Mathematics for economics and business administration and project-based learning

See discussions, s a s, and au ho p o iles o his publica ion a : h ps://www. esea chga e.ne /publica ion/264195334 Ma hema ics o Economics and Business Adminis a ion and p ojec Based Lea ning Con e ence Pape · May 2011 CITATION 1 READS 52 2 au ho s: Some o he au ho s o his publica ion a e also wo king on hese ela ed p ojec s: Análisis de compe encias labo ales y compe encias uni e si a ias View p ojec sis emas de ale a de c isis View p ojec M. J. Vazquez Cue o Uni e sidad de Se illa 69 PUBLICATIONS192 CITATIONS SEE PROFILE Inmaculada Mase o Mo eno Uni e sidad de Se illa 29 PUBLICATIONS14 CITATIONS SEE PROFILE All con en ollowing his page was uploaded by M. J. Vazquez Cue o on 08 Ma ch 2016. The use has eques ed enhancemen o he downloaded ile. MATHEMATICS FOR ECONOMICS AND BUSINESS ADMINISTRATION AND PROJECT-BASED LEARNING Inmaculada Mase o Mo eno, Mª José Vázquez Cue o Depa amen o de Economía Aplicada III, Uni e sidad de Se illa (SPAIN) imase [email protected], [email protected] Abs ac In subjec s like Ma hema ics o Economics and Business Adminis a ion he e a e no many inno a ions in eaching o p omo e he use o new ac i e eaching me hodologies. In his pape , we jus i y he use o he me hodology o p ojec -based lea ning using new echnologies o de elop gene al and speci ic skills associa ed wi h a signi ican pa o his cou se, he economic applica ions o Ma hema ics. This me hodology allows he eache o assume he ole o guide in s uden lea ning p ocess and de elop quali y eaching o mo i a e and in ol e s uden s in he eaching-lea ning p ocess as an ac i e pa o his. I also allows he de elopmen o gene al skills associa ed wi h he s udies o Economics and Business and speci ic skills associa ed wi h Ma hema ics applica ions. We desc ibe he adap a ion o he me hodology o achie e hese objec i es based on he cha ac e is ics o he subjec . Keywo ds: New me hodologies, P ojec -based lea ning, Ma hema ics, Economics. 1 INTRODUCTION Nowadays, educa ion aces wo impo an challenges: s uden s assuming he con ol o he lea ning p ocess which mus be guided by eache and de eloping he necessa y abili ies o hei u u e employmen which up o now had no been conside ed in he eaching o mos subjec s. This in ol es hei ede ini ion o eaching subjec s, in ou case he Ma hema ics o Economics and Business Adminis a ion. In hei planning i is e y impo an he p ac ice, which mus include s udying and analyzing o hose simple economic applica ions ela ed o he basic ma hema ical concep s. The li le in e es o s uden s o his subjec in he s udies o Economics and Business is caused by he di icul y o i and igno ance o he necessi y and use ulness o Ma hema ics in he s udy o se e al economic phenomenons. The economic applica ions a e use ul o show he impo ance o Ma hema ics in his kind o s udies and can be used o mo i a e s uden s owa ds he subjec and making hem play a leading ole in he lea ning p ocess. In addi ion, he eaching o hese applica ions acqui es g ea e ele ance now due o a o ing he de elopmen o gene ic compe ences such as he capaci y o applying knowledge in p ac ice and he capaci y o analysis and syn hesis. Fo his eason we belie e i is necessa y o sea ch o new eaching me hodologies o each he Applica ions o Ma hema ics in Economics and Business which allow he de elopmen o gene ic compe ences, assigning a he same ime s uden s a leading ole and he eache he guiding ole o he p ocess. Nowadays, i is used ways o eaching-lea ning which le us ace hese challenges, he p ojec -based lea ning on he In e ne among hem. This didac ic me hodology is cha ac e ized by he de elopmen o lea ning p ocesses and he cons uc ion o knowledge h ough he in o ma ion ob ained om he In e ne . I is used by WebQues , MiniQues and T easu e Hun . In his pape i is exposed an ac i i y c ea ed om he p o ile and s uc u e o WebQues and T easu e Hun o he eaching-lea ning o Ma hema ical Applica ions o Economics and Business. 