Beliefs and Mathematical Reasoning during Problem Solving across Educational Levels

Abstract

In this paper the status of empirical mathematical reasoning during problem solving across primary, secondary and tertiary education is studied. The main aim is to see whether the very same beliefs influence the students' performance in the same way across educational levels. The results show that despite sharing the same beliefs, the way these beliefs affect students' performance (positively or negatively) is different for different ages. More precisely, as we move from primary grades to college, the students' ability to employ empirical mathematical reasoning is inclined as they persist to ask for connections with more formal ways of working. Even though the students solved the same task and shared the same beliefs, the negative effects of these beliefs were stronger for older students.