models i the iteratioal framework. (2) From ow o, accordig to the Iteratioal Stadard Classificatio of Educatio ISCED 2011 (UNESCO, 2012), the therm secodary will refer to ISCED 2&3. 109
Characteristics of iitial educatio programs for secodary teachers After aalyzig iteratioal comparative studies based o iitial teacher educatio, we oticed broad differeces i key structural ad orgaizatioal characteristics of iitial educatio programs for secodary teachers i public istitutios i the set of cosidered coutries, such as duratio, orgaizatio, level of the degree awarded ad existece of etry requiremets to access ito iitial educatio programs. Iitial educatio programs are typically orgaized accordig to two well-distiguished structures: The cocurret model, i which geeral educatio ad professioal educatio occurs simultaeously i a sigle program. The cosecutive model, i which studets pursue their subject studies first ad after take a professioal course i educatio which provides them with the theoretical ad practical competeces ad skills eeded to succeed as a teacher. I the cocurret model studets are ivolved i specific teacher educatio right from the start of their studies, whereas i the cosecutive model this occurs after their bachelor degree (see Table I). Although the literature poits out that cocurret models allow prospective teachers to develop a true professioal idetity as a teacher sice the begiig of their iitial educatio (Esteve, 2006), there are o sigificat differeces betwee both models ad the results of studets learig (Valle & Maso, 2011). As show i Table II, the orgaizatio of iitial teacher educatio programs vary from coutry to coutry. While i Filad, Japa, Polad ad Turkey cocurret model is predomiat, i Frace, Germay, Italy ad Spai teacher traiig follows a cosecutive model. At the same time, both cocurret ad cosecutive models coexist i some atios such as Chile, Israel, Korea Republic, Norway, Uited Kigdom ad Uited States. I particular, i Germay iitial teacher educatio programs are differetly orgaized amog the differet states. 110
TAbLe I. Advatages ad disadvatages of cocurret ad cosecutive programs source: Adapted from Musset, 2010. TAbLe II. orgaizatio of iitial teacher educatio programs for secodary teachers source: ow elaboratio based o data from oecd, 2014; tatto et al., 2012. The duratio of iitial educatio programs for secodary teachers rages from 4 years i Israel, Japa, Korea Republic ad Uited States to betwee 6 ad 6.5 years i Germay, Italy ad Norway. Cocurret model commoly lasts 4 years, while for cosecutive model the first phase typically lasts betwee 3 or 4 years ad the secod phase 1 or 2 years. Furthermore, a teachig itership is madatory i most coutries. However, the required duratio vary sigificatly. For istace, i Israel, Japa, Korea Republic, Spai ad Turkey practicum lasts betwee 20 ad 111
60 days, as opposed to 120 days i Uited Kigdom, ad at least 282 days i Germay. Not all coutries impose educatioal requiremets for etry ito iitial teacher educatio programs. Besides that, selective criteria to eter educatioal traiig programs are used. For istace, i some coutries cadidates are selected based o their previous traiig grade-poit average, while i others selectio is based o a iterview or a competitive examiatio. Fially, the level of the degree awarded after completig a teacher traiig program also differ across coutries, maily depedig o its legth. I this way, master degree diplomas are obtaied after at least five years of tertiary educatio (see Table III). TAbLe III. Level of the degree awarded at the completio of a teacher traiig program source: ow elaboratio based o data from oecd, 2014; tatto et al., 2012. Iteratioal stadards for secodary mathematics teachers Teacher educatio is geerally guided by atioal stadards which specify what professioal qualificatios are expected from a studet teacher at the ed of iitial educatio program. However, i may coutries there is a lack of such teachig stadards, ad istitutios eve have a high level of autoomy i developig detailed competece requiremets i teacher educatio programs. I this way, while some coutries put forward very clear ad detailed stadards, i others very geeral guidelies are provided by educatioal miistries; some examples are: detailed lists of specific competeces liked to professioal 112