2 MATHEMATICS FOR ECONOMICS AND BUSINESS. THE ECONOMICAL APPLICATION OF MATHEMATICS Ma hema ical aining o a p o essional in Economics and Business mus allow him o unde s and he basic models o mode n Economics and he echniques used in he business managemen . The Ma hema ics subjec s in Deg ees o Economics, Business Adminis a ion and Finances and P oceedings o INTED2011 Con e ence. 7-9 Ma ch 2011, Valencia, Spain. ISBN:978-84-614-7423-3 000772 Accoun ing le he s uden unde s and o he subjec s based on logical-ma hema ical p emises such as Economical Theo y, S a is ics o Econome ics. The subjec o Ma hema ics o Economics and Business s udies echniques and ins umen s ha help quan i ying and sol ing speci ic p oblems o economical and business analysis. The eaching o quan i a i e echniques mus include he se ing ou and sol ing o ma hema ical p oblems. The p ac ical pa in his discipline is essen ial o show he impo ance and need o Ma hema ics in he s udy and analysis o many economical phenomenons and so, he p ac ical exe cises mus s a om an economical con en . The Economics Applica ions o Ma hema ics link ma hema ical con en s wi h economical ones and p o e in ob ious ways hei u ili y, s i ing he s uden ’s in e es owa ds he subjec and mo i a ing hem owa ds i s lea ning. 3 MATHEMATICS FOR ECONOMICS AND BUSINESS. THE ECONOMICAL APPLICATION OF MATHEMATICS The Eu opean Highe Educa ion A ea p omo es he compe ences-based lea ning. The knowledge o concep s and hei applying knowledge in p ac ice a e combined he e. Nume ous gene ic compe ences igu e in Deg ees Quali ica ions. Howe e , he e a e some ele an compe ences analyzed in he second phase o he p ojec Tuning such as: 1. Capaci y o analysis and syn hesis. 2. Capaci y o applying knowledge in p ac ice. 3. Basic gene al Knowledge in he ield o s udy. 4. In o ma ion managemen skills. 5. In e pe sonal skills. 6. Abili y o wo k au onomously. 7. Elemen al compu ing skills. 8. Abili y o in es iga ion. These can be de eloped in g ea e o smalle measu e depending on he subjec s p o ile and he eaching me hodology used. In he case o Ma hema ics o Economics and Business, i s de elopmen can be ackled by p ac ical exe cises based on he s udy and analysis o concep s and economical phenomenons. These applica ions analyze and s udy economical p oblems which use ma hema ical echniques o hei sol ing as i ollows: • Planning he sol ing o economical p oblems. • Se ing economic and business p oblems ou in ma hema ical e ms. • Selec ing igh ma hema ical ins umen s o he sol ing and using hem. • In e p e ing he ma hema ical esul s o each p oblem in economical e ms adequa ely. • Unde s anding economical and business concep s h ough basic ma hema ical no ions and models. • Dis inguishing and iden i ying ma hema ical concep s in economical p oblems. • Using he deduc i e me hod. The essay done by he s uden when dealing wi h a p ac ical exe cise o economical con en help hem de eloping skills ela ed o he h ee gene ic compe ences exposed abo e: he capaci y o analysis and syn hesis, he capaci y o applying knowledge in p ac ice, he basic gene al knowledge in he ield o s udy, and, o cou se, he capaci y o sol e p oblems. They can also de elop skills associa ed wi h he use o ce ain compu e packs and speci ic so wa e which can be used in he esolu ion o se e al kinds o p oblems. Howe e , some o he in e es ing aspec s o elemen al compu ing skills a en’ ackled, such as he use o wo d p ocesso and sp eadshee s o he use o echnology as an ins umen o ob ain in o ma ion and new ways o communica ion. In e pe sonal skills, au onomy, abili ies o in es iga e and he use o in o ma ion a e no di ec ly ela ed 000773 o he objec i es and con en s o his subjec , ha ’s why i s de elopmen depends on he eaching me hodology used and he lea ning ac i i ies o in es iga ion p oposed by s uden s. I ’s unusual o sugges a o ing he de elopmen o hese skills in subjec s o Ma hema ics o Economics and Business, since hey a e no di ec ly ela ed o he ma e . The e o e, eaching he economical applica ions o Ma hema ics allow he de elopmen o some gene ic compe ences bu doesn’ deal wi h he acquisi ion o o he s which a e also essen ial o he s uden ’s educa ion owa ds hei p o essional u u e. 4 THE METHODOLOGY OF WEBQUEST, MINIQUEST AND TREASURE HUNT AND THE OBJECTIVES OF THE EUROPEAN HIGHER EDUCATION AREA. The e a e eaching s a egies which include in hei