Informačný vek modifikuje metódy a formy vyučovania matematiky. Key words: dynamic geometric system, GeoGebra, math education, teacher training
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1 Informačný vek modifikuje metódy a formy vyučovania matematiky VPLYV VZDELÁVANIA UČITEĽOV NA MIERU VYUŽÍVANIA DYNAMICKÝCH GEOMETRICKÝCH SYSTÉMOV V MATEMATICKEJ EDUKÁCII THE IMPACT OF TEACHERS TRAINING ON USAGE INTENSITY OF DYNAMICAL GEOMETRICAL SYSTEMS IN MATH EDUCATION Katarína Žilková Abstract: This article describes the current situation in the use of dynamic geometric systems in teaching mathematics in Slovakia. Teachers of different grades have completed training in the field of digital technology in order to modernize processes in teaching of mathematics. The topic of dynamic geometric systems and their effective integration into teaching of mathematics has been important parts of the training. This article analyses the results of the training in the terms of impact of the training and practical use of different DGS in education process and at the same time it evaluates them from different aspects. Key words: dynamic geometric system, GeoGebra, math education, teacher training Úvod. V ú ú f ( 1999). H b : é ô lovenskej republike na ; b é f é ; ô b í. Z é é ť, é b b é ú é C b G. O é ď ú é ú é, b ť í,. í, b í ň ô. V ú ť í b é é (DG ) f í. C í
2 Katarína Žilková ť í é í DG í. 1 Dynamické geometrické systémy v matematickej edukácii zameranie výskumu Z b é é v. C b ť í í é, ť ô b í é ť í é é é é b. 1.1 Výskumný problém Pre potreby spracovania í bu ť b é é b é, b ť í é v ma, ä í í í é DG í. Č ť b ť v ú : DG ú í í b olventami é? A í ú DG C b G í ú é G G b ( b í )? N ú í pozorovania b í DG í, ú í é DG C b G, G G b, C R. U é DG b f í fó. V í MVP b b í DGS a v ď í é. U DG b é b é, é b ď b ch apletov. Z, ä ô (. ť f é, f í f é ),, b í í b ú f ť G G b d é. P b í, é, ň. H ú í ú í: 1. é ú ; 2. é b ( ť í í DG v ); 3. é é é í ( ť pred í,, í); 4. G b í. 146
3 Vplyv vzdelávania učiteľov na mieru využívania DGS v matematickej edukácii Š ú í b, b í ú :, ô b, a é é G G b í ú. Š ú í b b 1. V ď b, ô é é b é, ť b í, é b ť oblasti í é í, í po í é í ô. Obr. 1: H ú é í. 1.2 Získavanie údajov N í ú b (w b) í D é é é. N í b í f, í b b é í matematiky. P í b í, í garantovali a b b í b í ť f o b ú f. frekventantov lokalizov, b é. Zb ú b septembra V b 96 í. V ô b í (respondenti b í ) é ť ť í. N í ú (po í í ) je m é ť ť ro é í ú ovni 56%. U,, ä z ô é b, a ď el é í. Napriek é u ú é í é. 147
4 Katarína Žilková 1.3 Štruktúra Z é b ô ť, ú 66% a 34%. V matematiku na 8%, 42%, s 48% a,.. 2% roku. V ú b a grafoch b b.. 1 V ú vek počet rokov rokov rokov rokov rokov rokov rokov a viac 1 20" 15" 10" 5" 0" 26"'"30" veková&štruktúra&& 31"'"35" 36"'"40" 41"'"45" 46"'"50" 51"'"55" 56"'"60" 61"a"viac" Obr. 2: G f é é. počet&rokov&praxe& b.. 2 P roky praxe počet 1 rok alebo menej roky rokov rokov rokov rokov a viac 52 Obr. 3: Š ú pedagogickej praxe. Z ú é, ú b praxou ako 21 rokov a vekom J, í é í b í. V ú, ô ť, na zmena v oblasti b vy í é é é v í,, o ú. 148
