Dynamic software enhancing creative mathematical reasoning

Abstract: This thesis includes two articles and a coat. The articles present two studies investigating students’ reasoning when they were working in pairs, solving mathematics problems using the dynamic software, GeoGebra, The first study shows that the students used GeoGebra as a collaborative environment where they shared their individual reasoning to one another. Furthermore, GeoGebra provided the students with feedback that, to some extent, became a basis for their creative reasoning. The second study looked more closely into the relation between students’ reasoning and their utilization of the feedback generated by GeoGebra. The study showed that students who before entering computer commands used creative mathematical reasoning to hypothesize what the outcome may be, understood the feedback from software better and used it more efficiently. The students who engaged in imitative reasoning were mainly able to use feedback to determine if a solution attempt was correct or not, but did not fully understand the feedback and were less able to use it to make further progress in solving the task. The coat explains theories and methodologies more thoroughly and discusses the results of the two articles. In a concluding discussion the results of the articles are linked and possible implications for teaching are proposed. In school it is common that teachers and textbooks provide students with algorithmic solution templates to tasks, but in the study the didactic situation with dynamic software was found to invite students to create their own solution methods. Furthermore the thesis suggests that it could be beneficial for the students to be encouraged to pay more attention to their own solving strategies, i.e. to explain and evaluate their methods and results rather than merely looking for the correct answers.