Problems teaching probability in Tonga (in the South Pacific) led to the question on how language and culture affect the understanding of probability and uncertainty. The research uses a discursive approach to identify the endorsed narratives which underlie Tongans' reasoning in situations of uncertainty. I aim to justify the claim that the Tongan…

Despite increased appreciation of the role of "proof" in students' mathematical experiences across "all" grades, little research has focused on the issue of understanding and characterizing the notion of proof at the elementary school level. This paper takes a step toward addressing this limitation, by examining the characteristics of four major…

Explores the attempts of a group of preservice elementary school teachers to generalize a repeating visual number pattern. Discusses students' emergent algebraic thinking. Indicates that students' ability to express generalities verbally was not accompanied by algebraic notation, but participants often perceived complete and accurate solutions…

In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's own representations (in particular "diagrams") of mathematical problems. As a paradigmatic…

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…