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Ma hema ics o Economics and Business Adminis a ion and p ojec Based
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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
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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.
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• 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.
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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.
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