A pivotal information about the structure of students' comprehension underlying from which the knowledge is gained can be identified through the mental model. This study aimed at describing the six levels of students' mental model in comprehending the concept of the integer. The subject of this research was 40 students consisting of 20 students…

Based on a two-tiered epistemological model (preliminary physical concepts and emerging mathematical concepts), studied the construction of number among 91 kindergarten students in France, Canada, and the United States. Subjects' cognitive numerical structures were surprisingly similar despite differences in language and culture. (SV)

Validates a framework for assessing children's thinking in multidigit number situations and uses the framework to evaluate instructional programs. Key constructs--counting, partitioning, grouping, and number relationships--appear stable within each of 5 levels across 12 case studies, suggesting a possible hierarchy of thinking. (DF)

Proposes a framework that identifies the components of number sense and the attributes of students who possess it. Discusses various aspects of three areas where number sense plays a key role: number concepts, operations with numbers, and applications of number and operation. (MDH)