5 Vplyv vzdelávania učiteľov na mieru využívania DGS v matematickej edukácii 1.4 Výber z výskumných otázok W b í b 8 ( í ; ;.). V í b f é ú é b í. Tretia, pre potreby, ť í, b 4 y f é f b é b, 3 é, 3 é 3 ô é é é (C bri geometria, GeoGebra, Compass and Ruler). Š ť, é G G b, ú ô b í é é, b é, í ojov. C í b ť ť é é é z í í. V kontexte s f b b ť í é ú í, a to z ú :. 1. é DG ste poznali í?. 2. é DG ste používali í?. 3. S DG ste sa oboznámili?. 4. V í DG í b?. 5. K é DG používate v ú í b í? Vyhodnotenie položiek č. 1 a č Výsledky a ich interpretácia Z é 96 68, é, ú 70,8%. ď b é ť í, í tab. 4 ô ť : 62 z 96 í é C b, 65%. í é, é b v ú í (b C b ô ). 23, é G G b í. DGS s C R, E, C b ( í: 1, 3, 4 ). 27, í é. 5, é DG, ô í, é f é é, é ú é (. D ). Zí é ú potvrdili predpoklady o, é DG b ú. b í é C R f ť. 149
6 Katarína Žilková Z ú é, ť é f é é í. 62, C b í, í 33, ú 53%. G G b 23, í 9, 39%. A 59% é, í é í. J é, ď b é é é é,. V, C b ma é í DG b bí aktivitami. b.. 4 í, í DG DGS poznali DGS pred školením percentuálne vyjadrenie vzhľadom na celkový počet Cabri Geometria 62 65% GeoGebra 23 24% Compass and Ruler 1 1% Euklides 3 3% Cinderella 4 4% žiadne 27 28% iné 5 5% b.. 5 í, í po í z DGS DGS používali DGS pred školením percentuálne vyjadrenie vzhľadom na celkový počet Cabri Geometria 33 34% GeoGebra 9 9% Compass and Ruler 0 0% Euklides 1 1% Cinderella 0 0% žiadne 57 59% iné 3 3% Vyhodnotenie položiek č. 3 a č. 5 P f ô DG b. V í b b í é C b tria a GeoGebra a b. V í ô b f í ť C b G G b, ť é f,. ť é a na é. O, ť é, s respondenti a ň f í b ô ú v kontexte í. O ú s ú ú í í DG ú í. Z kontexte f h bude ú ť b é é úb, b í ( ú úb ), ť lnu zmenu v í í DG í. U, ú ( ) ú. 4, ť, í DG í b. (80%, í í DG í b í.) 150
7 Vplyv vzdelávania učiteľov na mieru využívania DGS v matematickej edukácii V b. 6 ú é, í í DG ú. Z 96 uviedlo Cabri geometriu 83, GeoGebru 92 a Compass and Ruler 17. O é DG í b é. Z í é,, b DG. (R t : DG í, í DG í, b DG, í DG í priebehu v ú í DGS.) P ô, í é, é a, é, é b í é. P b b é ť é. b.. 6 Z ú DG b.. 7 V DG b í DGS zastúpenie DGS počas školenia percentuálne vyjadrenie vzhľadom na celkový počet Cabri Geometria 83 86% GeoGebra 92 92% Compass and Ruler 17 17% Euklides 5 5% Cinderella 6 6% žiadne 1 1% iné 3 3% DGS využitie DGS po absolvovaní školenia percentuálne vyjadrenie vzhľadom na celkový počet Cabri Geometria 28 29% GeoGebra 76 79% Compass and Ruler 1 1% Euklides 1 1% Cinderella 0 0% žiadne 17 18% iné 1 1% Redukcia výskumného súboru analýza a interpretácia získaných údajov P ú 9 í, úb b ť 87. V ď í ú b í, aj ú, DG, to Cabri geometriu a G G b. N b ť DG, é b ť. N é zistenia ú é b. 8 b.. 8 Porovnanie Cabri geometrie a GeoGebry z í, í í 151
