Students often use incoherent strategies in their problem solving involving force and motion, as revealed, e.g. when they are asked to draw force diagrams for amusement rides involving circular motion, whether in horizontal or vertical planes. Depending on the questions asked, assignments involving circular motion can reveal different types of…

Mathematics education scholars have generally classified students' conception of the equal sign as either operational or relational. Adding to these conceptions, Jones (2008) introduced the idea of substitutional conception. Building off these scholars, I introduce a form of understanding the equal sign that includes a transformative equivalence…

There is a lack of research on students' conceptions of giftedness and intelligence, despite recognition of their influence on real-life factors such as achievement and motivation. This paper presents a cross-sectional mixed methods study that investigated Finnish students' (age 6-16 years; N = 1282) implicit conceptions of giftedness and…

Pictorial representations are often used to help children understand the situation described in a given number-sentence scheme. These static pictorial problems essentially attempt to depict a dynamic situation (e.g., one bird flies away while there are three birds still sitting on the fence). Previous research suggested that such pictorial…

An equal-armed balance at equilibrium--the bar is horizontal--tips into disequilibrium upon displacing a weight. Equilibrium is restored by reversing that move--putting the weight back where it was, or doing the same on the other side. Piaget adopted the idea of equilibration to describe how the intellect, in relating to the world, develops.…

The aim of this paper is on the one hand to discuss from an APOS (Action-Process-Object-Schema) theory perspective the mental constructions involved in the learning of linear algebra, through examples concerning the linear transformation concept and related notions. On the other hand, methodological issues related to the design of research…

Certain aspects of theoretical frameworks in mathematics education can remain unexplained in the literature, hence unnoticed by the readers. It is thus interesting to participate in a dialogue where they can be discussed and compared in terms of the aims, objects studied, results and their relation to teaching. This study is focused on how APOS…

Augmented reality (AR) can represent a contextualised scientific inquiry environment in which students may explore the real world and develop science process skills via interacting with rich information from virtual systems. However, it remains a challenge for most students to complete scientific inquiry tasks without proper support. Research…

Learning emphasizing fractions as a part-whole concept causes several limitations in developing fraction knowledge and inhibits proportional reasoning. We use fractions as quotients as the first context introduced in our learning trajectory. We report the teaching experiment results using the improved learning trajectory on thirty 4th grade…

This systematic review is aimed to explore the researches that established students' conceptual change process, both studies that facilitate conceptual change and studies that determined learner characters influencing conceptual change. Overall, 50 studies were examined in this review. The current study focused on the common characteristics of the…

Teachers face challenges when building the concept of substance with students because tensions of meanings emerge from students' daily life and canonical ideas developed in classrooms. A powerful tool to address learning, pedagogical, and research challenges is the conceptual profile theory. According to this theory, people employ various ways of…

Background: Educational robotics (ER) is increasingly used in classrooms to implement activities aimed at fostering the development of students' computational thinking (CT) skills. Though previous works have proposed different models and frameworks to describe the underlying concepts of CT, very few have discussed how ER activities should be…

The authors designed a course--Origami and Geometry--and describe one of the activities in which origami was used to fold a regular dodecahedron. They find that origami can provide students with concrete material for observing geometrical structures and give them opportunities to examine their thoughts on geometry.

According to a widespread view, one of the most important roles of education is the nurturing of common sense. In this article I turn to Gilles Deleuze's concept of sense to develop a contrary view of education--one that views education as a radical challenge to common sense. The discussion will centre on the relation of sense and common sense to…

Does language have a role to play in conceptual development, and if so, what is that role? Understanding the contents of another person's mind parallels the development in early childhood of mental state language. Does the conceptual understanding get reflected in and drive the language development, or does the language allow the representation of…