Using Robotics to Enhance Active Learning in Mathematics: A Multi-Scenario Study

ma hema ics A icle Using Robo ics o Enhance Ac i e Lea ning in Ma hema ics: A Mul i-Scena io S udy Edga Lopez-Caudana 1,* , Ma ia Soledad Rami ez-Mon oya 2, Sand a Ma ínez-Pé ez 3and Guille mo Rod íguez-Abi ia 4 1Tecnologico de Mon e ey, School o Enginee ing and Sciences, Mexico Ci y 14380, Mexico 2Tecnologico de Mon e ey, School o Humani ies and Educa ion, Mon e ey 64849, Mexico; [email p o ec ed] 3Depa men o Didac ics and Educa ional O ganiza ion, Facul y o Educa ion, Uni e si y o Ba celona, 08035 Ba celona, Spain; sma inezpe [email p o ec ed] 4 Gene al Di ec ion o Compu ing and In o ma ion and Communica ions Technologies, Uni e sidad Nacional Au ónoma de México, Mexico Ci y 04510, Mexico; [email p o ec ed] *Co espondence: [email p o ec ed] Recei ed: 31 Oc obe 2020; Accep ed: 27 No embe 2020; Published: 4 Decembe 2020   Abs ac : The use o echnology, which is linked o ac i e lea ning s a egies, can con ibu e o be e ou comes in Ma hema ics educa ion. We analyse he condi ions ha a e necessa y o achie ing an e ec i e lea ning o Ma hema ics, aided by a obo ic pla o m. Wi hin his amewo k, he ques ion aised was “Wha a e he condi ions ha p omo e e ec i e ac i e ma h lea ning wi h obo ic suppo ?” In e en ions a di e en educa ional scena ios we e ca ied in o de o explo e h ee educa ional le els: elemen a y, seconda y, and high school. Quali a i e and quan i a i e analyses we e pe o med, compa ing he con ol and ea men g oups o all scena ios h ough examina ions, di ec obse a ions, and es imonials. The indings poin o h ee key condi ions: le el, mo i a ion, and eache aining. The ob ained esul s show a e y a ou able impac on he a en ion and mo i a ion o he s uden s, and hey allow o es ablishing he condi ions ha need o be me o an e ec i e ela ionship be ween he eache and he echnological ool, so ha be e lea ning ou comes in Ma hema ics a e mo e likely o be ob ained. Keywo ds: educa ional obo ics; ac i e lea ning; educa ional inno a ion; ma hema ics lea ning; case s udies 1. In oduc ion Fo a long ime, human beings ha e endea ou ed o de elop new me hods o pe o m asks in an easie way, wi h he aim o doing hose ac i i ies ha bene i him in any a ea o his li e as e and mo e e icien ly. I is hen ha echnology comes in o play. Despi e he ac ha echnology has se e al pa hs, i can be assu ed ha each and e e y one o hem has a common pu pose: o help humani y sol e some p oblem ha is inhe en in i . In o ma ion and communica ions echnologies (ICTs) cu en ly occupy an ex emely impo an place in socie y and he economy. Thei impo ance has been inc easing eno mously. The concep o ICT has eme ged as a echnological con e gence o elec onics, so wa e, and elecommunica ions in as uc u e. Robo ics is one o he exp essions o echnology whose applica ion has ex ended o a ious con ex s o li e. In he educa ional ield, i becomes a aluable esou ce o acili a e lea ning and de elop gene al skills, such as socialisa ion, c ea i i y, and ini ia i e in s uden s oday [1]. Speaking o educa ion, he esul s in he la es PISA es showed ha Mexico’s pe o mance is below he OECD a e age in science (416 poin s), eading (423 poin s), and Ma hema ics (408 poin s) [ 2 ]. Ma hema ics 2020,8, 2163; doi:10.3390/ma h8122163 www.mdpi.com/jou nal/ma hema ics Ma hema ics 2020,8, 2163 2 o 21 Acco ding o [ 3 ], one o he main causes o school ailu e in s uden s is a lack o in e es and bo edom. This is mainly due o he ac ha , in mos cases, he cu en educa ion is no in e es ed in gene a ing inno a i e ac i i ies ha a ou he pa icipa ion o hei s uden s. Fo his eason, he use o ICTs has been p omo ed wi hin he class ooms. The use o new echnologies allows o an incen i e owa ds lea ning in s uden s o di e en educa ional le els, and he lea ning o Ma hema ics is a e y speci ic a ea. One o he mos ele an challenges in Mexico is he a i ude owa ds lea ning Ma hema ics. Cu en ly, i is a necessi y ha Ma hema ics ins uc o s ind be e ways o eaching; his would allow o s uden s o be mo e empa hic and make sense o his a ea o knowledge. Thus, in mos classes na ionwide, eache s do no imp o e he use o eaching ma e ials, due o a lack o c ea i i y, ime, p ope aining, o planning. Hence, he impo ance o showing how echnology allows o signi ican imp o emen s in a en ion and mo i a ion owa ds Ma hema ics, which, in u n, allows o an imp o emen in aining p og ams and eaching p ac ices; hus, achie ing a posi i e impac on s uden lea ning. The p inciples o ma hema ical modelling include lea ning on ou own; using echnological de ices and basic p oduc i i y ools o in es iga e and p oduce lea ning ma e ial in an e hical and e icien manne ; and, applying nume ical, algeb aic, and geome ic p ocedu es o he unde s anding and analysis o eal si ua ions. The use o a echnological pla o m would help o ul il he expec ed objec i es. Al hough he e a e al eady ways o inco po a e echnology in he class oom, i is s ill no e y common o use obo s as a suppo ool o lesson deli e y. Robo ics in he class oom no only allows o s udy opics o au oma ion and p ocess he con ol in he a ea o echnology and compu e science, bu i also se es as an aid in lea ning di e en a eas o knowledge. The obo s a ouse in e es in s uden s, as hey a e conc e e objec s s iking. An educa ional obo ic p oposal can be implemen ed unde an app oach ha akes he lea ning en i onmen , he planning o ac i i ies, esou ces, he ime needed o he ealisa ion o each o hese, and he me hodology o pe o m hem in o accoun . In his amewo k, ac i e lea ning wi h s a egies o doing, e iewing, lea ning and applying can be o suppo o con ibu e wi h he cons uc ion o ma hema ical knowledge. When joining hese esou ces, one could ask onesel : Wha a e he condi ions ha p omo e e ec i e ac i e Ma h lea ning wi h obo ic suppo ? 