This paper reports from a case study which explores kindergarten children's mathematical abstraction in a teaching--learning activity about reflection symmetry. From a dialectical perspective, abstraction is here conceived as a process, as a genuine part of human activity, where the learner establishes "a point of view from which the concrete…

This study investigates the relationship between children's subitizing activity and their construction of arithmetic units. In particular, the study hypothesizes a positive association between children's construction of subitized units and their construction of arithmetic units, and hypothesizes that children who can subitize larger units, such as…

Educators and several national standards highlight the role that problem solving should play in students' mathematics education: problem solving is recognized as one of the most significant activities of doing mathematics. From the research point of view, nowadays, it is well established that cognitive and affective factors come into play in…

In this 3-year longitudinal study, we examined the interplay of children's motivational orientations, spontaneous focusing on numerosity (SFON) and number sequence and arithmetical skills from kindergarten (at age 6) to grade 1 (at age 7). We also examined the direct and indirect contributions of motivation and SFON to the acquisition of…

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…

The researchers in this study investigated the impact of mathematics-focused parental involvement on Kindergarten to Grade 8 children and parents as well as factors prompting that impact. Qualitative analysis consisting of parent, child, and teacher interviews and 3-year quantitative testing showed significant improvements in students' mathematics…

The purpose of this longitudinal study is to investigate whether an early childhood intervention using an explicit and transparent number naming system will have a lasting benefit to English and Spanish speaking children in their mathematics achievement related to number sense by accelerating their acquisition of concepts of numeracy and place…

This paper focuses on kindergarten teachers' interactions with young children during mathematical learning activities involving the use of digital tools. We aim to characterise the teachers' roles and actions in these activities and extend considerations of teachers' orchestrations current in the research literature with regard to agency and…

In 2008, the research center "Individual Development and Adaptive Education" was constituted by the Goethe University, the German Institute for International Educational Research, and the Sigmund Freud Institute, all located in Frankfurt am Main, Germany (http://www.idea-frankfurt.eu). The research of the center focuses on the…

This study describes situations in German daycare facilities (Kindergarten) in which the development of mathematical thinking in children is specifically encouraged through examination of common play objects. Using micro-sociological methods of analysis, the mathematical potential of such interactions between teacher and child is elaborated within…

First results of the project "Mathematical Creativity of Children at Risk" (MaKreKi) will be presented. The project is conducted in the interdisciplinary research center "Individual Development and Adaptive Education of Children at Risk" (IDeA [http://www.idea-frankfurt.eu; accessed 7 June 2013]). Combining a…

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…

The objective of this study was to examine gender differences in the relations between verbal, spatial, mathematics, and teacher-child mathematics interaction variables. Kindergarten children (N = 80) were videotaped playing games that require mathematical reasoning in the presence of their teachers. The children's mathematics, spatial, and verbal…

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…

Twenty-three kindergarten and first grade children were asked to articulate the meaning and the need for punctuation marks in a list of numerals showing prices for a list of items. Despite not having been schooled yet formally on the use and roles of numerical punctuation, many children gave similar explanations regarding the purpose of…