Knowing How Students Build Conceptual Knowledge: A Study Of Mathematical Infinity

The concept of infinity is often confusing to students. This research investigates different concepts in adolescent and adult on the mathematical infinity. With the hypothesis that the notion of infinity is constructed which occurs through successive levels, the theoretical background is based on Constructivism. An interview and three experiments were created with concrete materials that lead an argument to the infinity state. The interview is used to observe how the people concerned deals with the difference between very large numbers and an infinity one. Furthermore, the abstraction is considered when carrying out the task to reduce the size to half when the materiality no longer exists. The methodological reference is the Clinical Interviewing. Data analysis categorizes the various notions of mathematical infinity. Based in how the subject interacted with the proposal activity the three following categories have being proposed: Does Not Grant The Infinity: The reasoning is sparse and attached to the concrete world; Existence Little Conceivable: Infinity means something big or not known; Infinity Cannot Be Measured: Thinking is disconnected from the material world coming to abstract, the subject's thought is able to understand that infinity is not a real number but an idea. The results indicate that the notions of mathematical infinity are built independently of the age, education level or work expertise. To be successful in teaching a specific content is crucial to know the mathematical notions of our students.