Cognitive development of eighth-grade students, as identified by Jean Piaget, occurs during a time when many of them are transitioning between concrete operations and formal operations where the ability to think in abstract concepts becomes possible. Because of this period of transition, many eighth-grade students find difficulty in demonstrating…

This paper addresses a problem that greatly complicates the implementation of dialogic educational approaches in schools: the dilemma between driving children's talk towards normatively accepted conceptions and, at the same time, avoiding the introduction of these normative conceptions into the dialogue by the teacher. I argue that this dilemma is…

In this article, the author, a teacher at Cookridge Primary School in Leeds, West Yorkshire, reflects on the teaching of science from reception across the year groups. To really compare and understand the differences of teaching science in early years, the author looks at its place in the progression of science throughout primary school. The…

The research completed by the authors into the teaching and learning of evolution and inheritance (2014 to 2018) seeks to understand the demands made by the revised National Curriculum in England (DfE, 2015) and to offer support. The commitment of the authors to applied research assumes more useful outcomes are likely when studies are conducted…

In this paper, a learning progression for geometric transformations is developed based on research that demonstrates the importance of viewing transformations as functions of the plane. The 5 levels of the progression reflect a student's evolving understanding of transformations as functions and their evolving understanding of the domain of these…

In formal education, the teaching of natural sciences begins when children are about 12 years old. Teachers justify this with the difficulty and abstraction of concepts in these sciences, and they refer to the theory of child development by Piaget. However, numerous examples from everyday life, from non-formal education, analysis of the…

Attention to core concepts in science and engineering in early education has grown recently, and understanding levers as force amplifiers can be recognized as one of these. Previous studies focused on two-sided levers and do not provide sufficient information about children's knowledge of levers as force amplifiers, nor about their learning and…

This article reports a study in which two researchers collaborated with five teachers to facilitate discourse activities aimed to enhance students' learning from practical activities. The paper explores how certain teacher practices support or hinder students' learning. Four cases from the study were analyzed in depth using…

There are many continuous quantitative dimensions in the physical world. Philosophical, psychological and neural work has focused mostly on space and number. However, there are other important continuous dimensions (e.g., time, mass). Moreover, space can be broken down into more specific dimensions (e.g., length, area, density) and number can be…

In this paper, we examine sixth grade students' degree of conceptualization of fractions. A specially developed test aimed to measure students' understanding of fractions along the three stages proposed by Sfard ("1991") was administered to 321 sixth grade students. The Rasch model was applied to specify the reliability of the test…

The aim of this study is to create understanding profiles of elementary school teachers who have been and have not been following the workshop PMRI, before and after they learned the learning resource about philosophy, principles, and characteristics of realistic mathematics approach. This type of research used in this study is a combination of…

According to Piaget, 5- or 6-year-old children gradually acquire the concept of time based on events (Piaget, 1969). In his experiment of investigating children's time concepts, Piaget found that children of these ages were able to place pictures based on sequential events with some errors; the younger children made more errors. The National…

Children's thinking follows natural developmental paths in learning math. When teachers understand those paths and offer activities based on children's progress along them, they build developmentally appropriate math environments. The authors explain math learning trajectories and why teaching math using the trajectories approach is effective. A…

Bar graph activities appropriate for four stages of development are given. (MK)

The author describes a Piaget based curriculum involving three main themes (classification, number measurement/space, and seriation) for young mentally retarded children. Students solve problems by doing something physically and mentally to the data, shuffling the facts about in their minds, so that they will come to a logical solution. Language…