Chinese Journal of Science Education

Abstract

This study aimed to investigate students’ thinking processes of mathematics conjecturing. Five grade eleven students, 5 undergraduate students and two mathematicians were interviewed with a special survey in the study. The survey included two parts: The Mathematics Conjecturing Test for students and The Expert’s Interview Questionnaire for mathematicians. It was found that pictorial representations of students’ thinking processes of mathematics conjecturing could be constructed as a unified model. It was further found that students’ conjecturing model and mathematicians’ conjecturing model are compatible. The conjecturing model contained two directed cycles, and inner cycle and outer cycle. The inner cycle represents the process of refining the primitive conjecture and the outer cycle represents and the process of rejecting the primitive conjecture and the outer cycle represents the process of rejecting the primitive conjecture and reforming a new conjecture. The conjecturing process appears to move dynamically and recursively between four stages: guessing, checking, confirming and refuting. When students work on tasks of guessing an unknown conclusion, the model reveals that the starting point of students’ thinking and their thinking paths are more complicated than the corresponding representations on tasks of judging the correctness of a proposition. This mathematics conjecturing model can be used to study the difficulty of the tasks and to evaluate the quality of individual thinking.

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