educa ional objec i es he eigh gene ic compe ences al eady exposed. WebQues , MiniQues and T easu e Hun a e among hem. These ac i i ies ha e a common p emise and p o ile bu di e en le el o di icul y. They a e classi ied wi hin he called p ojec -based lea ning which is cha ac e ized by de eloping lea ning p ocesses and cons uc ing knowledge h ough he in o ma ion ob ained om In e ne , s a ing wi h ixed con en s p e iously de e mined by he eache . WebQues was de eloped by Be nie Dodge in collabo a ion wi h Tom Ma ch in 1995 in San Diego Uni e si y. Ac i i ies de eloped in WebQues allow achie ing he objec i es o he Eu opean Highe Educa ion A ea ela ed o he de elopmen o high le el cogni i e p ocesses and he new oles o eache and s uden [2]. These ea u es a e sha ed by MiniQues and T easu e Hun . This me hodology is a ac i e o he s uden and le he eache inno a e de eloping a way o eaching- lea ning ocused on compe ences de elopmen [5]. This me hodology could be sui able o each he p ac ical pa o he subjec Ma hema ics o Economics and Business, he Ma hema ics Applica ions, by lea ning ac i i ies ocused on he de elopmen o gene ic compe ences. 5 ECONOMICS APPLICATIONS OF MATHEMATICS AND THE METHODOLOGY OF WEBQUEST, MINIQUEST Y TREASURE HUNT. The nex s ep is e i ying ha his pa o he subjec can be de eloped unde his me hodological app oach. Some applica ions o Di e en ial and In eg al Calculus a e he use o de i a i es in concep s o ma ginal unc ion and elas ici y o demand, he ma ginal a e o subs i u ion can be compu ed ia o he ela ionship be ween de ini e in eg al and he p oduce and consume ’s su plus. These applica ions deal wi h eal concep s and phenomenon so he s uden s know he p ocess used in economical s udies and some imes om di e en poin s o iew. I is necessa y o check i he Economics Applica ions o Ma hema ics a e sui able o be augh wi h he me hodology o WebQues using a p ojec which p omo es a signi ican lea ning p ocess. In his case, hey a e adjus ed o he ea u es which mus ha e a good and a ac i e WebQues [10]: • eal: The economical concep s and phenomena s udied a e eal. • en iching: The knowledge can be deal wi h om di e en poin s o iew and sou ces, and mus be ela ed hem o o he con en s. • ele an : Add esses issues o impo ance o he aining o he s uden o hei u u e employmen s. Now we can conside de eloping a ool o eaching Ma hema ics Applica ions o Economics and Business s a ing om he lea ning p inciples o WebQues and T easu e Hun . 6 ADAPTATION TO THE METHODOLOGY OF WEBQUEST AND TREASURE HUNT FOR TEACHING-LEARNING OF THE MATHEMATICS APPLICATION FOR ECONOMICS AND BUSINESS The idea we s a om is designing and c ea ing an “ac i i y” based in he me hodology o WebQues and T easu e Hun espec ing hei lea ning p inciples: • WebQues : s uden s deeply know abou a opic doing esea ch on i o sol ing a gi en p oblem. 000774 • T easu e Hun : s uden s acqui e knowledge s a ing om a se ies o ques ions whose answe s de elop using he a ailable in o ma ion in he selec ed esou ces o he Web. The sugges ed ac i i y allows he use o he in o ma ion a ailable on In e ne o c ea e a cons uc i is lea ning p ocess s a ing om he idea o going h ough an in es iga ion in which he s uden wo ks in g oup and ans o ms he in o ma ion a ailable o ob ain a inal p oduc . We ha e aken he basic ea u es o WebQues and T easu e Hun ha a e mos adequa e o unde s anding o economical and ma hema ical concep s, so bo h he philosophy and aims o he me hodology a e kep in. An “ac i i y” has he ollowing sec ions: • In oduc ion: I s a s wi h a b ie exposi ion abou he economical concep o phenomenon s udied in he ac i i y, poin ing he ma hema ical ool needed o i s analysis. • Task: he wo k he s uden mus de elop is indica ed. Some gene al indica ions a e p o ided o i s making such as he o ma ion o wo king g oups, he ime a ailable o de elop wo k, wha mus be made as a esul o he de eloped P ojec and how o o ganize he ime o de elop he ask. • Aims: The objec i es o knowledge ela ed o he ma hema ical and economical con en s o he ac i i y and he compe ences associa ed o he s udy o any economical applica ion o Ma hema ics. • Ques ions: In his sec ion a e de ailed a se ies o ques ions a