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…

This paper describes university students' grasp of inflection points. The participants were asked what inflection points are, to mark inflection points on graphs, to judge the validity of related statements, and to find inflection points by investigating (1) a function, (2) the derivative, and (3) the graph of the derivative. We found four…

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…

This paper indicates that prospective teachers' familiarity with theoretical models of students' ways of thinking may contribute to their mathematical subject matter knowledge. This study introduces the intuitive rules theory to address the intuitive, "same sides-same angles" solutions that prospective teachers of secondary school mathematics come…

Demonstrates how research-based knowledge about students' incompatible answers to different representations of the same task could be used in mathematics instruction. Describes the 'It's the Same Task' research-based activity which encourages students to reflect upon their own thinking about infinite quantities and avoid contradictions by using…

Describes a course in Cantorian Set Theory relating to prospective secondary mathematics teachers' tendencies to overgeneralize from finite to infinite sets. Indicates that when comparing the number of elements in infinite sets, teachers who took the course were more successful and more consistent in their use of single method than those who…