Generalizing, conjecturing, representing, justifying, and refuting are integral parts of algebraic thinking and mathematical thinking in general (Lannin et al., 2011). The activity described in this article makes a case for generalizing as an overall mindset for any introductory algebra or geometry class by illustrating how generalization problems…

Recent educational research has turned increasing attention to the structural development of young students' mathematical thinking. Early algebra, multiplicative reasoning, and spatial structuring are three areas central to this research. There is increasing evidence that an awareness of mathematical structure is crucial to mathematical competence…

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…

Some activities are provided to help students develop a conceptual understanding of perimeter, area, and volume, as well as developing skills in spatial visualization and formulating generalizations. (MNS)

Presents a methodology designed to strengthen the cognitive effects of using graphing calculators to solve polynomial equations using pattern matching, searching, and heuristics. Discusses pattern matching as a problem-solving strategy useful in the physical, social, political, and economic worlds of today's students. (DDR)

This document contains the second volume of the proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education. Conference papers are centered around the theme of "Learners and Learning Environments." This volume features 43 research reports by presenters with last names beginning between Adl…