e a isen he e in a way ha in o de o answe hem i is necessa y o desc ibe, schema ize, c ea e lis s, summa ize, e c and de elop some basic skills such as unde s anding and cons uc ion o knowledge. The e a e some s aigh o wa d ques ions a e di ec ones and a e use ul o iden i y economical and ma hema ical concep s. They a e comple ed wi h li le ac i i ies abou he eason o a esul (analysis), how o de elop he s udy o an economical phenomenon (p oblem sol ing) o wha o do (decisions making). Righ a e each ques ion he e a e links o websi es ha con ain he in o ma ion o answe , and so make he sea ching p ocess easie and a oiding s uden s ge los among he in o ma ion. Some esou ces a e documen s in a pd and/o a Powe Poin o ma , hey ha e been de eloped o hose cases in which he websi es didn’ con ain he in o ma ion o i wasn’ clea enough. • Big Ques ion: he s uden is asked o iden i y he economical and ma hema ical concep s s udied in he ac i i y and he ela ionship be ween hem. In o de o ge his, he s uden mus e lec and con e he in o ma ion hey ha e wo ked wi h du ing he ac i i y o ex ac a conclusion o deduc ion. This ques ion is ad anced in he ask so s uden s can s a selec ing he in o ma ion ha is going o be used o make he answe . • E alua ion: I is made by means o a alua ion ma ix o ub ic wi h he cha ac e is ics o alue. A nume ical sco e is assigned o he answe s as well. The ac i i y is adjus ed o he concep and s uc u e o T easu e Hun , bu i has impo an di e ences wi h his one. The ques ions o T easu e Hun don’ usually include p oblems o sol e o he exposi ion o inal conclusions [1] like in he ac i i y we p oposed. We can ind in WebQues his kind o ques ion and also he e alua ion made using a ub ic. The p ojec is conside ed o be de eloped in a g oup, al hough i is possible o wo k i indi idually. They a e designed o be de eloped in sessions du ing wo hou s and a hal . We had c ea ed ac i i ies o se e al economic applica ions dealing wi h di e en con en s bu ela ed among hem, so he economical concep s s udied in a pa icula ac i i y a e gene alized o ex end o he s ela ed o hem in la e ac i i ies. 7 CONCLUSIONS The economical applica ions o Ma hema ics a e an impo an pa o he discipline Ma hema ics o Economics and Business. They a e usually included wi hin he p ac ical pa o show s uden s he use ulness o Ma hema ics in he Economics and Business wo ld. In addi ion, i allows he s uden s o de elop some gene ic compe ences ele an o hei ea u e employmen such as he capaci y o analysis and syn hesis, he capaci y o applying knowledge in p ac ice, he basic gene al knowledge in he ield o s udy, and, o cou se, he capaci y o sol e p oblems. This p ojec s a s om he necessi y o looking o new me hodologies o eaching-lea ning he economical applica ions o Ma hema ics which would allow o include he de elopmen o ele an gene ic compe ences included in he Tuning P ojec , wi hin he lea ning objec i es o he subjec , con e ing he eache o guide o he p ocess and making he s uden play he leading ole. 000775 The ea u es o his pa o he subjec le hem adequa e hemsel es o he p ojec -based lea ning me hodologies h ough he In e ne , specially WebQues and T easu e Hun . S a ing om he p inciples and s uc u es o bo h o hem, some ac i i ies ha e been designed in which de elopmen he s uden himsel plays he leading ole o he eaching-lea ning p ocess, he eache ’s ole shi s o he backg ound as a guide in he p ocess. These can be de eloped in di e en con ex s in he Deg ees o Economics and Business o p omo e he de elopmen o gene ic compe ences. In his kind o subjec s i is no usual o ind me hodological inno a ions. These p ojec s allowed us begin o use a new me hodological pe spec i e o he lea ning o con en s and de elopmen o compe ences in a quan i a i e-kind subjec wi hin he s udies o Economics and Business. Wi h his pape we a e ying o in oduce new eaching ools ha allow us ul illing he objec i es o Eu opean Highe Educa ion A ea. REFERENCES [1] J. Adell (2003): In e ne en el aula: a la caza del eso o. Edu ec. Re is a Elec ónica deTecnología Educa i a, Núm. 16. On line: h p://edu ec. edi is.es/Re elec2/ e elec16/adell.h m [2] J. 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