That mathematics education has been one of the central concerns of educational systems worldwide is no secret. It is also an established consensus that as far back as eighty years ago, Russian psychologists such as Vygotsky, Luria, Meshcheryakov, and Davydov have pioneered work that contributed to the understanding of teaching and learning and…

This research focused on performance indicators for elementary and middle school students. Performance indicators are factors that could hinder or enhance early childhood education. For instance, poverty affects a child's development and educational outcomes beginning in the formative years, both directly and indirectly through mediated,…

After the onset of formal schooling, little is known about the development of children's understanding of the arithmetic concepts of inversion and associativity. On problems of the form a+b-b (e.g., 3+26-26), if children understand the inversion concept (i.e., that addition and subtraction are inverse operations), then no calculations are needed…

To investigate the development of function concepts and their relation to mathematical and logical abilities typically acquired during the age period of five to seven years, children were tested on nonnumerical function tasks, numerical tasks, and aspects of logical reasoning. (PCB)

A teaching experiment involving 30 third graders investigated the transformation of their concepts of numbers. Observations of their notations and problem-solving procedures show development that progresses from a focus on states to a type of reasoning in which changes become quantifiable "objects of awareness." (SLD)

A sequence of problem solving tasks of classification of geometric forms and biological organisms based on Piaget's theory of learning were developed and tested with elementary school children. One experiment involved third grade subjects with one treatment group directed to learn both simple and hierarchical operations, a second group directed to…

A study of interactions among Swedish intermediate-grade students as they solved a nonstandard mathematics task confronting the phenomenon of infinity shows that the children can reach a considerable understanding of the problem by contextualizing the problem in different ways. The collective orchestration of problem variations results in enhanced…

A new approach to teaching and curriculum takes seriously the knowledge children have when they enter school. Teachers use the knowledge each child has to make instructional decisions so that the child learns mathematics with understanding, how to solve problems, and the computational skills. Research concerning the problem-solving strategies…