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Wilkins, Jesse L. M.; MacDonald, Beth L.; Norton, Anderson – Educational Studies in Mathematics, 2022
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…
Descriptors: Arithmetic, Kindergarten, Grade 1, Elementary School Students
Papadopoulos, Ioannis; Gunnarsson, Robert – Educational Studies in Mathematics, 2020
When a number sentence includes more than one operation, students are taught to follow the rules for the order of operations to get the correct result. In this context, brackets are used to determine the operations that should be calculated first. However, it seems that the written format of an arithmetical expression has an impact on the way…
Descriptors: Mathematics Instruction, Elementary School Mathematics, Arithmetic, Foreign Countries
Chambris, Christine – Educational Studies in Mathematics, 2018
This paper examines the existence and impact of theoretical mathematical foundations on the teaching and learning of whole numbers in elementary school in France. It shows that the study of the New Math reform--which was eventually itself replaced in the longer term--provides some keys to understanding the influence of mathematical theories on…
Descriptors: Mathematics Instruction, Elementary School Mathematics, Elementary Education, Teaching Methods
Hitt, Fernando; Saboya, Mireille; Zavala, Carlos Cortés – Educational Studies in Mathematics, 2017
Part of the research community that has followed the Early Algebra paradigm is currently delimiting the differences between arithmetic thinking and algebraic thinking. This trend could prevent new research approaches to the problem of learning algebra, hiding the importance of considering an arithmetico-algebraic thinking, a new approach which…
Descriptors: Arithmetic, Algebra, Educational Technology, Thinking Skills
Thanheiser, Eva – Educational Studies in Mathematics, 2010
This study was designed to investigate preservice elementary school teachers' (PSTs') responses to written standard place-value-operation tasks (addition and subtraction). Previous research established that PSTs can often perform but not explain algorithms and provided a four-category framework for PSTs' conceptions, two correct and two incorrect.…
Descriptors: Preservice Teachers, Elementary School Teachers, Subtraction, Mathematics Instruction
Katz, Karin Usadi; Katz, Mikhail G. – Educational Studies in Mathematics, 2010
The view of infinity as a metaphor, a basic premise of modern cognitive theory of embodied knowledge, suggests in particular that there may be alternative ways in which one could formalize mathematical ideas about infinity. We discuss the key ideas about infinitesimals via a proceptual analysis of the meaning of the ellipsis "..." in the real…
Descriptors: Number Systems, Epistemology, Mathematics Education, Evaluation
Kaasila, Raimo; Pehkonen, Erkki; Hellinen, Anu – Educational Studies in Mathematics, 2010
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…
Descriptors: Preschool Teachers, Elementary School Teachers, Foreign Countries, Questionnaires

Semadeni, Zbigniew – Educational Studies in Mathematics, 1984
The principle of the permanence of the rules of calculation is contrasted with the concretization permanence principle. Both apply to situations where some arithmetical operation known to children for numbers of a certain kind is to be extended to include further numbers. (MNS)
Descriptors: Arithmetic, Computation, Elementary Education, Elementary School Mathematics
Okazaki, Masakazu; Koyama, Masataka – Educational Studies in Mathematics, 2005
When we consider the gap between mathematics at elementary and secondary levels, and given the logical nature of mathematics at the latter level, it can be seen as important that the aspects of children's logical development in the upper grades in elementary school be clarified. In this study we focus on the teaching and learning of "division with…
Descriptors: Grade 5, Misconceptions, Mathematics Instruction, Arithmetic
Fluckiger, Annick – Educational Studies in Mathematics, 2005
This paper is based on a long-term didactic engineering about division problems (only in a numerical setting) at primary school. Situations and students' work are analyzed by means of a double theoretical framework: the theory of situations and the theory of conceptual fields (Vergnaud 1991). The analysis focuses mainly on classroom interactions…
Descriptors: Teaching Methods, Recall (Psychology), Arithmetic, Numbers