Due to the learning paradox, students cannot have real difficulty in understanding a mathematical concept that they have not yet understood. There is a gap between real difficulties, directly experienced by students, and illusionary ones, only observed by researchers. This paper aims to offer a critical reflection on our understanding of the term…

An important educational goal is enabling students to learn scientific concepts. The scientific concepts learned in class are developed within students' cognitive structures. Despite the successful application of Semantic Network Analysis (SNA) to study these cognitive structures, there has been limited examination of students' concept networks…

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…

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…

The purpose of this research is to better understand the uses and potential of triadic dialogue (initiation-response-feedback) as a dominant discourse pattern in test-driven environments. We used a Bakhtinian dialogic perspective to analyze interactions among high-stakes tests and triadic dialogue. Specifically, the study investigated (a) the…

Background: Fractions continue to pose a critical challenge for students and their teachers alike. Mathematics education research indicates that the challenge with fractions may stem from the limitations of part-whole concepts of fractions, which is the central focus of fractions curriculum and instruction in the USA. Students' development of more…

Awareness of one's own strengths and weaknesses during visualisation is often initiated by the imagination -- the faculty for intuitively visualising and modelling an object. Towards exploring the role of metacognitive awareness and imagination in facilitating visualisation in solving a mathematics task, four secondary schools in the North West…

This paper describes five growth points in linking representations of function developed from a study of secondary school learners. Framed within the cognitivist perspective and process-object conception of function, the growth points were identified and described based on linear and quadratic function tasks learners can do and their strategies…

We examined the influence of several students' cognitive and motivational factors on 8th graders' science achievement and also gender differences on factors that significantly contribute to the science achievement model. A total of 99 girls and 83 boys responded all the instruments used in this study. Results showed that girls outperformed boys on…

Linear algebra is one of the most challenging topics to learn and teach in many countries. To facilitate the teaching and learning of linear algebra, priority should be given to epistemologically analyze the concepts that the undergraduate students have difficulty in conceptualizing and to define their ways of reasoning in linear algebra. After…

The study involved evaluating the efficacy of a conceptual change instructional programme involving cognitive conflict in (1) facilitating form 2 (grade 8) students' understanding of algebra concepts, and (2) assessing changes in students' attitudes towards learning mathematics, in a mixed quantitative-qualitative research design. The…

Problem Statement: History is a science that helps people guide their futures; it is an indispensable part of education. It is important for students to know the past well in order to understand the present better and direct their future. History does not have magical laws to generalize in predicting future. However, we have to know that history…

A total of 136 eighth-grade math students from 2 Singapore schools learned from either productive failure (PF) or vicarious failure (VF). PF students "generated" solutions to a complex problem targeting the concept of variance that they had not learned yet before receiving instruction on the targeted concept. VF students…

In line with current efforts to understand the piece-by-piece structure and articulation of children's mathematical concepts, this case study compares the reversibility schemes of two eighth-grade students. The aim of the study was to identify the mechanism through which students reverse their thought processes in a multiplicative situation. Data…

A study designed to investigate a method examining some of the processes involved in students' forming of mathematical concepts in an experimental mathematics course. Results suggest that the card sorting task offers a useful tool for use in evaluation programs. (FL)