stadards ad professioal developmet; e.g. Uited Kigdom, Uited States. specific stadards to guide the assessmet of ewly traied teachers i lie with the competeces to be developed durig the educatio program; e.g. Chile, Germay. framework of teacher competeces expected o completio for preparig both pre-service ad i-service teachers; e.g. Turkey. geeral stadards for teachers defiig the assessmet of traiee teachers; e.g. Israel, Japa, Korea Republic. curricula for iitial teacher educatio metioig teachers competeces required for iitial teacher educatio; e.g. Filad, Polad, Spai Cosiderig those coutries with a deeper developmet i teacher stadards as well as specific stadards for secodary mathematics teachers established by iteratioal associatios such as NCTM (Natioal Coucil of Teacher of Mathematics) or AAMT (Australia Associatio of Mathematics Teachers) we ca defie a commo list of core stadards for secodary mathematics teachers i the iteratioal framework (see Table IV). Besides, i a few coutries such as Uited Kigdom or Korea Republic, a comprehesive list of bechmarks has bee established i order to determie to what extet teacher stadards should be attaied. Therefore bechmarks specify the rage of skills, abilities, kowledge, uderstadig ad values prospective teachers should developed, ad i regards to which they might be assessed. This aims to esure a high quality teacher educatio system, sice they clearly defie iitial teacher educatio programs, actig as a template for a balace assessmet. However, this is ot a commo feature i the iteratioal framework. 113
TAbLe IV. core stadards for secodary mathematics teachers source: ow elaboratio. 114
Iitial educatio for secodary mathematics teachers i Spai Iitial teacher educatio programs have udergoe several chages durig recet decades. Due to the itroductio of the Bologa reform, the former Certificate of Pedagogical Aptitude (CPA, CAP i Spaish) was replaced with the Master Degree i Teacher Traiig i Secodary Educatio (MDTTSE). The disappearace of the CPA has bee a substatial improvemet, but the implemetatio of the MDTTSE has ot bee exempted from difficulties. Both programs are described below. A brief historical review: the CPA Before 2009, secodary educatio programs were based o a short-term course i view of obtaiig the CPA. This certificate was regulated by miisterial order, dated July 14, 1971. The legth of this classroom-based teachig program was iitially 300 hours, with a uequal balace betwee theory ad practice. The program was structured i two stages. I a first step, studet teachers acquired pedagogical kowledge about psychology ad sociology priciples ad teachig theories, while the secod step was based o a itership i a high secodary school. I practice, the duratio of CPA was reduced, becomig i some cases 80 hours of theory versus 40 hours of practice. Next to its short legth, its ustructured ad iefficacious orgaizatio, its lack of pedagogical cotet kowledge, ad teacher educators improperly traied, researchers criticized the fact that the CPA was ot adequate to trai prospective teachers. Moreover, graduatig studet teachers felt usatisfied. Thus, i 2010 the Spaish educatio system lauched a ew iitial educatio program, the MDTTSE. Cosequetly, the CPA disappeared. The MDTTSE I the academic year 2009/2010, the MDTTSE was implemeted ad regulated by the Miistry through order ECI/3858/2007, dated December 27, 2007 (Miisterio de Educació y Ciecia, 2007). I additio, it is to be verified by the Natioal Agecy for Quality Assessmet ad Accreditatio (ANECA, Spaish acroym). 115
This program, cosidered as a brach withi the social scieces, eables studets to teach i secodary educatio ad it is madatory to apply for a teachig post i lower ad upper secodary schools ad vocatioal traiig ceters; both i public ad/or private secodary schools. The MDTTSE shares characteristics of the CPA. For istace, both programs follow a cosecutive model ad build o a theoretical versus a practice-orieted stage. However, both are also dissimilar. For example, while the govermet used to regulate all CPA guidelies such as etry requiremets, awardig the diploma ad accreditatio, cotrol ad maagemet of the MDTTSE has become the full resposibility of higher educatio istitutios. Moreover, the practical compoet of the MDTTSE is close to 40%, while i the CPA was less tha 10%. The