GeoGebra in project-based learning (Geo-PJBL): A dynamic tool for analytical geometry course

Jou nal o Technology and Science Educa ion JOTSE, 2022 – 12(1): 112-120 – Online ISSN: 2013-6374 – P in ISSN: 2014-5349 h ps://doi.o g/10.3926/jo se.1267 GEOGEBRA IN PROJECT-BASED LEARNING (GEO-PJBL): A DYNAMIC TOOL FOR ANALYTICAL GEOMETRY COURSE Muhammad Noo Kholid1, Lingga Nico P adana2, Swas i Maha ani3, Annisa Swas ika1 1Ma hema ics Educa ion - Uni e si as Muhammadiyah Su aka a (Indonesia) 2P ima y Educa ion - Uni e si as PGRI Madiun (Indonesia) 3Ma hema ics Educa ion - Uni e si as PGRI Madiun (Indonesia) [email protected], [email p o ec ed], swas i.ma he[email p o ec ed], annisa.sw[email p o ec ed] Recei ed Ma ch 2021 Accep ed Sep embe 2021 Abs ac The in eg a ion o lea ning models and so wa e is a end in ma hema ics cou ses. Howe e , no exis ing lea ning model o geome y cou ses in ol es he s uden s in he making o a ool o media p ojec . The esea che s no iced he po en ial o he p ojec -based lea ning (PjBL) model and GeoGeb a in analy ical geome y cou ses. This s udy e ealed di e ences in he in luence o he Geo-PjBL and PjBL models on s uden s’ achie emen . The subjec s consis ed o 137 p ospec i e ma hema ics eache s. The Basic Geome y Ins umen (BGI) was used o measu e he subjec s’ ini ial abili y in basic geome y, and he Geome y Analy ic Ins umen (GAI) was used o e alua e he model and p ospec i e eache s’ pe o mance. The Geo-PjBL and PjBL class oom ac i i ies las ed o 15 weeks. Bo h class ooms ecei ed he same con en ; he di e ence be ween he Geo-PjBL and PjBL class ooms was he ools used o p esen he p oblems and he p ojec esul s. An analysis o co a iance (ANCOVA) was conduc ed o analyze he da a (α = 0.01). The Geo-PjBL model is mo e e ec i e in applying analy ical geome y subjec s ha equi e p ecision and accu a e isual illus a ions. Meanwhile, in he ange o algeb aic ope a ions, he Geo-PjBL model is as e ec i e as he PjBL model. Keywo ds – GeoGeb a, P ojec -based lea ning, Dynamic ool, Analy ical geome y. To ci e his a icle: Kholid, M.N., P adana, L.N., Maha ani, S., & Swas ika, A. (2022). GeoGeb a in p ojec -based lea ning (Geo-PjBL): A dynamic ool o analy ical geome y cou se. Jou nal o Technology and Science Educa ion, 12(1), 112-120. h ps://doi.o g/10.3926/jo se.1267 ---------- 1. In oduc ion Geome y is he science o ma hema ics in he spa ial domain (Casa, Fi mende , Ga in & Ca oll, 2016). A p ospec i e ma hema ics eache in Indonesia is equi ed o lea n abou and each geome y. The esea che s conduc ed in es iga ions ega ding geome y cou ses a his le el and de e mined he a e age sco es o some geome y cou ses in he las i e yea s. The s udies included plane, space, analy ical, and non-Euclidean geome y. Figu e 1 shows ha o e he las i e yea s, he a e age sco e in analy ical -112- Jou nal o Technology and Science Educa ion – h ps://doi.o g/10.3926/jo se.1267 geome y cou ses is lowe han hose in o he geome y cou ses. Al hough he s uden s’ basic geome y abili ies a e ela i ely good, he s uden s ace di icul ies in analy ical geome y cou ses. The esea che s also e iewed a ious p io s udies and ca ego ized hem in o wo ocuses. Fi s , s udies ocusing on he de elopmen o applica ion o lea ning models on geome y include he ollowing: deep lea ning 3D-shaped su aces (Sinha, Bai & Ramani, 2016), model-based deep hand pose es ima ion (Zhou, Wan, Wei, Xue & Wei, 2016), he lipped lea ning model (Vo onina, Mo oz, Suda iko , Rakhimzhano a & Mu a bakee , 2017), and