1.1. Lea ning Ma hema ics in Mexico Ma hema ics is a uni e sal language ha con ibu es o he de elopmen o logical hinking, he abili y o eason, and o ace new challenges. Lea ning Ma hema ics is a subjec ha emphasises p oblem sol ing. I s uden s hink c i ically, hey can sol e p oblems e ec i ely [ 4 ]. Ma hema ical compe ences, acco ding o he O ganisa ion o Economic Coope a ion and De elopmen [ 5 ] e e o s uden s’ abili ies o analyse, eason and communica e e ec i ely when hey iden i y, o mula e, and sol e ma hema ical p oblems in di e en si ua ions [ 6 ]. Ma hema ical compe ence “implies he abili y and willingness o use ma hema ical modes o hinking (logical and spa ial hinking) and hei ep esen a ion ( o mulas, models, g aphs, and diag ams)” [ 7 ] (p. 164). Ma hema ical compe ences mus be placed as pa o he key elemen s wi hin lea ning o li e. The Go e nmen o Mexico s a es ha he gene al pu poses o lea ning Ma hema ics a e: (a) o concei e Ma hema ics as a social cons uc ion in which ma hema ical ac s and p ocedu es a e o mula ed and a gued; (b) acqui e posi i e and c i ical a i udes owa ds Ma hema ics; and, (c) o de elop skills ha allow hem o pose and sol e p oblems while using ma hema ical ools, make decisions, and ace non- ou ine si ua ions (Go e nmen o Mexico, n.d.). Thus, he p o ile o he p eschool g adua e in ma hema ical hinking is [ 8 ]: “he o she coun s a leas o 20, easons o sol e p oblems o quan i y, builds s uc u es wi h igu es and geome ic bodies, and o ganises in o ma ion in simple ways” (p. 68). Fo he p ima y educa ion p o ile: “he o she includes concep s and p ocedu es o sol ing a ious ma hema ical p oblems, and o applying hem in o he con ex s” (p. 74). Finally, o seconda y educa ion: “he o she expands his knowledge o ma hema ical concep s and echniques Ma hema ics 2020,8, 2163 3 o 21 o pose and sol e p oblems o a ying deg ees o complexi y, as well as o model and analyse si ua ions. He o she alues he quali ies o ma hema ical hinking a ou able o Ma hema ics” (p. 80). In Mexico, no all o he s uden s ha e he same oppo uni ies o lea n. Those who canno access ma hema ical con en in school a e a a li elong social and economic disad an age. Acco ding o [ 2 ], he lack o equal lea ning oppo uni ies in he Mexican educa ion sys em leads o he ein o cemen o gaps and inequali ies in socie y. Lea ning in Reading, Ma hema ics, and Science emains below he in e na ional a e age. Acco ding o he PISA epo , only 1% o s uden s pe o med a he highes le els o compe ence and 35% o s uden s did no achie e a minimum le el o compe ence. The ob ained esul s con inue o show a lack o compe ence in Ma hema ics [3]. Mexico seeks quali y educa ion ha is inno a i e in i s pedagogical p ac ices, and ha has he necessa y means o he in eg al de elopmen and g ea e well-being o i s socie y. In o de o achie e his, socio-educa ional policies sea ch o new oppo uni ies in o de o educe inequali ies be ween communi ies, p omo e aining in alues, minimise gaps, and p omo e equi y [ 9 ]. In his ega d, he Sec e a y o Public Educa ion (SEP) and he Na ional Ins i u e o he E alua ion o Educa ion (INEE), highligh ed he impo ance o e iewing and edesigning exis ing educa ional p og ammes and modali ies wi h he aim o : (a) acili a ing access o all ci izens, (b) encou aging he de elopmen and use o new echnologies, and (c) p omo ing he skills o all s uden s in o de o ensu e a ull li e. The in eg a ion o echnologies and, in he case o educa ional obo ics, helps o de elop a ious skills and p omo e he cons uc ion and acquisi ion o knowledge in gene al, and Ma hema ics in pa icula . To his end, hey designed he Na ional Plan o he E alua ion o Lea ning (PLANEA), which classi ies hose e alua ed in o ou le els o mas e y: I (insu icien ), II (basic), III (sa is ac o y), and IV (ou s anding). This plan aimed o assess he eaching-lea ning p ocesses and he lea ning achie emen s in Language-Communica ion and Ma hema ics [10]. Thus, he Sec e a y o Public Educa ion [ 8 ] aises he need o ensu e quali y o lea ning in basic educa ion, and educa ional inclusion and equi y o he cons uc ion o a mo e jus socie y. I we ocus on he a ea o Ma hema ics, we seek o modi y he ac ions wi h inno a i e p ac ices, in eg a ing he use o echnologies in eaching me hodologies o lea ning hem, and p omo ing he de elopmen o ma hema ical skills. 1.2. Educa ional Robo ics Educa ional obo ics (ER), which is also known as pedagogical obo ics, is a discipline ha aims a he concep ion, c ea ion, and implemen a ion o obo ic p o o ypes and specialised p og ams o pedagogical pu poses [ 11 ]. ER is no a new concep , bu , a he , i has been g owing exponen ially in ecen yea s. I has a majo impac on lea ning [ 12 ], and i is associa ed wi h he STEAM disciplines (Science, Technology, Enginee ing, A , and Ma hema ics) o he de elopmen , skills, and unde s anding o ma hema ical, physical, enginee ing, and ela ed concep s [ 13 – 15 ]. Ac oss he a ious acul ies and uni e si ies, and in o de o educe he gende gap in STEAM ca ee s, we ha e o ain s uden s in/wi h obo ics ela ed skills in all disciplines. Addi ionally, in his way, p omo e lea ning cen ed on he s uden , on his o he in e es s, and on he demands o socie y, using inno a i e me hods; and, p omo ing c i ical aining, in o de o de elop ac i e and co-pa icipa ing ci izens in oday’s socie y [16,17]. I could be de ined as “an in e disciplina y discipline, which equi es he cons uc ion o a echnological objec wi h a speci ic pu pose (some au ho s call i an educa ional obo , o he s call i a obo ic p o o ype, o he s e e o au oma isms . . . ); i