A possible contributing factor to students' difficulty in learning advanced mathematics is the conflict between students' "natural" learning styles and the formal structure of mathematics, which is based on definitions, theorems, and proofs. Students' natural learning styles may be a function of their intuition and language skills. The purpose of…

Discusses the performance of Malaysian secondary school students on a probability concepts test covering various intuitive and taught probability concepts. Describes the establishment of a probability concepts hierarchy and considers probability understanding in relation to independent variables. Boys, Form Six students, and students with a higher…

Counterintuitive moments in the classroom challenge common sense and practice and can be used to help mathematics students appreciate the need to explore, reflect, and reason. Proposed are four examples involving geometry, systems of equations, and matrices as counterintuitive instances. (MDH)

Describes two intuitive rules underlying students' conceptions in mathematics and science that are not always compatible with usually accepted scientific ideas. The intuitive rules are: "More of A, more of B" and "Subdivision processes can always be repeated." In teacher education, it is important to raise instructors'…

To investigate the origins and nature of intuitive obstacles affecting the learning of elementary probability theory, 618 Italian elementary and middle school students were interviewed about their methods of solution for several problems dealing with probability. The discussion focuses on four varieties of obstacles to learning prevalent within…