The dual processes hypothesis in mathematics performance: Beliefs, cognitive reflection, working memory and reasoning

• Positive interaction of cognitive reflection with respect to mathematical reasoning
• The belief systems of students correlate with working memory in mathematical learning.
• New key interpretation of the possible conflicts between System 1 and System 2 outputs
• Interaction of cognitive and metacognitive components involved in mathematical performance
• The difficulties students have with deductive and probabilistic reasoning problems

In this paper, using data provided by an empirical study of students in a high school science course, we discuss key variables in the interaction between System 1 (S1) (intuitive and unconscious processes) and System 2 (S2) (analytical and conscious processes) in mathematical reasoning. These variables are: beliefs about oneself and about mathematics; cognitive reflection understood as a self-regulatory skill; working memory; and the evaluation of the deductive and probabilistic reasoning of students. The results confirm the interaction between these variables and their predictive power on performance in mathematics. The study also adds novel considerations related to the function and interaction of cognitive and metacognitive components involved in mathematical performance.