Background: Teaching using manipulatives is emphasised, especially in the early grades, to help learners conceptualise operations on whole numbers. Therefore, teachers' competencies in using manipulatives is the key in helping learners master these basic operation skills. Aim: Drawing from the literature on using manipulatives to improve learners'…

In this study, effects of 2 physical manipulative instructions on students' geometrical knowledge acquisition were compared. Geometry topics' presentation was conducted via using physical manipulative and the practice stage in two different forms: (1) practice consisting of problems supported with explicit metacognitive questions and (2) practice…

Three game examples using L-shaped tri-cubes in alternative arrangements are presented. Each game example challenges you to think who might win, and what alternative playing strategies could be implemented to change the final outcome.

This paper offers insight into teachers' perspectives on the role of manipulatives in the mathematics classroom on either side of the primary to post-primary transition (sixth class teachers in Irish primary schools and first year mathematics teachers in post-primary schools) to examine if discontinuities exist around their usage. The transition…

Abundant prior research has compared effects of physical and virtual manipulatives on students' conceptual learning. However, most prior research has been based on conceptual salience theory; that is, it has explained mode effects by the manipulative's capability to draw students' attention to conceptually relevant (visual or haptic) features.…

The purpose of this article is to describe a couple of challenging mathematical problems that involve paper folding. These problem solving tasks can be used to foster geometric and algebraic thinking among students. The context of paper folding makes some of the abstract mathematical ideas involved relatively concrete. When implemented…

This article investigates the potential of utilizing technology to apply Lesh's representations for teaching mathematical concepts. Lesh's model includes written symbols, verbal symbols, real life situations, pictorial representations, and concrete representations. The author suggests that, with the wealth of technological applications, teachers…

Geometric thinking affects success in learning geometry. Geometry is studied from elementary school to university level. Therefore, in higher education and basic education, it is necessary to carry out a systematic review in order to obtain tips for improving geometric thinking skills. A systematic review of geometric thinking was done in this…

The goal of this design-based research study was the creation and evaluation of a mini-unit intended to foster perceptually grounded understandings of the concept of slope in middle-school students. Central to this unit was an innovative device designed to create a productive pedagogical space between student intuition for steepness and formal…

Sustainability management is rapidly progressing from an operational task to a strategic imperative one as environmental and social concerns shape the business environment. Scenario planning is increasingly being used by companies and governments to explore the potential impact of future challenges. Applied in a management education context…

In scientific inquiry learning, manipulatives have been widely utilized as learning resources. Studies have explored the advantages of virtual manipulative (VM) for conceptual understanding and knowledge construction in science education. However, research on the mental engagement and perception of students during collaborative learning under…

Manipulative artefacts are considered useful scaffolds of arithmetic during early years education, but their use is considered less important as children get older. Yet adult arithmetic performance often recruits artefacts to improve accuracy and efficiency, and so the same benefits should accrue to children beyond early years. We propose that…

Students' attitudes and motivations toward mathematics decrease as they intensively confront cognitive information along the process of mathematics teaching in general. One of the most important reasons for this is the lack of activities for affective and psychomotor domains in the mathematics teaching process. One way to overcome this problem is…

The actions carried out by children are a mechanism that enables them to come into contact with their environment, assimilating it, acting on it, and thereby transforming it. From this perspective, an exploratory study has been designed to analyse the actions carried out by 87 children aged 1-3 years old in two task-situations involving the…

This paper links early foundations in science for young children to the eventual achievement of science literacy for adults. There are five key arguments being made: (i) the early-years foundation stage (EYFS) specialists need to have a view for exactly what foundations "are" being laid in classrooms; (ii) that they all need to be --…