8 Katarína Žilková dynamický geometrický systém počet percentuálne vyjadrenie vzhľadom na redukovaný počet (87) poznali pre školením Cabri Geometria 61 70% GeoGebra 23 26% používali pred školením Cabri Geometria 33 38% GeoGebra 9 10% zastúpenie počas školenia Cabri Geometria 80 93% GeoGebra % využívanie po skončení školenia Cabri Geometria 27 31% GeoGebra 72 83% N é b é úb a í ú í ô ť, é (Cabri Geometria a GeoGebra) z h í, é í é. B, aktivity prebehli v prostrediach obo DG. A ď ú b. 8 C b 93%- é ú í C b í, ô ú í b ú, C b G í respondenti poznali í,, s ktorými DGS sa oboznámili počas školenia, é b. Z í C b G G G b í f b. 4. A ď ú í é f G G b é, rozdiel. V í boli vy é é í, í b b f é é produkty a b é é é b é. C b Geometria zaznamenala mierny pokles v í í í í atiky z 38% na 31%, tak GeoGebra svoje postavenie posilnila z 10% 83% í í. 152
9 Vplyv vzdelávania učiteľov na mieru využívania DGS v matematickej edukácii Miera&využívania&DGS&Cabri&Geometria&a&GeoGebra & 80" 70" 60" 50" 40" 30" 20" 10" 0" pred"školením" Cabri"Geometria" po"skončení"školenia" GeoGebra" Obr. 4: í DG C b G GeoGebra pred a. P, ú ( í ) í G G b í f (. ť G b, í, CA.), f ť. N é f ť í í, b ť í. P í ť ô ť f, b, í b é b. Z DG 53%. ú, í é ú. é C b 35% é G G b 92%, í é. A ú ú ú zmene v í é í. é é f é é b. ú. Záver í nielen od V ú, í é, ň ú parametrov: f ť spektre DGS a ich dostupnosti; zn ť DG ; ť f í ť DG é. 153
10 Katarína Žilková Z, ( b í é ) f ôsobom determinuje é í DG. Poznámka: Z ť é ď a lektormi matematiky v é. P í b ú ť Š R KEGA 028UK-4/2011 s é modelovanie v í é. Literatúra [1] BRE EN Á, B., ABÁ OVÁ,., ALAŠ,., OLAJOVÁ,., PE ÁROVÁ, J., ZAR A,., VANÍČE, J. (2010). Premena školy s využitím IKT. E f :. [2] HANZEL, P. (2007). D é í. In: Matematika 3. Olomouc: U P é O, S [3] HOHENWARTER, M., JARVIS, D., LAVICZA, ZS. (2009). Linking Geometry, Algebra, and Mathematics Teachers: GeoGebra Software and the Establishment of the International GeoGebra Institute. In: The International Journal for Technology in Mathematics Education. Volume 16, Number 2, p [4] KARATAS, I. (2011). Experiences of Student Mathematics Teachers in Computers-Based Mathematics Learning Environment, International Journal for Mathematics Teaching and Learning. D é [5] OREŇOVÁ, L. (2011). í í í GeoGebra. In: Užití počítaču ve výuce matematiky. Volume 5., Number 1, p [6] KOKOL-VOLJC, V. (2007). Use of mathematical software in pre-service teacher training: the case of DGS. BSRLM Proceedings, Volume 27, Number 3. [7] LU ÁČ,. a kol. (2010). Využitie IKT v predmete Matematika pre stredné školy. Elfa:. [8] AJERČÍ OVÁ, J. (2007). L-otázky a ich využitie vo výskumnom nástroji. P revue. Volume 59, Number 2, p [9] E AN Š NOVÁ, I. a kol. (2010). Využitie IKT v predmete Matematika pre základné školy. E f :. [10] SOURY-LAVERGNE, S., JAHN, A. P., TRGILOVA, J. (2011). I2Geo quality assessment process: a tool for teacher professional development? In: The Electronic Journal of Mathematics & Technology, Volume 5, Number 3. [11] ŠED VÝ O., VALLO D., V DER ANOVÁ. [ed.]. (2011). Nové trendy v teórii vyučovania matematiky. Dynamický softvér vo vyučovani : b í 154
11 Vplyv vzdelávania učiteľov na mieru využívania DGS v matematickej edukácii é é 1. bra 2010 na KM FPV UKF v Nitre. Nitra : UKF, s. [12] [8 September 2012] doc. PaedDr. Katarína Žilková, PhD. Ústav pedagogických vied a štúdií Pedagogická fakulta UK v Bratislave katarina@zilka.sk 155
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