aims a he pedagogical ield; and i de elops key compe ences and skills o he s uden s o he 21s cen u y” [18] (p. 4). The in eg a ion and use o educa ional obo ics in he eaching-lea ning p ocess in p e-school, p ima y, and seconda y le els can become isible, and be a u ning poin , as a esou ce o add ess he di e si y o he class oom, as a means o help he inclusion o all s uden s, as well as keep hem ac i e and mo i a ed [ 15 , 19 – 21 ]. Addi ionally, i can be u ilised as a ool o p omo e he cons uc ion o knowledge and he achie emen o esul s. The e o e, when wo king wi h ER, apa om wo king Ma hema ics 2020,8, 2163 4 o 21 on science and echnology, he aim is o p omo e o he c oss-disciplina y skills, such as: c ea i i y, communica ion, collabo a ion, c i ical hinking, eamwo k, inno a ion, he de elopmen o solu ions o p oblems, digi al skills, and compu a ional hinking [ 22 , 23 ]. In o de o do his, eache s mus ha e basic knowledge o be able o each he con en s wi h obo s [24]. In oducing s uden s o he a easo scienceand echnology, in he caseo Ma hema ics, h ough play and cons uc ionis lea ning in o de o gene a e new knowledge, is one o he goals o he usabili y o ER in he class oom. Lea ning wi h obo s o e s s uden s in insic mo i a ion, and in i es hem o in es iga e, os e hei cu iosi y and imagina ion, o ask ques ions, o wo k in eams, o o e come challenges, o make decisions, and o be esponsible o hei own p ocess [12,25]. The e a e many obo s on sale, acco ding o shape, size, unc ion, wo king en i onmen , and au onomy. Depending on he shape, we ind: zoomo phic (imi a ion o a c ea u e, e.g., bee), humanoid ( ep oduc ion o he shape o a human and i s mo emen s, in his case, he NAO obo ), hyb id (combina ion o he abo e), and polymo phic (di e en shapes, adap ing i s s uc u e acco ding o he ask). The size o he obo s can be: obo s, mic o obo s, nano obo s, o nanobo s ( hesmalles , nanome ic size). Func ion: domes ic, medical, mili a y, en e ainmen , space, educa ional, among o he s. In ela ion o he wo k en i onmen : s a iona y obo s ( hey a e ixed and immo able, hey a e he majo i y o indus ial obo s), g ound, unde wa e , ai , and mic og a i y obo s. Addi ionally, in e ms o hei au onomy: ele-ope a ed (d ones) and semi-aqua ic [26]. The NAO obo , humanoid obo , was bo n in 2008 and de eloped by he company So bank Robo ics, we a e cu en ly acing he model e olu ion 5. The NAO obo measu es 58 cm, weighs no mo e han 5 kilos, speaks, lis ens, sees, ela es o he en i onmen as p og ammed, and in e ac s na u ally. I is capable o pe cei ing i s en i onmen om mul iple senso s. I is composed o wo came as, ou mic ophones, nine ac ile senso s, wo ul asonic senso s, eigh p essu e senso s, an accele ome e , a gy oscope, a oice syn hesise , and wo speake s [ 27 ]. The obo includes a g aphic p og amming so wa e, Cho eg aphe, which allows accessible communica ion wi h he NAO; his so wa e is a g aphic p og amming in e ace by means o blocks, which p o ide speci ic asks o he NAO [28]. NAO has wo key ad an ages: (1) i s e sa ili y (cus omising i s unc ions and indi idualising i s uses) and (2) i s body language ( eedom o mo emen , adap ed o he en i onmen , manageable and iendly, and i is designed o any age). In ela ion o Educa ion, NAO is designed o be used om he age o i e up o uni e si y. I s use in he class oom means ha he s uden s a e mo e play ul, mo i a ed in he lea ning p ocess, able o in e ac and communica e, and es ablish a link be ween heo y and p ac ice. On he pa o he eaching s a , hey ha e mo e engaged s uden s, and mo e dynamic classes, p omo ing s uden in e es , and ob aining esul s o he p og amming in eal ime. As a as esea che s a e conce ned, NAO has been used in di e en uni e si ies, as i is conside ed o be ideal o p ac ical expe imen s, as i is an in ui i e so wa e ha o e s endless possibili ies wi h mul i-language p og amming [27]. 1.3. Ac i e Lea ning and Robo ics in Ma hema ics Lea ning en i onmen s o Ma hema ics equi e he di e si ied use o me hods, echniques, and s a egies ha suppo he acquisi ion o p ocesses o analysis and cons uc ion. One echnique ha has p o en o be e ec i e in de eloping ma hema ical skills is ac i e lea ning. In ac i e lea ning, he eache uses a me hodology ha seeks o p omo e he pa icipa ion o he s uden as a p osume o knowledge [ 29 ]. In his echnique, he eache mus plan con inuous s imula ion ac i i ie, so ha he s uden indi idually o collec i ely pe o ms p ocedu es o highe o de : analysis, syn hesis, in e p e a ion, in e ence, and e alua ion [ 30 ]. Acco ding o [ 31 ], he amily and communi y socio-p oduc i e ac i i ies in which s uden s pa icipa e in on a daily basis cons i u e a eas o expe ience ha demand hei inco po a ion in o he didac ics o Ma hema ics ocused on p oblem sol ing. I is impo an ha he p ac ical expe ience ha s uden s ha e had ega ding ma hema ical easoning be conside ed wi hin he eaching o Ma hema ics in a o mal school space, wi h he Ma hema ics 2020,8, 2163 5 o 21 suppo o p ac ical esea ch. In he s udy [ 32 ], he impac o he use o an Adap i e Tu o ing Sys em (ATS) on he de elopmen o h ee ma hema ical compe ences was measu ed: he use o symbolic language, modelling o ma hema ical p oblems, and p oblem sol ing h ough ma hema ical easoning. Resea ch [ 33 ] sugges ed inc easing he le el o s uden mas e y o ma hema ical concep s, while applying he concep o ac i e lea ning ha in ol es collabo a i e me acogni i e ac i i ies among s uden s du ing he lea ning p ocess. Th ough his s a egy, i was possible o imp o e he unde s anding and mas e y o ma hema ical concep s. The cu en educa ional p ac ices pos ula e lea ning as a cons uc ion o knowledge, he a en ion has special ele ance in he