Pattern generalisation has become an important feature of mathematics classrooms around the globe. Sometimes these activities focus purely on given numerical terms, but the use of pictorial or figural patterns is now becoming part of the standard repertoire for such generalisation exercises. From a pedagogic point of view, the investigation of…

Mathematics is rich in visual representations. Such visual representations are the means by which mathematical patterns "are recorded and analyzed." With respect to "vocabulary" and "symbols," numerous educators have focused on issues inherent in the language of mathematics that influence students' success with mathematics communication.…

Most future teachers are familiar with number patterns that represent an arithmetic sequence, and most are able to determine the general representation of the "n"th number in the pattern. However, when they are given a visual representation instead of the numbers in the pattern, it is not always easy for them to make the connection between the…

Patterning is an essential skill in early mathematics learning, particularly in the development of spatial awareness, sequencing and ordering, comparison, and classification. This includes the ability to identify and describe attributes of objects and similarities and differences between them. Patterning is also integral to the development of…

This report is the first in a two-part series introducing an interactive activation model of context effects in perception. A model for the perception of letters in words and other contexts is described and applied to a number of experiments. It is proposed that the model accounts for (1) the perceptual advantage for letters in words compared to…

This report is the second in a two-part series introducing an interactive activation model of context effects in perception. In the first part, a model for the perception of letters in words and other contexts was described and applied to a number of experiments. This second part applies the same model to a number of new experiments designed to…