This paper reports on concept images of 38 secondary school mathematics prospective teachers, regarding the evenness of numbers. Written assignments, individual interviews, and lesson transcripts uncover salient, erroneous concept images of even numbers as numbers that are two times "something" (i.e., "2i" is an even number),…

This study focuses on adults who are neither preschool teachers nor professional caregivers and investigates their beliefs regarding the importance of engaging young children with numerical activities. It also examines the types of numerical activities adults report having observed children engaging with, as well as the types of activities they…

This paper describes kindergarten children's engagement with two patterning activities. The first activity includes two tasks in which children are asked to choose possible ways for extending two different repeating patterns and the second activity calls for comparing different pairs of repeating patterns. Children's recognition of the unit of…

This article reports on young children's self-efficacy beliefs and their corresponding performance of mathematical and nonmathematical tasks typically encountered in kindergarten. Participants included 132 kindergarten children aged 5-6 years old. Among the participants, 69 children were identified by the social welfare department as being abused…

Engaging students with multiple solution problems is considered good practice. Solutions to problems consist of the outcomes of the problem as well as the methods employed to reach these outcomes. In this study we analyze the results obtained from two groups of kindergarten children who engaged in one task, the Create an Equal Number Task. This…

In this paper we examine the possibility of differentiating between two types of nonexamples. The first type, "intuitive nonexamples," consists of nonexamples which are intuitively accepted as such. That is, children immediately identify them as nonexamples. The second type, "non-intuitive nonexamples," consists of nonexamples that bear a…

Discusses two possible approaches to (-8)1/3. Considers the pros and cons of each of these approaches and specifies some implications to teacher education. (AIM)

Discusses the place of infinity in the history and epistemology of mathematics. (Author/MM)

Assessed are the extent to which the beliefs, "multiplication always makes bigger" and "division always makes smaller," are explicitly held by preservice elementary teachers. Insight into the sources of preservice teachers' beliefs and into the relationship among preservice teachers' beliefs, computational skills, and performance on word problems…

Analyzes two aspects of teachers' planned presentations of subject matter (knowledge about subject matter and knowledge about students); illustrates using functions and undefined mathematical operations; and discusses the interconnectedness of subject-matter knowledge, knowledge about students, and knowledge about ways of presenting subject…

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)

Investigates four seventh-grade teachers' awareness of students' tendency to conjoin or "finish" open expressions and teachers' ways of coping with this tendency. Concludes that two experienced teachers were aware of this tendency, whereas the novices were not, and teaching approaches related to this tendency differed considerably. Contains 24…

Students react similarly to a wide variety of conceptually unrelated situations. Describes a rule that is manifested when two systems are equal with respect to certain quantity A, but differ in another quantity B. Indicates that in such situations students often argue that the same amount of A implies the same amount of B. (Contains 30…