s o age and in eg a ion only o he in o ma ion ha is ele an , becoming an elemen ha he s uden mus ac i ely ain. Thus, ac i e, dynamic, pa icipa i e lea ning, a om passi i y, is done wi h he a en ion and concen a ion ocused and di ec ed owa ds he signi ican elemen s o i ; only in his way, he acqui ed knowledge will be pe manen and e ec i e. In conclusion, a en ion and concen a ion a e bo h basic elemen s o all lea ning. P ojec based lea ning has a key place in ac i e lea ning. P ojec -based lea ning is an example o ac i e lea ning and i is a cu en ins uc ional s a egy ha is d i en by s uden s in an in e disciplina y, collabo a i e, and echnology-based manne [ 34 ]. S uden s who implemen p ojec -based lea ning pe o m be e a e using his me hod in eaching and lea ning sessions [35]. The phases o ac i e lea ning a e di e en ly de ined, depending on he au ho who w i es abou hem. None heless, he main elemen s emain common among models. One e sion ha is qui e easy o unde s and is p esen ed in [36,37], and desc ibed in de ail in Table 1. Table 1. S ages o ac i e lea ning. S age Wha Is I ? S uden ’s Responsibili y Lea ning abou Ac i e Lea ning Do The asks s imula e he s uden s’ ac i i y (games, discussion o cases, dynamics, p oblem sol ing . . . ) S uden s choose and plan hei wo k s a egies. S uden s a e encou aged o obse e aspec s o hei lea ning while hey a e in ol ed in he asks. Re iew S uden s s op o become awa e o wha happened in he p ocess, wha was impo an , how hey el . S uden s moni o hei p og ess and e iew hei plan. S uden s desc ibe wha hey obse ed and e iew hei lea ning (objec i es, s a egies, eelings, con ex , e c.). Lea n The new ideas and pe spec i es ha he ac i i y allowed o gene a e a e made explici . S uden s can iden i y o hemsel es wha hey ha e lea ned. Elemen s a ec ing p og ess a e iden i ied and new s a egies p oposed. Apply Fu u e ac ions a e planned in he ligh o he new indings o knowledge. The possibili y o ans e ing wha was lea ned o o he si ua ions is discussed. S uden s e iew hei plans aking in o accoun hei ecen lea ning. S uden s plan how hey will con inue o obse e and expe ience hei lea ning s a egies. Sou ce: [36] (p. 30). Fu he mo e, in [ 38 ], i is explained how ac i e lea ning is no a subjec a ea compe ence (Table 2), bu ha he e is a wide a ie y o ways in which i can be used in he li e o he class oom: om an indi idual ac i i y o he de elopmen o a g oup p ojec . In all o hem, he same p ocesses and p inciples a e applied: Do, Re iew, Lea n, and Apply. Table 2. Examples o ac i e lea ning in a ange o subjec s. Subjec Do Re iew Lea n Apply Ma hs Tackle a p oblem Re iew s a egies Compa e e ec i eness P epa e o nex challenge English C ea e a d a T y ou wi h a eade Conside eedback Red a and publish Technology Cons uc a p oduc Tes i s unc ion Examine e alua ions Redesign His o y Collec sou ces Iden i y poin s o iew Syn hesise Make sense o ano he si ua ion Sou ce: [38] (p. 76). Ma hema ics 2020,8, 2163 6 o 21 The examples ha a e shown in Table 2 ollow a simila p ocess, a p ocess ha can be desc ibed as a cycle. This cycle models he p ocess o lea ning om expe ience wi h ou phases: Do, Re iew, Lea n, and Apply [ 37 , 38 ]. To his cycle, i is also impo an o add a p e ious s age in doing, Planning, as shown in Figu e 1, below. Figu e 1. The ac i e lea ning p ocess (adap ed om [36]). When planning he eaching-lea ning p ocesses, eache s ocus on he expe ience hey wan o show and ca y ou wi h he s uden s. To his end, he model o he phases p esen ed by [ 37 ] can help hem o acqui e he lea ning. Ac i e lea ning has been in eg a ed o suppo he cons uc ion o ma hema ical knowledge, bo h a he basic educa ion le el while using open educa ional esou ces and lea ning objec s [ 39 ] and in highe educa ion in i ual and emo e labo a o y en i onmen s [ 40 ]. P ojec -based lea ning enhances s uden s’ academic pe o mance. When planning he eaching-lea ning p ocesses, eache s ocus on he expe ience ha hey wan o show and ca y ou wi h he s uden s. To his end, he model o he phases ha a e p esen ed by [ 36 ] can help hem o acqui e he lea ning. Ma h eaching can ind g ea suppo in he use o echnology. Ma h lea ning should be done while using ins uc ional media [ 41 ], pa icula ly isual lea ning media, wi h he suppo o echnology-based ecosys em en i onmen s) [ 42 ]. Re . [ 43 ] con i med, h ough hei esea ch, ha s uden s who access a mul imedia en i onmen p o ided by hei eache on a blended lea ning basis can pe o m signi ican ly be e han hose ha a e augh in he class oom. In [ 44 ], he design p inciples ha unde lie he de elopmen and deli e y o a blended lea ning p o essional de elopmen p og am o high school ma hema ics eache s we e analysed and heo e ical amewo ks whe e ace- o- ace and compu e -media ed ins uc ion, eache iden i y o ma ion, and s uc u al and basic cha ac e is ics o e ec i e eache p o essional de elopmen a e coo dina ed we e iden i ied: he o m, du a ion, and cohe ence o ac i i ies; he na u e o eache pa icipa ion; ocus on con en knowledge Ma hema ics 2020,8, 2163 7 o 21 (ma hema ics); and, oppo uni ies o engage in ac i e lea ning. The implemen a ion o isual and echnological esou ces has had good esul s in he eaching-lea ning p ocess o Ma hema ics. Nume ous s udies ha e been conduc ed on echnology applied o he eaching o Ma hema ics. Re . [ 45 ] de eloped a esea ch ha allowed concluding ha cogni i e, a ec i e, and me acogni i e ac o s can be modelled and suppo ed by in elligen u o ing sys ems. The sys em also helped o imp o e Ma h pe o mance on s anda dised es s, as well as imp o e s uden engagemen and a ec i e ou comes. In [ 46 ], hei s udy ound ha s uden s who lea ned using Mic oso Ma hema ics pe o med highe on hei assessmen s and a posi i e e ec on s uden con idence in Ma hema ics was obse ed. The wo k [ 47 ] ocuses on he desc ip ion o he p inciples on which a hype media ool (Hipa ia) is based and hen analyses i s impac in h ee key a eas: he lea ning p ocess o s uden s in Ma hema ics, hei sel -managemen , and a ec i e-mo i a ional a iables, such as pe cei ed u ili y, pe cei ed compe ence, in insic mo i a ion, and anxie y owa ds Ma hema ics. The s udies ocus no only on he cogni i e aspec , bu hey also analyse o he elemen s, such as mo i a ion and con idence. 