size of the ew teacher educatio program is 60 ECTS (Europea Credit Trasfer ad Accumulatio System) ad is set up as a oe year fulltime program. Geerally, it cosists of two theoretical classroom-based modules ad a itership module, comprisig of at least eighty percet of the credits. The itership module is set up by uiversity faculties ad higher secodary schools. Also distace/olie uiversities guaratee such a face-to-face itership compoet. The MDTTSE helps to trai cotet specialist teachers, qualified to teach oe specific subject. The most commo specializatios are: mathematics, physics ad chemistry, biology ad geology, techology, computig, laguage ad literature, Eglish, Frech, draw, music, philosophy, geography ad history, ecoomy, classical laguages, professioal traiig ad guidace, educatioal guidace, ad physical educatio. Structure ad orgaizatioal features The MDTTSE is structured - as stipulated i the miisterial order - ito three modules, which make up at least 52 of all the 60 ECTS: Geeric module (at least 12 ECTS) cosists o topics cosidered relevat for all teacher to kow, such as educatioal theory, geeral priciples of istructio, classroom maagemet, curriculum theory, ad so o. It is divided i three areas: Persoality developmet ad 116
learig, Educatioal cotexts ad processes, ad Society, family ad educatio. Specific module (at least 24 ECTS) icludig mathematics cotet kowledge ad mathematics pedagogical cotet kowledge. It is also divided i three areas: Additioal traiig specific to the specialty chose, Learig ad teachig process specific to the specialty chose, ad Research ad teachig iovatio. Itership (at least 16 ECTS) icludig a school-based experiece (practicum) ad the master s thesis. Each istitutio has the autoomy to distribute the remaiig 8 ECTS amog geeric, specific or optioal courses. Cosequetly, we ca expect broad differeces i the umber of ECTS assiged to each module whe comparig differet MDTTSE. Etry requiremets Miisterial order ECI/3858/2007 (Miisterio de Educació y Ciecia, 2007) establish the followig etry requiremets to start the MDTTSE i Spai: accredited mastery of the competeces related to the specializatio the studets wish to atted. a B1 level mastery of a foreig laguage accordig to The Commo Europea Framework of Refereces for Laguages. If cadidates are ot accredited at this level, they must pass a laguage test orgaized by each istitutio. Accordig to the first coditio, the etry requiremets deped o the specialty chose. I mathematics, applicats must either pass a mathematics test orgaized by each istitutio, or hold a direct admissio bachelor degree. Nevertheless, each Spaish uiversity has a high level of autoomy i determiig which bachelor degrees allow studets to eroll directly ito the MDTTSE i mathematics. For istace, some uiversities accept ay bachelor degree as etry requiremet as log as studets have attaied a miimum of 60 to 120 ECTS i a bachelor degree coverig mathematical subjects such as algebra, calculus, geometry or statistics. I additio, some istitutios prioritize certai bachelor degrees, such as mathematics ad statistics. Moreover, some uiversities let a fittig bachelor degree prevail over passig the specializatio etry test. The former suggests a strog heterogeeity i Spaish etry requiremets. 117
Stadards for secodary mathematics teachers i Spai Accordig to Miisterial order ECI/3858/2007 (Miisterio de Educació y Ciecia, 2007), o fiishig the MDTTSE, graduates will be able to: Kow the cotet of curricula i the correspodig teachig specialty, as well as relevat teachig ad learig processes. Pla, develop ad assess the teachig ad learig process, ehacig educatioal processes which facilitate the acquisitio of competeces of the respective teachig levels, takig ito accout studets level ad backgrouds as well as their orietatio, both idividually ad i collaboratio with other teachers ad professioals i the school. Seek, retrieve, process ad commuicate iformatio (oral, prited, audiovisual, digital or multimedia), trasform it ito kowledge ad apply it i the teachig ad learig processes of their area of specializatio. Specify the curriculum to be implemeted i a school, collaboratig i its plaig. Develop ad implemet teachig methodologies both i groups ad idividually, adapted to the studet diversity. Desig ad develop learig eviromets with special attetio to