Argumentative problem solving in mathematics classrooms is a crucial practice that supports important student learning goals via collaborative deliberation and consensus building, but also places substantial cognitive and affective demands on both students and teacher. In this in-depth qualitative study, we considered how students' emotions during…

Decades of research have documented young students' misinterpretations of the equal sign and the impediments these present for children's mathematical development. Much less is known about individual differences in adults' knowledge of the equal sign. We assessed 182 college students from developmental math courses and present analyses from a…

The act of explaining can help students to develop new understandings of mathematical ideas, construct rules for solving problems, become aware of misunderstandings or a lack of understanding and develop their mathematical communication. Their explanations can also offer opportunities for a teacher to understand more fully what the students are…

Existing studies have quantitatively evidenced the relatedness between problem posing and problem solving, as well as the magnitude of this relationship. However, the nature and features of this relationship need further qualitative exploration. This paper focuses on exploring the interactions, i.e., mutual effects and supports, between problem…

Investigates the thinking process underlying students' improper linear reasoning and how this process is affected by their mathematical conceptions, beliefs, and habits. Explores the actual process of problem solving from students falling into the linearity trap and the mechanism behind it. Discusses specific mathematical conceptions, habits, and…

Reviews research indicating that students' cognitive models hold random events to be equiprobable Examined 87 students between the ages of 15 and 17 to determine whether masking a random event using geometric figures would affect the students' view of the event as equiprobable. Results indicated that masking overcame the equiprobable bias of the…

In the international community of mathematics and science educators the intuitive rules theory developed by the Israeli researchers Tirosh and Stavy receives much attention. According to this theory, students' responses to a variety of mathematical and scientific tasks can be explained in terms of their application of some common intuitive rules.…

Described are the conceptions held by United States and Israeli students about multiplication and division that may impede their work with decimals. Included are the introduction, method, division and multiplication task results, and the implications for education and textbook development. (KR)

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…