2. Ma e ials and Me hods In all scena ios, he obo was used as a suppo ool, which acili a ed he eache ’s ac ion in he execu ion o explana ions, in e ac ions wi h s uden s, and e iew o esul s. The design and execu ion o he obo in e en ion was di e en o each scena io. I is impo an o poin ou ha decisions by he adminis a ion o each school limi ed he pa icipa ion o he p o ocol in each one o hem; he e o e, he numbe o isi s, du a ion o in e en ions, and applica ion o es s was di e en , in acco dance wi h he guidelines ha each school de e mined and app o ed o he execu ion o he p o ocol. 2.1. Plan To de elop his p ojec , se e al aspec s we e conside ed, and a selec ion o opics was ca ied ou o he planning o obo suppo o he di e en scena ios. The main aspec s o conside a e he numbe o isi s, measu emen ools, exams, and in e iews, as desc ibed below. Visi s: in he case o he p ima y school, wo isi s we e ca ied ou on consecu i e days, ha ing almos one and a hal hou s o ca y ou he planned ou ines in ma hema ical easoning, h ough ac i i ies o wo k wi h dis ance measu emen and ac ions. Ou p ojec eam ca ied ou he isi s. Fo he seconda y school case, he obo assis ed in ou ull 50-min. classes, one o each isi . In each session, he eache used he obo a ce ain imes ha we e p e iously de ined in he design o he sessions. Finally, in he case o high school, he obo isi ed he class on a daily basis o a week. Th ee isi s we e done a di e en imes o he semes e . The i s isi was ca ied ou in an in oduc o y way, so ha he obo had al eady been p esen ed wi h he s uden s o c ea ing a i s imp ession by hem. The nex wo we e o suppo he eache in he opics es ablished om he beginning. I was he eache s who manipula ed he obo when hey needed i . Measu emen s: in each scena io, a con ol g oup and an expe imen al g oup we e es ablished. Same in e en ions o classes we e ca ied ou wi h he in e en ion o he ins uc o o wi h he ins uc o using he obo . The in en ion was o compa e and be able o measu e he impac ha he obo had among he s uden s. The e o e, es s wi h nume ical esul s we e applied, as well as obse a ion scales in o de o measu e mo i a ion [ 48 ]. Bo h o he ools we e applied in wo ypes o g oups. Only in high school we e he es s we e gi en be o e and a e s a ing he obo in e en ions. In addi ion, in e iews we e ca ied ou on he expe ience ca ied ou wi h he pa icipa ing eache s and, in he case o high school, wi h he s uden s. Tes s: he es s we e di e en o each scena io. A elemen a y school, a ques ionnai e was applied, and he s uden s had o sol e a ma hema ical exe cise based on he explana ion o he opic made by he obo . This exe cise was chosen om he Ma hema ics book ha was used by he cou se eache , and he numbe o co ec answe s, in his ques ionnai e, was accoun ed o . Fo seconda y school, an exam was conduc ed on he opics chosen by he eache , hose whe e he e was suppo om he obo . Almos all o he exe cises we e abou Analy ical Geome y. The design o hese exams was Ma hema ics 2020,8, 2163 8 o 21 done by he eache s in cha ge o he wo g oups. In he case o high school, he applied exams we e designed and we e conside ed in he planning o he cou se om he beginning. Tha is, hey we e he s anda d exams ha a e commonly applied in he subjec o T igonome y, coo dina ed by he Depa men o Ma hema ics o he ins i u ion in ques ion. In e iews: hey we e ca ied ou in o de o ind ou he opinion o he eache s in ol ed, and he mo e o mal implemen a ion o he s uc u e o he in e iew, as well as he es imonies o he s uden s and eache s, was es ablished in he high school. As can be app ecia ed, he p o ocol became mo e o mal as expe ience was gained om he p e ious scena ios. In Sec ion 3.1 o his documen , mo e de ails o each scena io a e gi en, and a mo e de ailed quan i a i e analysis o he ob ained esul s is ca ied ou . The planning o he p ojec is summa ised in he ollowing h ee aspec s: (1) The obo : as men ioned abo e, a NAO obo was used o suppo he eache . The obo deli e ed he explana ion o he opic o be de eloped, p o ided ha he app op ia e en i onmen was pu in place. In addi ion, some imes i guided he exe cises ha we e es ablished by he eache . Fu he mo e, he obo con i med o he s uden s whe he he exe cises had co ec esul s. Figu e 2 shows he gene al way in which he obo in e ac ed. Figu e 2. S uc u e o he sessions. (2) The scena ios: p ima y school, wo g oups o 3 d and 5 h g ades we e isi ed, wi h he comple ion o ma hema ical easoning exe cises in wo consecu i e isi s. The eache did no di ec ly use he obo , which ca ied ou demons a ions o p e iously chosen opics, bu was au onomous in ca ying ou he ac i i ies. Be o e and a e , ques ionnai es we e made o he s uden s in o de o compa e he pe o mance ob ained. Fo seconda y school, ou isi s we e made o he school, wi h a con ol g oup and a ea men g oup (using he obo ), be o e and a e exams we e compa ed, in addi ion o he obse a ion scales o mo i a ion and a en ion o he s uden s. The eache s selec ed and designed Ma h exe cises o hei execu ion. In high school, pe o mance and mo i a ion we e obse ed in i e g oups, wo expe imen al and h ee con ol g oups, du ing an academic