This study examines the presence of three conceptual metaphors for fractions -- The measuring stick metaphor, Arithmetic is motion along a path, and Arithmetic is object construction -- in four common and popular Swedish mathematics textbook series for years 1-3. I analyse the introduction of fractions and the kinds of tasks students are given in…

The intention of the study was to examine the effects of a fraction intervention in a whole-class environment. The intervention aimed to enhance students' conceptual fraction knowledge, with a major focus on fraction magnitude understanding. This study included 120 fifth-grade students in standard classroom settings. Utilizing a cluster randomized…

We report here on an intervention implementing a structural approach to arithmetic problem-solving in relation to learning outcomes among preschoolers. Using the fundamental principles of the variation theory of learning for developing the intervention and as an analytical framework, we discuss teaching and learning in commensurable terms. The…

Mastering traditional algorithms has formed mathematics teaching in primary education. Educational reforms have emphasized variation and creativity in teaching and using computational strategies. These changes have recently been criticized for lack of empirical support. This research examines the effect of teaching two differently structured…

This paper uses a post-qualitative philosophical perspective to find new ways of understanding teaching and learning. The paper presents a series of examples that were used in a longitudinal study, with the aim of creating variation patterns that would make it possible for students to discern the use of the four basic arithmetic operations in…

Purpose: The purpose of this paper is to contribute to the understanding of the processes that make teachers learn in a collaborative arrangement similar to lesson study (LS) and learning study (LearS). The teachers in this collaboration wanted to enhance teaching and student learning (grades 4-7) about decimal numbers.…

Mathematically speaking, a "difference" is the result of a subtraction. However, when the number domain is extended from natural numbers to integers, the separation of the magnitude of a number from its value creates "different differences," where the connection to subtraction is no longer straightforward. Based on…

This article portrays action research conducted in relation to students' faulty use of the equality sign in a Grade Four mathematics classroom in Sweden. Substantial background on teacher-researcher collaboration that prepares ground for the action research is offered. Drawing on cultural-historical and activity theory perspectives, the conduct of…

The field of mathematics is complex, areas such as arithmetic, and geometry each consist of several sub-domains and encompass many cognitive processes. Achievement tests for elementary pupils assess a wide range of arithmetic skills such as number sense, procedural knowledge, and using problem solving strategies. Although mathematical tests often…

In a longitudinal intervention study, the effects of three intervention strategies on the reading skills of children with reading disabilities in Grade 2 were analyzed. The interventions consisted of computerized training programs: One bottom-up intervention aimed at improving word decoding skills and phonological abilities, the second…

This article focuses on spontaneous and progressive knowledge building in ''the arithmetic of the child.'' The aim is to investigate variations in the behavior patterns of eight pupils attending a school for the intellectually disabled. The study is based on the epistemology of radical constructivism and the methodology of multiple clinical…

This article focuses on spontaneous knowledge-building in the field of "the arithmetic "of" the child." The aim is to investigate the conceptual progress of fifteen children during their early school years in the compulsory school. The study is based on the epistemology of radical constructivism and the methodology of…

The present study examines the effect of three different structured methods, traditional, independent and problem-solving, of teaching children arithmetic in the beginning of 7th grade in Sweden, age 13 years. The progress made by these students is presented by measures of their arithmetic ability, calculation and quantitative concept, as well as…

The original objective of the nursery school was that acting in cooperation with the home, it should develop children motorically, intellectually, emotionally, and socially. A comparison of objectives with effects reveals many to be non-existent. A 1966 study of nursery school effects on child development revealed the following breakdown: (1)…