disco e y lea ning using a scien i ic app oach (Ummah, Inam & Azmi, 2019). Second, s udies ha de elop o apply ools in geome y lea ning include GCLC (Janičić, 2006), an augmen ed eali y–assis ed lea ning sys em (Lin, Chen & Chang, 2015), con ex -awa e ubiqui ous lea ning (C omp on, 2015), BLOG-GOTHIC (Indahwa i & Ta ilyan o, 2018), Wingeom So wa e (Fonna & Mu salin, 2019), and Sc ap-Mod (Hidayah & Des a i, 2019). Based on hese s udies, no exis ing lea ning model o geome y cou ses in ol es he s uden s in he making o a ool o media as a lea ning p ojec . The esea che s no iced he po en ial o he p ojec -based lea ning (PjBL) model and GeoGeb a in analy ical geome y cou ses. By in eg a ing he PjBL model and GeoGeb a (Geo-PjBL), he s udy aims o e eal whe he he e a e di e ences in he in luence o he Geo-PjBL and PjBL models on he lea ning achie emen o analy ic geome y cou ses o p ospec i e ma hema ics eache s. The quan i a i e da a was obse ed acco ding o ac ual condi ions. Figu e 1. A e age geome y sco es (2015–2019) 2. Me hodology 2.1. Resea ch Goal and Design This s udy u ilized quasi-expe imen al esea ch o examine he e ec i eness o he Geo-PjBL model in an analy ical geome y cou se. The i s phase o he s udy was collec ing da a on he ini ial pe o mances and achie emen s o he s uden s employed o de e mine consis ency in he da a be o e he beginning o he cou se. The second phase las ed o 15 weeks (Geo-PjBL class oom and PjBL class oom). E e y i e weeks, he esea che s e alua ed he s uden s by ollowing hei p og ess in he analy ical geome y cou se. In he hi d phase, he esea che s hen analyzed he da a om he s uden s’ es esul s o examine he e ec i eness o he Geo-PjBL model in he cou se. -113- Jou nal o Technology and Science Educa ion – h ps://doi.o g/10.3926/jo se.1267 Figu e 2. Resea ch design model 2.2. Pa icipan s The pa icipan s in his s udy we e p ospec i e eache s in he Depa men o Ma hema ics Educa ion, Cen al Ja a, Indonesia. A o al o 137 p ospec i e eache s we e en olled in six class ooms. Each class oom was labeled ei he Geo-PjBL o PjBL. The Geo-PjBL class oom included 63 p ospec i e eache s (mean age = 19.32; ange age = 18.74-20.21), and he PjBL class oom included 74 p ospec i e eache s (mean age = 19.36; ange age = 18.66-20.12). The Geo-PjBL class oom used p ojec -based lea ning wi h GeoGeb a as a ool o p esen he p oblem and he p ojec . Meanwhile, he PjBL class oom used p ojec -based lea ning wi h pape -based illus a ions o p esen he p oblem and he p ojec . The esea che s con olled he class oom condi ions s a is ically ia mean class sizes and mean age, and no signi ican di e ence exis ed be ween mean class sizes (F (1, 6) = 4.79, p = 0.38) and mean age (F 1, 136) = 4.82, p = 0.13). Apa om including p ospec i e eache s as he pa icipan s, his s udy in ol ed wo lec u e s in he Geo-PjBL and PjBL class ooms wi h a leas eigh yea s o expe ience in eaching analy ical geome y. 2.3. Design Ac i i y The analy ic geome y cou se ac i i ies used he PjBL model and GeoGeb a (Geo-PjBL) as ools. The p ojec s in he lea ning ac i i ies aimed o sol e p oblems ela ed o analy ic geome y by p esen ing a ious pe spec i es in he GeoGeb a so wa e. GeoGeb a has an ad an age in deli e ing spa ial objec s dynamically o display objec s (poin s, lines, and ields in space) om mul iple pe spec i es. 2.4. Ma e ial Two ins umen s we e adminis e ed in his s udy: he Basic Geome y Ins umen (BGI) and he Geome y Analy ic Ins umen (GAI). The BGI was conduc ed o measu e he college s