semes e wi h daily isi s in ull in e en ion weeks. The subjec was igonome y and he eache s designed and planned he exe cises, wi h g ea e con ol Ma hema ics 2020,8, 2163 9 o 21 o e he way he obo s in e ened. Be o e and a e , he esul s in he semes e we e compa ed as well as he measu emen o he s uden s’ a en ion. (3) The measu emen s: o quan i a i e analysis, acco ding o he scena io, eache s applied es s and/o exe cises, aimed a measu ing he s uden s’ lea ning, and mos o hem we e con en ional exams. In all o he scena ios, a quali a i e analysis was ca ied ou , based on p e ious wo ks [ 47 ]. In hese analyses, he applied scale was composed o he ollowing indica o s: concen a ion (p ecision and ecall), habi ua ion, wi hd awal, dis ac ion (neglec ), and in e es in he ask (mo i a ion and en husiasm). Based on he de ini ion o ca e and he indica o s ha compose i , ope a ional de ini ions o hese indica o s we e de eloped o be la e ansla ed in o obse able i ems o dimensions o ca e. The analysis and aking o he scales we e ca ied ou by s uden s o Psychology, aking ca e o obse e he guidelines o he e e ence indica ed in e ms o human beha iou . 2.2. Me hodology We explo ed di e en app oaches in h ee di e en scena ios in o de o shed ligh on wha cons i u es a success ul applica ion o a obo ic pla o m o enhancing ac i e lea ning. The scena ios we e di ided by educa ional le el. Tha is, elemen a y, seconda y, and high school se ings. Each one o he in e en ions is desc ibed below. Scena io 1: elemen a y school. The e we e wo in e en ions unde aken o wo sec ions o he hi d and i h g ades, wi h 28 s uden s each. Fo hese isi s, ac i i ies we e planned wi hou eache s’ in ol emen . They limi ed hei pa icipa ion o allowing he esea ch g oup o en e he oom and coo dina e he ac i i ies, manipula e he obo ic pla o m, and pe o m a b ie in e iew a he end o he session, bo h o s uden s and eache s. E alua ion was done by applying quizzes o sec ions whe e he obo was used, and o o he s whe e i was no , so ha a esul s compa ison could be made. Scena io 2: seconda y school. Fo his scena io, isi s we e pe o med e e y F iday o an en i e mon h. This ime, wo sec ions we e p o ided use o he obo ic pla o m, and ano he one was obse ed as a con ol wi h no ea men . Each sec ion had 25 s uden s en olled. Ano he a ia ion was ha , his ime, eache s we e in ol ed in planning he ac i i ies, including he opic o co e , and he way ha he obo ic pla o m was o be used. A g oup o psychology s uden s was ac i e making obse a ions h oughou he p ocess, and cap u ing bo h quali a i e and quan i a i e in o ma ion o la e in e p e a ion. In e iews wi h s uden s we e also pe o med. The emphasis was on assessing he le els o a en ion and mo i a ion gained by he s uden s ansla ed in o measu emen scales, as well as pe o mance on he subjec ma e . Scena io 3: high school. Fo his scena io, he ac ions became mo e complex. The obo ic pla o m was applied o wo ea men g oups, and obse a ions we e also made o h ee con ol g oups. The obo was used in e e y class du ing an en i e week a he beginning o he cou se, hen i was done again in he middle, and a he end o he cou se. The in ol emen o eache s in his case was in ensi e, being ained in he use o he obo , and deciding oge he he momen s and hemes whe e he obo would in e ene. P e- and pos - es s we e pe o med o all sec ions, in o de o compa e pe o mance esul s. Addi ionally, as in he p e ious scena io, Psychology s uden s unde ook beha iou al obse a ions and made in e iews and es imonials. Fo all scena ios, an assessmen on how well he p ocess me he equi emen s o he ou ci ed phases o ac i e lea ning was made, assigning a ub ic-like success ca ego isa ion o each. This assessmen was made quali a i ely, and was based on panel expe discussions, d awing om he expe iences ha we e ob ained a each scena io. A compa ison was hen de i ed in o de o iden i y he app op ia e success ac o s. Figu e 3summa ises he o e all me hodological p ocess. Ma hema ics 2020,8, 2163 16 o 21 In he elemen a y case, he objec i es o he exe cise we e made explici by s uden s wi h he au ho isa ion o hei eache . Addi ionally, he e was a con e sa ion space p o ided o hem o e balise wha he expe imen consis ed o , bu sugges ions we e only gi en as commen a ies by he s uden s. These elemen s d i e o gi e a sco e o medium, in e ms o he i s wo elemen s, bu de icien in he p oposi ion o new s a egies. The seconda y school scena io, on he o he hand, coun ed wi h a planned s a egy o de elop ia he obo and he eache oge he o make he lea ning ou comes explici . E en hough i was posi i e o e all, i was no as e ec i e as expec ed, since i esul ed in being somehow con using o he s uden s. Some exe cises we e assigned o ex e nalise wha was being lea ned, and s uden s we e in e iewed a he end. The commen s ga he ed had no in luence in he planning o he nex sessions. This phase was conside ed o be posi i e in making lea ning explici , bu medium o iden i ying ba ie s and deciding s a egies. Fo he high school le el, a space was gi en o analyse he lea ning p ocess wi h he s uden s, and oge he de ine s a egies o he nex sessions. The iden i ica ion o ba ie s ell, in u n, a li le sho . Phase 4. Apply This s age is ce ainly he mos complex, and i equi es he g ea es ma u i y o he s uden s in he use o ac i e lea ning. The e o e, i is he mos di icul o achie e. Fi s , u u e ac ions a e planned based on new disco e ies and lea nings, and he possibili y o ans e ing he knowledge gained o o he si ua ions is examined. S uden s a e in cha ge o e iewing hei plans, building on hei ecen lea ning expe iences, and hey mo e o wa d o plan u u e obse a ions and expe imen a ion o hei lea ning s a egies. Fo he