Algebra is critical in shaping future mathematics success and is integral to the K-12 curriculum. Despite its inclusion, a common challenge arises as students' progress to higher grades without a solid foundation, resulting in challenging learning experiences. This action research study focuses on the algebraic learning experience of a Grade 7…

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…

A case study of calculus instructional material (comprising of lecture notes and tutorial practice worksheets) designed by teachers from a Singapore pre-university is presented in this paper. As textbooks have not been available for mathematics at the pre-university levels, the instructional material was a product of the teachers' collaborative…

The purpose of the research is to describe and analyze the implementation of Scaffolding based on Cognitive Conflict in correcting the students' errors in Algebra material. The research uses Mix Method, that is a combination of quantitative and qualitative methods. There are 25 students that are involved and tested on Algebra material. They are…

The purpose of this study was to determine if online reflections through social networking affect students' sense of community and levels of perceived conceptual learning in Algebra I courses. Social constructivism, connectivism, and computer-mediated communication in relation to reflective practices form the theoretical and practical framework…

The theory of conceptual fields is a developmental theory. It has two aims: (1) to describe and analyse the progressive complexity, on a long- and medium-term basis, of the mathematical competences that students develop inside and outside school, and (2) to establish better connections between the operational form of knowledge, which consists in…

Previous research on children's conceptual and procedural understanding of fractions, and other arithmetic skills, has led to contradictory conclusions. Some research suggests that children learn conceptual knowledge before procedural knowledge, some suggests that they learn procedural knowledge before conceptual knowledge, and other research…

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…

The developmental psychology of mathematical thinking and the clinical interview method can make major contributions to education by transforming the process of formative assessment--the attempt to use information concerning student performance, knowledge, learning potential, and motivation to inform instruction. The clinical interview is a…

This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…

Effective teaching should focus on representational change, which is fundamental to learning and education, rather than conceptual change, which involves transformation of theories in science rather than the gradual building of knowledge that occurs in students. This article addresses the question about how to develop more efficient strategies for…

A schema based view of addition development is compared with Siegler's latest strategy-choice model, which includes an addition goal sketch (a basic understanding of "the goals and causal relations" of addition; Siegler & Crowley, 1994, p. 196). This metacognitive component in the latter model is presumed to develop as a child practices a basic…

The texts gathered in this document come from work done in the framework of two postgraduate courses at the Faculte des Sciences de l'Education, Geneva: (1) "Learning: Meta-cognitive et socio-cognitive dimensions" course; and (2) "Didactical analysis of the interactions in class: Case study of mathematics at school" course. The problematics dealt…

Explores developing a concept image of functions. Includes assessment items, describes students' responses to these items, and interprets those responses. (KHR)

Presents an approach to quadratic functions that draws upon knowledge of linear functions by looking at the product of two linear functions. Then considers the quadratic function as the sum of three monomials. Potential advantages of each approach are discussed. (Contains 17 references.) (MDH)