uden s’ ini ial abili y in basic geome y (2D and 3D geome y). The 30-i em mul iple-choice es , p oducing a maximum sco e o 20, was adminis e ed in 60 minu es and conduc ed wo weeks be o e he design ac i i y began. The in e nal eliabili y o his es was 0.711. The GAI, used o e alua e he model and p ospec i e eache s’ pe o mance, included h ee subjec s wi h di e en i em cha ac e is ics. Each scope has a se en-i em essay es ; he GAI has a 21-i em essay es . The in e nal eliabili y o each subjec is shown in Table 1. The i ems in he GAI a e non-dicho omously sco ed ( he maximum sco e o each ange is 140). The GAI was adminis e ed a di e en imes o each subjec . The pa icipan s we e es ed in each class oom, and he es session las ed app oxima ely 70 minu es. -114- Jou nal o Technology and Science Educa ion – h ps://doi.o g/10.3926/jo se.1267 Subjec I em Cha ac e is ics T ans o ma ion ( = 0.821) Iden i ying and cons uc ing e lec ion, o a ion, ansla ion, and enla gemen Conic Sec ion ( = 0.736) D awing and analyzing he ci cle, ellipse, pa abola, and hype bola Dis ance ( = 0.758) De ining and measu ing he dis ances o poin s, lines, and shapes Table 1. Subjec s in he Geome y Analy ic Ins umen 2.5. P ocedu e A he beginning o he s udy, he p ospec i e eache s ca ied ou he BGI as an ini ial es . Two weeks a e he es , he Geo-PjBL and PjBL class oom ac i i ies began. Comple ing all he ac i i ies and he h ee GAI es s ook 15 weeks. Figu e 3 illus a es ha each ans o ma ion, conic sec ion, and dis ance ac i i y was conduc ed in ou weeks. Bo h class ooms ecei ed he same con en ; he di e ence be ween he Geo-PjBL and PjBL class ooms was he ools o p esen he p oblems and he p ojec esul s. The weekly ac i i y las ed 100 minu es, and e e y i e weeks, he GAI was adminis e ed o e alua e each subjec . In he i h week, [GAI] T ans o ma ion was dis ibu ed o he p ospec i e eache s, wi h [GAI] Conic Sec ion adminis e ed in he en h week and [GAI] Dis ance in he i een h week. 2.6. Da a Analysis Da a analysis was used o show he e ec i eness o he Geo-PjBL and PjBL ac i i ies in he class oom in e ms o h ee subjec s. An analysis o co a iance (ANCOVA) was conduc ed o analyze he da a (α = 0.01) and o wo main pu poses. Fi s , he ANCOVA was used o compa e he means o he p ospec i e eache s’ pe o mance in each subjec . Da a on each ange was collec ed ia he GAI es esul s. Second, he ANCOVA was used o ind he co ela ion among he eache s’ pe o mances in he h ee es s. Apa om he op alues, he e ec sizes a e epo ed. Figu e 3. Schedule o model and non-model class oom 3. Findings and Discussion The esul s a e p esen ed in wo main sec ions. They compa e he means o he wo classes and he co ela ion among he h ee subjec s. 3.1. The Consis ency Model Ac i i y A e he BGI was conduc ed wo weeks be o e ac i i ies began, he esea che s compa ed he means o he wo classes (Geo-PjBL and PjBL class ooms). No signi ican di e ence was ound be ween he p ospec i e eache s’ pe o mances be o e each ac i i y (F (1, 136) = 2.63, p = 0.200). Thus, bo h g oups o p ospec i e eache s in he Geo-PjBL and PjBL class ooms displayed he same pe o mance in he BGI. -115- Jou nal o Technology and Science Educa ion – h ps://doi.o g/10.3926/jo se.1267 Figu e 4. Means and s anda d de ia ions o he GAI es Class d F p Decision Geo-PjBL s PjBL (1, 136) 2.63 0.200 H0 accep ed Table 2. Resul s o Consis ency Tes 3.2. The E ec i eness Model Ac i i y These esul s epo he e ec i eness o he Geo-PjBL and PjBL class oom ac i i ies by compa ing he