Katedra matematiky - Katolícka univerzita v Ružomberku
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Katedra matematiky - Katolícka univerzita v Ružomberku

Katedra matematiky - Katolícka univerzita v Ružomberku Katedra matematiky - Katolícka univerzita v Ružomberku

math.ku.sk
12.07.2015 Views

160 Tadeusz RatusińskiThey are based on questionaries in which pupils had to evaluate themselves.If we compare "how pupils claimed" in questionary and "how theyplayed" (table 2) based on analysis of collected materials (recorded films)we formulate surprised conclusion: pupils had applying the strategyinsensible! They played right flowers, but they didn’t know it’s strategy.Table 2Let’s sort the same data from analysis of films by school classes (Meadow 1- figure 3, Meadow 2 - figure 4).Figure 5 - Meadow 1 Figure 6 - Meadow 2Few more conclusions can be formulated:The winning strategy for Meadow 1 has been easier to discover thenthe other one. In this situation the first strategy seems to be some kind ofepistemological obstacle [8]. Pupils who had found the winning method forMeadow 1 had problems with discovering next one.If we concentrate on Meadow 1 we’ll observe:• ∼45% of each class (primary school and secondary school) noticedlucky flowers - they observed: If I put Beep on this flower I’ll win.They didn’t make any reasoning for this fact, just observation.• ∼33% of each group - find out incomplete strategy - it means theyforgot about one flower (most often the first - the very bottom one -the last step of reasoning).

Examples of using ICT for forming reductive reasoning at school 161• ∼15% of oldest classes (6th primary school and 1st secondary school)discovered full strategy (full reductive reasoning).• Significant majority of all pupils discovered at least lucky flowers onfirst board.The analysis of recorded films shows that quite a lot of pupils solved thisproblem in both cases (on both boards):IV SP (4th primary school) - ∼30%,V SP (5th primary school) - ∼56%,VI SP (6th primary school) - 50%,I Gimnasium (1st secondary school) - ∼94%.Additional from observation two more conclusions can be formulated:• Pupils cooperation has been better way to discover winning strategythan their contest.• Weakest pupils learned more observing opponents. It helped them tofind out the right way of reasoning.Described game Maths Meadow is a part of collection of math’s didacticsgames. Working over such project we realize that this product is dedicatedfor children. Well-made educational game can become an object of interesteven of the most demanding player. Under colourful, breath taking graphic,interesting music and the sound effects, in easy way we can smuggle mechanismsresponsible for formatting logical and creative thinking as well asskill of discovering the strategy.The desire of victory is natural helping factor for uncovering winningstrategy. It seems, that such didactic games are proper for pupil independentlyof age. Results of researches show, that suitably constructed gamescan help in teaching reductive reasoning. At the beginning the pupils playwithout any analisation of situation. However, after several played partsappears question: what should I do to win? This the motivates to analysenext steps of the game and search for strategy which allows winning. Strategicgames used in didactics have to be always adapted to child’s intellectualpossibilities.The research has showed, that it is possible and may be effective toteach reduction from 10 years old. Educational games help to develop wayof thinking which should be the basic aim of education at school, but it isnot possible without general introducing computers. The computers allowteaching in a way that was unavailable up to now.Maths meadow is example of such game, which we can use to teach reduction,starting from 10 years old pupils of primary school. Experiences

160 Tadeusz RatusińskiThey are based on questionaries in which pupils had to evaluate themselves.If we compare "how pupils claimed" in questionary and "how theyplayed" (table 2) based on analysis of collected materials (recorded films)we formulate surprised conclusion: pupils had applying the strategyinsensible! They played right flowers, but they didn’t know it’s strategy.Table 2Let’s sort the same data from analysis of films by school classes (Meadow 1- figure 3, Meadow 2 - figure 4).Figure 5 - Meadow 1 Figure 6 - Meadow 2Few more conclusions can be formulated:The winning strategy for Meadow 1 has been easier to discover thenthe other one. In this situation the first strategy seems to be some kind ofepistemological obstacle [8]. Pupils who had found the winning method forMeadow 1 had problems with discovering next one.If we concentrate on Meadow 1 we’ll observe:• ∼45% of each class (primary school and secondary school) noticedlucky flowers - they observed: If I put Beep on this flower I’ll win.They didn’t make any reasoning for this fact, just observation.• ∼33% of each group - find out incomplete strategy - it means theyforgot about one flower (most often the first - the very bottom one -the last step of reasoning).

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