equality, emotioal educatio, values, equal rights ad opportuities betwee me ad wome, citizeship educatio ad respect for huma rights that facilitates life i society, decisio-makig, ad build a sustaiable future. Acquire strategies to stimulate studet effort ad ecourage his ability to lear both idividually ad i collaboratio with others, ad develop thikig ad decisio skills which ehace persoal autoomy, cofidece ad iitiative. Kow the iteractio ad commuicatio processes i the classroom, master ecessary social skills to ecourage learig ad a team workig i the classroom, ad deal with disciplie disorders ad coflict resolutio. Develop formal ad iformal activities fosterig participatio ad culture withi the school ad its eviromet. Assume metorig ad guidace roles i a collaborative ad coordiated way. Participate i the assessmet, research ad iovatio of teachig ad learig processes. 118
Kow the curret regulatios ad istitutioal orgaizatio i the educatio system, ad quality improvemet approaches applicable to schools. Kow ad aalyze the historical characteristics of the teachig professio, its curret situatio, perspectives ad relatio to differet social realities. Iform ad advise families about the teachig ad learig process, ad persoal, academic ad professioal guidace of their childre. Teacher traiig should be orgaized towards teachig professioal stadards. However, how these competeces are defied ca be questioed. Some competeces are completely redudat sice some are cotaied i others, ad there is potetial ambiguity i how they should be uderstad. O oe had, it seems to be a slight cofusio betwee teacher competeces ad teacher stadards. Notice that teacher competeces refer to a combiatio of kowledge, skills, values ad attitudes which lead to effective achievemet of a task, while teacher stadards describe what teachers believe, kow, uderstad ad are able to do as specialists i their fields. O the other had, cosiderig the iteratioal list of stadards for secodary mathematics teachers described above, it is possible to observe importat differeces whe comparig Spai to other coutries. The lik betwee the twelve iteratioal stadards for secodary mathematics teachers ad the teacher competeces stadardized i Spai is fairly weak (see Table V). 119
TAbLe V. Aalysis of the iteratioal stadards for teachers i the spaish curriculum source: ow elaboratio. For istace, oe of the Spaish competeces refers to two of the iteratioal teacher stadards: mathematical pedagogical kowledge (stadard 2) ad developmetal psychology (stadard 7). I Spai, competeces are commo to all specializatios available i iitial educatio programs for secodary teachers. Competeces developed for mathematics teachers are exactly the same as competeces for other subjects. Explicit competeces related to mathematical pedagogical kowledge do ot exist. Cosequetly, uiversities should develop ad specify these competeces accordig to the differet specializatios followig their ow criteria. Furthermore, oe of the competeces metio that prospective teachers should kow ad uderstad the stages of studets persoality developmet i order to adapt the teachig ad learig to support their eeds. I the same way, some other stadards are barely metioed. For istace, whe it comes to mathematical cotet kowledge (stadard 1), the depth of competecy is very low. Also, i relatio with teachig ad learig theories ad processes (stadard 3), competeces do ot 120
allude to strategies for teachig ad learig mathematics, ad they either specify the importace of justifyig the approaches take to learig ad teachig mathematics ad their impact o studets. At the same time, the techology kowledge (stadard 9) required seems to be pretty scarce. Beyod kowig ad usig iformatio ad commuicatios techology systems, future teachers should desig ad develop learig experieces ad assessmets usig digital tools. At the same time, previous studies poit at the doubtful relevace of teachig commitmet (stadard 12) i the competecy framework, i particular whe it comes to itrapersoal skills ad professioal developmet. I this sese, prospective teachers should commit to the cotiual improvemet of the teachig practice participatig i activities for persoal professioal developmet. Besides, i Spai, there is a lack of bechmarks which specify to what extet these teacher competeces should be pursued ad assessed. The