means o he GAI es esul s. Wi h espec o [GAI] T ans o ma ion, a signi ican di e ence was ound in he mean sco es be ween he Geo-PjBL and PjBL class ooms (F (1, 136) = 13.84, p < 0.01); he pe o mance o he p ospec i e eache s in he Geo-PjBL ac i i ies was be e han ha in he PjBL ac i i ies. In [GAI] Conic Sec ion, no signi ican di e ence was ound be ween he mean es sco es (F (1, 136) = 4.97, p = 0.042). Thus, bo h g oups o p ospec i e eache s in he wo classes showed he same pe o mance in he conic sec ion ac i i ies. Fu he mo e, in [GAI] Dis ance, a signi ican di e ence was ound in he mean es sco es (F (1, 136) = 9.58, p < 0.01); he pe o mance o he p ospec i e eache s in he Geo-PjBL ac i i ies was be e han ha in he PjBL ac i i ies. The esul s we e unique because wo ca ego ies a o ed p ospec i e eache s in he Geo-PjBL class oom ( ans o ma ion and dis ance) and he e was one ca ego y whe ein bo h g oups o eache s had he same pe o mance (conic sec ion). Geo-PjBL s PjBL d F p Decision [GAI] T ans o ma ion (1, 136) 13.84 <0.01 H0 ejec ed [GAI] Conic Sec ion (1, 136) 4.97 0.042 H0 accep ed [GAI] Dis ance (1, 136) 9.58 <0.01 H0 ejec ed Table 3. E ec i eness o Geo-PjBL 3.3. The Co ela ion among he Tes Subjec s In e ms o T ans o ma ion × Conic Sec ion, no co ela ion was ound be ween pe o mances in he subjec s ( (135) = 1.67, = 0.211, p = 0.173). In e ms o T ans o ma ion × Dis ance, a posi i e co ela ion was ound be ween pe o mances in he subjec s ( (135) = 4.18, = 0.635, p < 0.01). Thus, i he p ospec i e eache s displayed good pe o mance in he ans o ma ion subjec , hey did he same in he dis ance subjec . Fu he mo e, in e ms o Conic Sec ion × Dis ance, no co ela ion was ound be ween pe o mances in he subjec s ( (135) = 1.48, = 0.014, p = 0.193). Co ela ion d (Pea son) p Decision T ans o ma ion × Conic Sec ion 135 1.67 0.211 0.173 H0 accep ed T ans o ma ion × Dis ance 135 4.18 0.635 <0.01 H0 ejec ed Conic Sec ion × Dis ance 135 1.48 0.014 0.193 H0 accep ed Table 4. E ec i eness o Geo-PjBL -116- Jou nal o Technology and Science Educa ion – h ps://doi.o g/10.3926/jo se.1267 3.4. Discussions The esul s showed ha he p ospec i e eache s’ achie emen s in he ans o ma ion and dis ance subjec s we e be e on he Geo-PJBL model. In acqui ing ans o ma ions and dis ances, hey need accu a e isualiza ions so ha he esul s o he ans o ma ion and dis ance calcula ions can be ealized. GeoGeb a in he Geo-PJBL class is in aluable o hem in sol ing ans o ma ion and dis ance p oblems; hus, hei achie emen s in he Geo-PJBL class a e mo e eliable. As a esul , he Geo-PjBL model g ea ly aids p ospec i e eache s in making g aphical illus a ions o he p oblems. I is ele an o no e in he esea ch ha isual g aphics help lea ne s achie e mo e unde s anding o he subjec (Janičić, 2006; Mis om, Abdu ahman, Abdullah, Osman, Hamzah & Fauzan, 2020; P adana, Sholikhah, Maha ani & Kholid, 2020). Meanwhile, he p ospec i e eache s’ pe o mance in he conic sec ion subjec showed no di e ence because he p ospec i e ma hema ics eache uses mo e algeb a ope a ions o iden i y each conic sec ion’s cha ac e is ics. P ecise and accu a e isual illus a ions a e no necessa y; by c ea ing a ske ch (Kholid, Sa’dijah, Hidayan o & Pe madi, 2020), he eache can sol e he p oblem. The e o e, he Geo-PjBL model is mo e e ec i e in subjec s ha equi e a lo o isual illus a ions. S uden s can c ea e such illus a ions using so wa e, in his case GeoGeb a. This is ele an o he esea ch o Fa ahillah, Puspi asa i and Hussen (2020), in