This paper deals with one aspect of the endeavor to generate a theory of the development of mathematical thinking of children in the early years ages 3 to 10. By comparing two scenes, one from preschool and one from a first grade mathematics class, the relationship between diagrammatic and narrative argumentations among children and teachers is…

Gender differences in mathematical achievement have been examined in a wide range of age groups but only a few studies addressed this issue in preschool children. We compared preschool girls (n?=?570) and boys (n?=?524) from Germany with regard to numerical competencies. Differences in overall group means and the frequency of representation at…

This study examines the beginning of the conceptual understanding of the first number-words and what role language can play in developing the notion of numbers. To that end, 2 1/2- and 3 1/2-year-old Basque and Spanish monolingual children's (N = 131) basic numeracy skills are analysed by means of two different experimental procedures: "Give-N"…

In this paper, we focus on Finnish pre-service elementary teachers' (N = 269) and upper secondary students' (N = 1,434) understanding of division. In the questionnaire, we used the following non-standard division problem: "We know that 498:6 = 83. How could you conclude from this relationship (without using long-division algorithm) what 491:6 = ?…

The aim of this study is to investigate the efficiency of cooperative learning on preschoolers' verbal mathematics problem-solving abilities and to present the observational findings of the related processes and the teachers' perspectives about the application of the program. Two experimental groups and one control group participated in the study.…