experiece of other coutries like Uited Kigdom shows that teacher stadards serve to assess ad improve teacher traiig programs. Research desig ad method Sample The MDTTSE is curretly offered by 68 uiversities out of the 80 curretly accredited i the Spaish Uiversity System 3. Oly 56 of them 38 public ad 18 private provide mathematics as a specialty. The MDTTSE is usually coordiated by Teacher Traiig ad Educatio faculties sice its establishmet i the academic year 2009/2010. It is importat to ote that the umber of MDTTSE offered by uiversities ca chage every academic year, due to a miimum umber of studets required for a program. Apart from that, some istitutios offer the mathematics specializatio together with techology ad computig. Furthermore, some MDTTSE i mathematics are set up as a iter-uiversity master degree. Thus, the actual umber of iitial teacher educatio programs i mathematics is dow to 51; 33 i public (3) Further iformatio about uiversities ad master studet populatio ca be foud i http://www.mecd.gob.es/ (Misisterio de Educació, Cultura y Deporter, 2013). 121
uiversities ad 18 through private uiversities. Moreover, 39 uiversities offer oly classroom-based learig. These courses - set up durig two cosecutive semesters - ca be followed o a full-time or part-time basis. Methodology As it is metioed before, the miisterial order that regulates iitial teacher educatio programs i Spai puts forward quite geeral guidelies. Therefore, uiversities are largely autoomous i detailig the curriculum. Oce commo characteristics of teacher traiig programs have bee described, our ext goal is to aalyze the sigificat differeces arisig from istitutios autoomy amog the 51 iitial educatio programs i mathematics offered i Spai. For our purpose, we first represet the distributio of ECTS i a multiple box plot (see Figure I) i order to detect structural dissimilarities. FIguRe I. distributio of Ects i each module i the MdttsE i mathematics source: ow elaboratio based o the data available o MdttsE curriculums. To develop a more comprehesive picture about the disparities i etry requiremets, we aalyzed iformatio about the set of bachelor degrees accepted to egage directly i the MDTTSE i mathematics. 122
Buildig o the available iformatio o uiversity websites, a comprehesive list of 40 istitutios 29 of which are public, ad 11 are private providig iitial educatio for secodary mathematics teachers i Spai was cosidered. Due to the heterogeeity of direct admissio bachelor degrees, they were classified accordig to 10 kowledge fields (see Table VI). TAbLe VI. classificatio of fields of kowledge source: adapted from. 123
For the descriptive aalysis, we represet i a bar graph (see Figure II) the umber of uiversities providig iitial educatio for secodary mathematics teachers that have at least oe direct admissio bachelor degree i the field of kowledge that it belogs to. FIguRe II. Admissio bachelor degrees to eroll directly ito the MdttsE i mathematics source: ow elaboratio. A deeper aalysis shows disparities betwee private (11) ad public (29) istitutios whe it comes to givig access o the base of specific bachelor degrees (see Figure III). 124
FIguRe III. differeces betwee public ad private istitutios providig the MdttsE i mathematics whe acceptig specific bachelor degrees as etry requiremets source: ow elaboratio. Results Figure I clearly reflects a uequal distributio of ECTS betwee differet iitial educatio programs ad questio the extet to which all these programs ca be aliged i terms of the competeces beig pursued ad attaied. I specific ad geeric modules, the values of miimum, maximum ad outliers poit out a high degree of dispersio i the data. That meas that there are broad differeces betwee the load of geeric ad specific cotets amog the set of iitial educatio programs. At the same time, media values idicate a asymmetric distributio i all variables. I itership module, despite a smaller spread, variace betwee programs is also evidet. Accordig to the secod box plot, a wide spread i practicum explais variace i itership module. With a miimum of 125
