Students’ thinking process when using abductive reasoning in problem solving

Background: abductive reasoning is the process of making conjectures to explain surprising observations. Although this conjecture is not certain to be true, in solving a problem, this reasoning is very helpful to determine the best solution strategy. Objectives: the study aims to investigate whether all types of abductive reasoning lead to the formation of new schemes. Design: this research used a qualitative approach with a descriptive exploratory design. Setting and participants: a total of 41 students of the research degree in mathematics education programme were involved in solving a task. Then, eight of them were chosen for an in-depth interview, representing the undercoded and overcoded abductive reasoning types. Data collection and analysis: the data collected were the results of the students’ works and task-based interviews. Piaget’s schema theory was used to analyse students' thinking processes using abductive reasoning. The analysis was carried out at all steps of problem solving, namely understanding the problem, devising a plan, carrying out the plan, and looking back. Results: those who carried out overcoded abductive reasoning used this reasoning to determine problem solving strategies. Meanwhile, those who carried out undercoded abductive reasoning used it to determine problem solving strategies as well as to form new schemes. Conclusions: the results showed that students who did abductive reasoning did not always produce new schemes. This study also notes that the truth value of answers from the application of abductive reasoning in problem solving was open and the importance of the look back step to perform accommodation