elemen a y school scena io, his was no co e ed, since only some documen a ion o he expe ience was made by he esea ch eam and conside ed o applica ion in o he simila con ex s. None heless, his ac i i y did no include eache s o s uden s, making i de icien . The esul s imp o ed ma ginally o he seconda y le el s uden s, whe e he expe ience li ed allowed o p epa ing and imp o ing he p ocess o u u e si ua ions. Howe e , no signi ican pa icipa ion by he s uden s was obse ed o expe imen ing lea ning s a egies, beyond some e lec ions on he e ec i eness o he obo ic pla o m as an aid o hei lea ning p ocess. Finally, he ou comes a e a be e o he high school scena io, whe e ime was gi en o e lec on lessons lea ned o assess he applicabili y o he p ocess o o he con ex s and de ine pe inen imp o emen s. This was explici also as an ac i i y eques ed o he s uden s whe e hey had o desc ibe how o apply he knowledge ob ained o o he domains. The weak poin , conside ed o be a medium success, is ha ela ed o he ela i ely low impac o s uden s’ ecommenda ions o ede ine he cou se s a egies in u u e scena ios. Table 3p esen s he summa y o he success sco es assigned in each case. The i s sco e is he p edominan one, and he one a e he hyphen indica es he e is a small componen in a highe o lowe ca ego y. Table 3. Success sco es. Scena io Do Re iew Lea n Apply Elemen a y school Medium-high Medium-low Medium-low Low-medium Seconda y school Medium-high High-medium Medium-high Low-medium High school High-medium High Low-medium High-medium In summa y, Table 4shows he mos ele an aspec s ega ding he es s ca ied ou in he h ee scena ios, no only quali a i e and quan i a i e, bu also a commen ha we highligh abou each expe ience ob ained. Ma hema ics 2020,8, 2163 17 o 21 Table 4. Summa y o obse a ions and es esul s. Scena ios Compa ison Quan i a i e esul s Quali a i e esul s Gene al commen s Elemen a y school E en hough he esul s ob ained in his scena io canno be conside ed conclusi e because he s udy is explo a o y and no s a is ical analyses a e pe o med, i is easonable o de i e om he obse a ions ha s uden s ha e an imp o emen in g ades when he obo ic pla o m is p esen in he session. This we can obse e wi h he g oup a e age, o he es ha was applied o all g oups, since i was always highe in he g oups wi h obo ic in e ac ion. By obse ing he esul s ob ained, i was de e mined ha he a ou able poin s o he obo we e: T-Concen a ion (memo y) -Less dis ac ion -In e es in he ask (en husiasm) -In e es in he ask (mo i a ion) The mo i a ion was clea ly inc eased; pe haps a no so adequa e ai is ha he con ol o e he g oup was no so a ou able. Teache s somehow also became an audience o he obo ic pla o m. Seconda y school I can be seen ha he e was an imp o emen be ween he p e- es and pos - es esul s in bo h g oups. This esul was expec ed because, du ing he applica ion o he es s, he s uden s did no ha e enough knowledge o sol e he exam. None heless, he e we e many con ounding ac o s, since g oups a ied in scheduled hou s o ins uc ion and assigned eache s, so esul s should be iewed wi h cau ion. The esul s showed ha he majo i y conside ed he p esence o he obo made he class mo e in e es ing. Some s uden s assu ed ha he obo helped o unde s and he issues, and mos denied eeling uncom o able wi h he p esence o he obo . The eache ’s commen s s and ou , as he had no used his ype o obo ic ool be o e. He was mo e in e es ed in knowing how he obo wo ks, and held a a ou able posi ion on he in oduc ion o new echnologies in educa ion, so he s a ed ha he g oup was mo e a en i e and i was easie o con ol High school The esul s a e only desc ip i e, ha is, analysing he dis ibu ions o g ades in he g oups (minimum and maximum sco e, and he concen a ion o he majo i y o he s uden s be ween ce ain sco es), he esul s we e be e g ades in he expe imen al g oups, and in his case, he pa icipa ion o he eache s was undamen al. When compa ing he gene al esul s o he adi ional g oups wi h he expe imen al one, he obo ic pla o m is use ul o he imp o emen o in e ac ions be ween s uden s. Fu he mo e, when compa ing he es esul s and he opinions o he s uden s, i is p e e able o use he pla o m in ewe and mo e speci ic sessions We obse ed ha s uden s a e p o agonis s o hei own lea ning and he echnological pla o m allows a cons uc i e dialogue be ween s uden and eache , p omo ing e lec ion on he con en s e iewed in each session scheduled o a isi o he obo . Simila ly, in he design o each o he classes, he eache s included ac i i ies whe e he s uden is he axis o hei own lea ning Ma hema ics 2020,8, 2163 18 o 21 4. Discussion These esul s lead o hink ha he e a e many ac o s a play ha need o be conside ed. The obo ic solu ion will ne e esul in signi ican lea ning imp o emen unless accompanied by he igh s a egy. Howe e , i is a g ea ool o a ac ing in e es and mo i a ing s uden s o pa icipa e, ega dless o le el. The ac i e lea ning p ocess, on he o he hand, needs o be ca e ully planned acco ding o le el, since he cogni i e capabili ies and s yles o he s uden s a y g ea ly depending on i . In a iably, he obo ic pla o m and he ac i e lea ning s a egy ha e a g ea po en ial o gene a e syne gy and be mo e e ec i e when well ha monised. Ano he issue ha is wo h men ioning is he le el o in ol emen o he eache s. The mo e p epa ed and com o able o use he obo , he be e hey can plan and adap hei s a egy, based on he eedback and ou comes ha we e p o ided by he s uden s. This allows o he lexibili y needed o cus omise lea ning s a egies o each s uden and makes hem esponsible o hei own lea ning. In he long un, hey may de elop he igh le el o ma u i y o be eal ac i e lea ne s. I is also impo an o no e ha digi al