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…

Investigated the pedagogical quality of physical space by adapting a classroom to create a material "educational field" and testing children's performance on a "go to the front and right of the tower" activity. Found that the educational field made it possible for children to put into relation two spatial reference systems and…

Investigates the convergence of three measures on a representation of cognitive structure and examines the correspondence between these representations and the representation of subject matter structure. (Author/DEP)

The problem of solving mathematical equations can be quite tough for some students hence they face a great difficulty when applying ideas to the actual process. Students in algebra classes are taught coding in which they write down what they will need to do to solve the equation and this coding makes the students more adept at solving equations…

The paper presented relates to a study done examining the ability of children from grades one through six to locate a point in one, two, and three dimensions and to order a temporal series of events in one, two, and three dimensions. The performance of the subjects was also used to examine a small part of Piaget's theory of cognitive development.…

Observed gesture and speech to investigate patterns of change in third and fourth graders' strategies for solving mathematical equivalence problems before and after an intervention. Children who received instruction were more likely to generate new strategies. Gradual change was more common. Abrupt strategy change was more common in children who…

This book represents a compilation of the views and ideas of the late Hans Freudenthal, representing his last major contribution to the field of mathematics education. Rather than a presentation of new views, Freudenthal selected and streamlined old ideas, many gathered from his lectures in China, and formed a review of questions and issues in…

The aim of this paper is to contribute to the understanding of the possible influence of the use in class of Internet resources which offer mathematical exercises for the students' activity and learning processes. I present an exploratory study grounded on a teaching design set up in two French grade six classes about proportional reasoning…

Current knowledge about cognitive development in mathematics is reviewed, specific effective strategies for presenting materials in class are described, and effective strategies for mathematics program content and organization are outlined. Substantial information on recent research and on instructional materials is included. (MSE)

This paper presents a theoretical framework for investigating the role of algorithms in mathematical thinking using a combined ontological-psychological outlook. The intent is to demonstrate that the processes of learning and of problem solving incorporate an elaborate interplay between operational and structural conceptualizations of the same…

The introduction of addition, subtraction, multiplication, and division to children is seen to require a compatible and sequential methodology. The sequence of learning is seen as: (1) physical action; (2) emotional involvement; and (3) conceptual learning. A learning sequence should involve the following steps: (1) connectinq number experience to…

Pragmatic and semantic problem solving are examined as processes that enhance acquisition of mathematical knowledge. It is suggested that development of mathematical cognition involves restructuring and that math teachers can help restructure children's knowledge systems by providing them with situations in which semantic and pragmatic problem…

In an attempt to bridge the perceived distinction between internalized conceptions of mathematics and their external representations, this discussion treats mathematics both as an individual, constructive activity and as a communal, social practice. It is argued that this approach might transcend the tripartite scheme of teacher, student, and…

In a study of mathematics learning, taking a rule-oriented approach, students were taught to trade objects of type A for objects of types B and C. Children ranging from ages 7 to 9 were given rules for converting A to B and B to C and were then presented with the task of converting A to C. Of the 30, 6 succeeded. Of the 24 who failed, half were…

Reports misconceptions identified in students with respect to the topic of parallel lines and the teaching strategies found to be useful in challenging those misconceptions. (11 references) (MDH)