Katedra matematiky - Katolícka univerzita v Ružomberku

Examples of using ICT for forming reductive reasoning at school 159above flowers. It is possible in case, when the opponent doesn’t apply thewinning strategy.Now let’s look at the next board (Meadow 2 - picture 4). There areonly four differences between them - opposite directions of three arrows andabsence one middle arrow. But it changes the winning strategy.The series of analogical questions allow to discovery which flowers are"the way for victory" (fields marked on scheme). The first lucky flower isjust field marked "O". But there is new element on this board - loop. Thenopponent puts pawn on flower "X" and player who knows winning strategycan turn back to flower "O" and he will win. Another important fact is thatthere is no symmetry on this board. It’s easy to explain why flower markedas "?" doesn’t guarantee the succeed and flower "O" does.As we can see game Maths meadow requires strategic and logical thinking.To win, player has to uncover winning strategy.Using deduction to discover strategy is hardly useful, because there aretoo many paths to analyze (over 150 ways to go from beginning to the end).But if we use reduction we will solve this problem quickly. The reductionis very attractive and effective method in this situation.So, is it proper to think, do pupils will discover strategy playing thecomputer game by reduction?6. Research and some conclusionsThe research has been applied to 164 pupils 10 - 14 years old - 76 boys and88 girls (there were only one 9 years old and one 15 years old).They all played couples so many times and as long as they want. Theywere observed and additionally all they did was recorded as films (this waygave next materials for analyse). Research based also on special preparedquestionary.There are results of pupils" observations in table 1.Table 1