which GeoGeb a is help ul o imp o e bo h s uden s' pe o mances and concep ual unde s anding (Kholid, Imawa i, Swas ika, Maha ani & P adana, 2021). I is because GeoGeb a p o ides pe ec isualiza ion in geome y (Sholihah & Ma yono, 2020). P oblem: Wha is he pa icula posi ion o V: x + y + z = 0? P ojec in Geo-PjBL Class: S uden ’s Answe T ansla ed Ve sion: V in e sec s he s a ing poin O(0,0,0). (a) S uden ’s wo kshee in Geo-PjBL class wi h dynamic ool. P oblem: Wha is he pa icula posi ion o V: x + y + z = 0? S uden ’s Answe : T ansla ed Ve sion: V is a poin ha e e s o O(0,0,0). (b) S uden ’s wo kshee in PjBL class wi h no dynamic ool. Figu e 5. Sample s uden s’ wo kshee s The GeoGeb a so wa e applica ion in he analy ical geome y cou se gi es signi ican ly di e en isual illus a ions compa ed wi h 2D ske ches because GeoGeb a can p esen dynamic g aphic pic u es (Caglayan, 2014; Haciome oglu, 2011; Sangwin, 2007; Zeke iya & Douglas, 2011). This means ha s uden s can pe cei e he objec s om a ious poin s o iew. Fo example, p ospec i e ma hema ics eache s mo e easily iden i y he pa icula posi ion o a plane. This bene i is no ob ained om a 2D isual illus a ion (addi ional s eps a e necessa y o loca e i s posi ion). The so wa e helps eache s in p oblem sol ing and p o ides a a ie y o pe spec i es in sol ing p oblems (Nielsen & Solo ’yo , 2019). The Geo-PjBL model in his s udy emphasizes p ojec s c ea ed by p oblem sol e s o gain a be e unde s anding o hem. The p ojec ocuses on c ea ing a ious isual illus a ion media wi h algeb a so wa e. The p og am can de elop p oblems (P adana e al., 2020) and al e na i e solu ions o p oblem -117- Jou nal o Technology and Science Educa ion – h ps://doi.o g/10.3926/jo se.1267 sol ing (Sangwin, 2007). Mo eo e , he p ospec i e ma hema ics eache can concei e analy ical geome y con en independen ly wi h no assis ance om he lec u e . The Geo-PJBL model’s p oduc is a collec ion o digi al illus a ions ha can be eopened a any ime o lea ning. 4. Conclusions In gene al, he Geo-PjBL model has he po en ial o help p ospec i e ma hema ics eache s gain an unde s anding o analy ical geome y. Un o una ely, he esul s a e no applicable o all subjec s. The Geo-PJBL model is mo e e ec i ely applied in analy ical geome y subjec s ha equi e p ecision and accu a e isual illus a ions. Meanwhile, in he ange o algeb aic ope a ions, he Geo-PjBL model is as e ec i e as he PjBL model. Fu he esea ch mus de elop mo e e ec i e lea ning models when applied o subjec s wi h he p edominance o algeb aic unc ions. This s udy used echnology in he Geo-PJBL model, and he use o echnology in he lea ning p ocess is c ucial. Lec u e s a e ecommended o use so wa e o p o ide isual illus a ions o abs ac ma hema ical objec s. 5. Sugges ions and Limi a ions The PjBL model equi es s uden s o ake an ac i e ole in c ea ing lea ning media ha i s hei pe spec i e. Mo eo e , GeoGeb a is a suppo i e lea ning medium o he p ojec . I is highly ecommended ha geome y eache s o lec u e s use a i ual media–in eg a ed lea ning model such as he Geo-PjBL model. The e o o employ s uden s in a p ojec ha u ilizes echnology can hone hei ICT skills as ea ly as possible as a gene a ion o Socie y 5.0. The s uden s ha e o possess ma hema ics and ICT skills in making lea ning media wi h GeoGeb a. In making shapes o media, hey need o unde s and he ma hema ical equa ions inpu ed in he so wa e. O he wise, he esul ing media will no be p ecise. 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