8 ECTS ad a maximum value of 18 ECTS, a wide disparity is observed betwee some programs whe it comes to the attetio paid to the practicum. Bear i mid that a practicum commoly cosists of two parts: a observatioal ad a itervetio practicum. Durig the observatioal practicum, studets sped a short period of time observig professioals i their day-to-day teachig activities: plaig, developig ad orgaizig istructio, classroom maagemet, assessmet, metorig, amog other professioal resposibilities, while i the itervetio practicum they demostrate their micro-level teachig skills. O the other had, i aroud 92% of iitial educatio programs i mathematics, the master s thesis requires 6 ECTS. Figure II shows that while some istitutios accept a large variety i iitial degrees, others are very restrictive. As expected, i all uiversities cadidates with a bachelor degree i the field of mathematics ad statistics (F) ca eroll directly ito a MDTTSE i mathematics i Spai. It should be oted that statistics degrees iclude a broad mathematical kowledge, ad are ot limited to the study of mere statistics ad probability. The same situatio is foud i physical scieces (E) ad egieerig, maufacturig ad costructio (H): almost all uiversities (97.5% ad 92.5%, respectively) accept them as a direct admissio bachelor degree. However, ot all the egieerig degrees reflect the same mathematics cotet load. Uiversities vary largely to the extet they accept other bachelor degrees. About 50% of Spaish uiversities cosider computig degrees (G) as a alterative pathway, ad early 38% believe the same about social scieces, busiess ad law (C) degrees. I this respect, it is importat to ote, that most part of the admissio degrees i the field of social scieces, busiess ad law (C) are coected with ecoomics, fiace, busiess admiistratio, ad accoutig, which are more closely related to mathematical kowledge as compared to other degrees i the field of law, sociology, or geography. But, aroud 15% of the uiversities still cosider that a bachelor degree i humaities ad arts (B), life scieces (D), agriculture (I), or/ad health ad welfare ( J) preset a sufficiet mathematics base to become a higher secodary educatio teacher. This ca be questioed. For istace, i most life scieces ad health ad welfare bachelor degrees the oly mathematical kowledge beig taught is limited to statistics. Algebra, 126
calculus, or geometry kowledge are ot studied. This strage situatio results from a situatio i the 80 s ad first 90 s, because due to a lack of graduates i mathematics, it became accepted that graduates i biology or chemistry, without a high-level traiig i mathematics, were evertheless employed as mathematics teachers i secodary schools. I the same way, there is a lack of mathematical cotet i degrees such as occupatioal therapy or agricultural ad food idustry that are also accepted as etry degrees i some uiversities. Oly i oe uiversity, studets holdig a degree i educatio (A) are admitted. I additio, these studets have to atted complemetary courses related with ifiitesimal calculus, matrix ad vector calculus, ad statistical kowledge. But, is there ay differece betwee public ad private istitutio whe acceptig specific bachelor degrees as etry requiremets? As figure III shows, while i some fields of kowledge there are cosiderable differeces betwee public ad private istitutios, a weighted balace is reflected i others. The oly istitutio wherei studets havig a educatio degree ca eroll directly i the MDTTSE i Spai is public. Bear i mid that some extra mathematical courses are required. I social scieces, busiess ad law (C), physical scieces (E), mathematics ad statistics (F), ad agriculture (I), there are barely ay differeces betwee public ad private uiversities, whereas i humaities ad arts (B), ad egieerig, maufacturig ad costructio (H) differeces betwee both variables are larger. I life scieces (D) as well as i health ad welfare (J) there is a major predomiace of private istitutios. As we have poited out before, bachelor degrees related with these kowledge fields have a substatial amout of statistical cotets, ot coverig other mathematical braches such as algebra, calculus or geometry. O the other had, more public istitutios accept computig (G) bachelor degrees for direct admissio tha private. However, these degrees almost always iclude, at least, algebra, calculus ad statistics kowledge, ad i some cases discrete mathematics. Thus, the mathematical cotet i computig degrees is larger tha i life scieces ad health ad welfare degrees, ad they are strogly promoted i public istitutios as a etry requiremet. 127
