This article centers on studying the progress of algebraic syntax once students have surmounted initial obstacles found in the transition toward symbolic algebra. It specifically analyzes students' progress concerning the operation on the unknown, when the latter is represented by an expression that involves a 2nd unknown. In curricular terms,…

The purpose of this research is to describe and understand the ways in which deaf middle school students understood and solved compare word problems, and to examine their overall strategy use in learning mathematics. The participants in the study were deaf middle school students, attending a residential state school for the deaf. Most of them used…

The purpose of this paper is to offer a framework for categorizing and describing the different types of processes that undergraduates use to construct proofs. Based on 176 observations of undergraduates constructing proofs collected over several studies, I describe three qualitatively different ways that undergraduates use to construct proofs. In…

This paper outlines the syntactic structures which represent a stage in the cognitive development of children, and focusses on an aspect of cognitive development known as conservation. The cognitive components of conservation are presented as the primordial base for the set of syntactic structures which map or mirror them. Piaget proposed four…

Three experiments with small samples of elementary school students were conducted to: (1) investigate the impact of syntactic complexity on analytic assistance; (2) extend the research on analytic assistance to younger subjects; and (3) determine the relative importance of analytic assistance when compared to an example-only comparison group.…

Theoretical tools from cognitive science were used to put together a framework for a fine-grained theory of how students learn elementary algebra in the classroom. Developing the framework included assessing the shortcomings of current models, evaluating whether unified theories of cognition can be adapted for learning mathematics in the…