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

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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 .
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