skills acquisi ion has g ea ly inc eased i s ele ance, no only o s uden s, bu o eache s. Today’s digi al agendas in oduce wo essen ial axes o wo k: on one hand, he end owa ds a digi al educa ion, and on he o he , he acquisi ion o digi al compe ences and skills o digi al ans o ma ion [ 49 ]. S udies, such as [ 50 , 51 ], highligh he sho age o digi al compe ences in ini ial aining and he lack o knowledge and skills on educa ional echnologies o eaching p ac ice in p e-school, p ima y, and seconda y class ooms. The ime o exposu e also seems o be an impo an issue. Those who we e exposed longe o he obo , and o well planned ac i i ies, ob ained mo e signi ican esul s. One o wo sessions migh e en be coun e p oduc i e, as hey aise expec a ions ha will no longe be me , causing discou agemen o he s uden s. Finally, cap u ing beha iou al da a and obse a ions may be g ea ly en iched when combining echniques, e en including he s uden s hemsel es as sel -documen e s. Quan i a i e and quali a i e echniques and assessmen s will p o ide a be e pano ama o he si ua ion. The documen s ob ained always need be sha ed and discussed, o gain collec i e in elligence, and p o ide mo e obus changes. 5. Conclusions In p e ious yea s, di e en scena ios ha e been de eloped, in which a humanoid obo ic pla o m has been used in o de o inc ease mo i a ion and in e es in s uden s owa ds Ma hema ics. The p esen ed case s udies show ha he p ope use o a obo ic pla o m, oge he wi h an app op ia e eache pa icipa ion, can mean gi ing high-quali y hyb id classes, enhancing he s uden ’s a en ion o he opics ha a e exposed by changing he s imulus, and ob aining e ec i e lea ning. The esul s p esen ed abo e show a nume ical imp o emen in he scales ha a e used o assess he p esence o speci ic beha iou s, and pe o mance in all scena ios. E en hough hese esul s should be looked a wi h cau ion, hey p o ide a good pe spec i e o he po en ial use ulness o Robo ics in Ma hema ics eaching. The ul ima e goal is o make lea ning mo e meaning ul, which should ansla e in o be e g ades and be e abili ies o s uden s o e all. The s udy highligh s he mo i a ion o eache s o lea n mo e abou he use o obo s. Beyond he mo i a ion ha can be conside ed on he pa o he s uden s, i was he eache s hemsel es who exp essed an a i ude o lea ning in o de o in eg a e hem in o he educa ional expe iences. The obo is a media ing ool, bu he eache is he one who has he capaci y o in en i eness o in eg a e i in he classes. This in eg a ion helps o p omo e hyb id sys ems in lea ning en i onmen s, wi h he eache - obo binomial ( his was obse ed, o a g ea e ex en , in he uppe -middle le el). This s udy was guided by he ques ion: wha a e he condi ions ha p omo e e ec i e ac i e Ma h lea ning wi h obo ic suppo ? The indings poin o h ee key condi ions: le el, mo i a ion, and eache aining: (a) Encou aging ac i e lea ning wi h eme ging echnologies (in his case, wi h obo ics), in ol es conside ing he educa ional le el whe e he lea ning en i onmen s a e a ge ed, wi h he p o ile o s uden s (le els o cons uc ion o lea ning) as a cen al ocus. (b) The mo i a ion, acco ding o Ma hema ics 2020,8, 2163 19 o 21 he p o ile o he s uden s o he o ma i e expe ience, whe e obo ics helps pe sonalised lea ning. The in oduc ion o obo ics suppo s p esen ing he con en s in a di e en way in o de o change how hey a e augh in an o dina y si ua ion. (c) The o ma ion o eache s as a ele an aspec , whe e he pedagogical ounda ion goes beyond “p og amming he obo ”, he eache s a e he ones who “should be p og ammed” o he didac ic use ha s a s om he planning, he a icula ion o s a egies, he s a egic a angemen o he momen s in which he use o he obo s is in eg a ed, and he e alua ion o he e ec s. Thus, obo ics is one o many echnologies ha can suppo he p ocesses o inc easing ma hema ical lea ning, whe e s a egies canno be le aside, ega dless o he echnology ha is being in eg a ed. C i ical hinking skills, digi al skills, and eamwo k skills a e ein o ced wi h he in oduc ion o hese echnologies, linked o he s ages o doing, e iewing, lea ning, and applying ha a e encou aged h ough ac i e lea ning. Fu u e s udies could be gea ed owa ds deepening he explo a ion o he e ec s o he use o obo ics on he s ages o ac i e lea ning, and hei con ibu ion o conc e e ma hema ical knowledge acquisi ion. Simila ly, i is wo h analysing he eaching p ocesses in o de o demons a e he esul s o heo e ical and p ac ical knowledge when applying eme ging echnologies, such as obo s in hei class ooms. I is equi ed, in i sel , o expand he s udies o managemen , psycho-pedagogical, and socio-cul u al issues, in he applica ion o echnologies in inno a i e lea ning en i onmen s. Au ho Con ibu ions: Concep ualisa ion, E.L.-C. and M.S.R.-M.; Fo mal analysis, G.R.-A., S.M.-P. and E.L.-C.; Funding acquisi ion, E.L.-C. and M.S.R.-M.; In es iga ion, E.L.-C., G.R.-A., S.M.-P. and M.S.R.-M.; Me hodology, G.R.-A. and E.L.-C.; P ojec adminis a ion, E.L.-C., M.S.R.-M., G.R.-A. and S.M.-P.; W i ing—o iginal d a , E.L.-C., G.R.-A., S.M.-P. and M.S.R.-M.; W i ing— e iew & edi ing, G.R.-A. All au ho s ha e ead and ag eed o he published e sion o he manusc ip . Funding: The au ho s would like o acknowledge he inancial suppo o No us and W i ing Lab, TecLabs, Tecnologico de Mon e ey, Mexico, in he p oduc ion o his wo k. Acknowledgmen s: To he eache s, s uden s and ins i u ions in ol ed. To I zel He n á ndez a UNAM o he o iginal illus a ion o he ac i e lea ning p ocess. Con lic s o In e es : The au ho s decla e no con lic o in e es . Re e ences 1. Pachidis, T.; V ochidou, E.; Kabu lasos, V.G.; Kos o a, S.; Bonko i´c, M.; Papi´c, V. 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