In this pedagogical action research study, we, as post-secondary mathematics teacher educators, built on an existing effort to improve pre-service teachers' mathematical vocabulary understandings by intentionally addressing their struggles related to polygonal area formulas. Utilizing cognitive load theory and Bruner's levels of developmental…

The paper focuses on students' understanding of the concepts of axial and central symmetries in a plane. Attention is paid to whether students of various ages identify a non-model of an axially symmetrical figure, know that a line segment has two axes of symmetry and a circle has an infinite number of symmetry axes, and are able to construct an…

Research on naive physics and naive optics have shown that people hold surprising beliefs about everyday phenomena that are in contrast with what they see. In this article, we investigated what adults expect to be the field of view of a mirror from various viewpoints. The studies presented here confirm that humans have difficulty dealing with the…

In the field of human cognition, language plays a special role that is connected directly to thinking and mental development (e.g., Vygotsky, "1938"). Thanks to "verbal thought", language allows humans to go beyond the limits of immediately perceived information, to form concepts and solve complex problems (Luria, "1975"). So, it appears language…

Presents a framework for differentiating between five levels of extension of knowledge: basic features, forms, rules, application, and elaboration. Comparison of the extent of knowledge use exhibited by (n=14) Year-11 Australian students on a range of plane geometry problems found that high-achieving students exhibited greater extension of…

Contains an analysis of the activities of 12-year-old students solving problems of polygonal tilings and presents two categories of the thinking processes of these students: instantaneous thinking resulting in perceptions of simple structures and discursive thinking appearing in drawing activities and arguments of proofs. (13 references)…

This article describes how children build increasingly abstract knowledge of linear measurement, emphasizing ways they relate space and number. Assessments indicate children struggle to understand measurement, especially concepts related to complex paths as in perimeter tasks. This article draws on developmental accounts of children's knowledge of…

Geometry is a fundamental part of the mathematics foundation provided by elementary education. Children have an intuitive understanding of geometry that they draw on when dealing with geometric concepts in activities like drawing, playing hopscotch, defending their "half of the room," and playing sports. This book offers no instruction…