Currently, many relevant problems about intuitive imagination literacy have been studied except the cognitive degree of pre-service high school mathematics teachers about it. To address this gap, this study investigates 51 pre-service high school mathematics teachers. Results showed that: (1) The cognitive scope of them about intuitive imagination…

This study introduces an effective intuitive rule focusing on "tending to the midpoint" in individuals' mathematical thinking. The rule concerns the intuitive tendency towards choosing the midpoint of a change, as a salient point among all the points. To test the proposed rule, 120 students in grade 9 were interviewed. We analyzed the…

Theories of grounded and embodied cognition offer a range of accounts of how reasoning and body-based processes are related to each other. To advance theories of grounded and embodied cognition, we explore the "cognitive relevance" of particular body states to associated math concepts. We test competing models of action-cognition…

Theories of grounded and embodied cognition offer a range of accounts of how reasoning and body-based processes are related to each other. To advance theories of grounded and embodied cognition, we explore the "cognitive relevance" of particular body states to associated math concepts. We test competing models of action-cognition…

Student cognition in response to intuitive and counterintuitive stimuli in the school science curriculum is not well understood. To address this issue, this study examines high school students' cognitive responses to three counterintuitive physics problems. Our analysis reveals that student success in arriving at counter-intuitive physical…

Structure sense can be interpreted as an intuitive ability towards symbolic expressions, including skills to perceive, to interpret, and to manipulate symbols in different roles. This ability shows student algebraic proficiency in dealing with various symbolic expressions and is considered important to be mastered by secondary school students for…

High school students normally encounter the study and use of formal proof in the context of Euclidean geometry. Professional mathematicians typically use an informal trial-and-error approach to a problem, guided by intuition, to arrive at the truth of an idea. Formal proof is pursued only after mathematicians are intuitively convinced about the…

One theoretical framework which addresses students' conceptions and reasoning processes in mathematics and science education is the intuitive rules theory. According to this theory, students' reasoning is affected by intuitive rules when they solve a wide variety of conceptually non-related mathematical and scientific tasks that share some common…