The purpose of the study is to enumerate the representations in high school geometry, to narrow the focus to the most common ones, and to describe how the common representations are coordinated. To achieve this purpose, I analyzed several sections of a popular geometry textbook using thematic analysis, semiotics, and a pragmatic approach to…

In this paper, the authors present results of their pilot research on nonverbal elements' perception. They pay attention to a not yet well established system of evaluation in mathematics textbooks from the perspective of nonverbal elements and sum up their findings from pilot researches on pupils' operations with nonverbal elements. Pilot surveys…

Presents activities where students visualize three dimensional figures, construct tables, discover patterns in the tables, and use the patterns to make predictions. (PK)

A four-year longitudinal study of concept attainment and uses of concepts, as specified by the Conceptual Learning and Development Model, is described. Data collected during the first two years were based upon the assessment of the concept, equilateral triangle. The assessment battery was administered to 351 children (grades K, 3, 6, and 9) in…

A total of 100 3- and 5-year-old children were trained and assessed individually on the concept of equilateral triangle at three levels of attainment: concrete, identity, and classificatory. Five training conditions existed: (1) visual inspection; (2) visual inspection and verbal orienting instruction; (3) visual inspection, free haptic activity,…