Discussio Spaish iitial educatio programs for secodary mathematics teachers preset broad differeces compare to other coutries i relatio with orgaizatio, duratio, etry requiremets, level of the degree awarded at the completio of a teacher traiig program, ad stadards for future secodary mathematics teachers. I Spai, prospective secodary teachers must, after obtaiig a bachelor degree, complete a official oe-year master course of 60 ECTS providig them with the theoretical ad practical skills eeded to joi the teachig professio. Therefore, traiig programs for secodary teachers i Spai follow a cosecutive model as i Frace, Germay ad Italy. I other coutries, iitial teacher educatio programs are orgaized accordig to the cocurret model, while i others both routes are available. At the same time, duratio of iitial educatio programs for secodary teachers vary widely from coutry to coutry, maily depedig o the model. I Spai, the overall legth of study for secodary mathematics teachers is 5 (4+1) years, sice the access to traiig programs is coditioed o graduatio from a bachelor degree. Other coutries with the same structure are Chile, Frace ad Uited Kigdom. I most coutries, the miimum requiremet to start secodary teacher educatio is a upper secodary educatio diploma, ofte i combiatio with umerus clausus policies, ad/or further requiremets such as competitive examiatios, stadardized tests or persoal iterviews. This is ot the case i Spai. I view of erolmet i Spaish iitial secodary teacher educatio, studets must already hold a bachelor degree ad a B1 level mastery of a foreig laguage. However, there are glarig discrepacies betwee Spaish uiversities i the type of bachelor degrees they allow to eroll i the traiig program. While some istitutios accept a large assortmet of iitial degrees, others are quite restrictive. At the same time, there are disparities betwee public ad private uiversities. Fially, i Spai, the qualificatio awarded at the completio of a teacher traiig program is a master degree, comparable to the approach adopted i most Europea coutries, ad i cotrast to other coutries where the qualificatio is merely a bachelor degree (mostly orgaized accordig to the cocurret model). 128
Worldwide, a critical poit of iitial teacher educatio programs is the lack of educatioal stadards establishig what skills, abilities, kowledge ad values must be pursued ad attaied i teacher traiig programs. I few coutries - such as Chile, Germay or Uited Kigdom - stadards for iitial teacher educatio are clearly defied. This is ot the case of Spai where mathematics teacher traiig programs lack specific stadards ad bechmarks specifyig a miimal level of attaimet of the stadards. I the view of the authors of this report - buildig o examples preseted i the iteratioal framework - alterative approaches should be adopted to esure the quality of the teacher educatio system. I particular, they stress the establishmet of explicit ad operatioal stadards to assess to what extet prospective - mathematics - teachers are qualified. The, it will be ecessary to supervise how uiversities implemet these competeces. O the other had, a stadardized mathematics test should be set i order to settle differeces betwee istitutios i relatio with the large variety i admissio degrees to eroll ito the secodary mathematics teacher educatio program. The results of this descriptive research preset aveues for prospective actio. First, we ca aalyze to what extet secodary mathematics studet teachers curretly attai stadards as put forward i our iteratioal framework. This could be studied from the viewpoit of studet teachers, recet graduates, teacher educators ad pricipals. Secodly, this first aveue gives way to a aalysis of critical competeces weakly attaied/pursued durig the theoretical ad practical teacher educatio experiece. For this purpose, a atioal survey will be set up. To coclude, we repeat that the curret ad future studies aim at improvig ad esurig the quality of mathematics teacher educatio i the Spaish teacher educatio system. Refereces Avalos, B. (2005). Secodary Teacher Educatio i Chile: A assessmet i the light of demads of the kowledge society. Retrieved from http://ifo.worldbak.org/etools/docs/library/211118/b_avalos.pdf 129
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