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…

This article describes the release of the second edition of "The National Atlas of Korea" (Choe 2015), published in December 2014 by the National Geographic Information Institute (NGII) of South Korea (the Republic of Korea) in both Korean- and English-language versions. This second edition is a major update and improvement over its 2009…

An extraordinary variety of experimental (e.g., flicker, magnetic fields) and clinical (epilepsy, migraine) conditions give rise to a surprisingly common set of elementary hallucinations, including spots, geometric patterns, and jagged lines, some of which also have color, depth, motion, and texture. Many of these simple hallucinations fall into a…

Most teachers feel confident espousing the benefits of using picture books in English lessons, talking about the importance of using the illustrations to enhance the text, engaging students and fostering a love and appreciation of literature. How many teachers passionately advocate the use of these same picture books in mathematics lessons? This…

The National Board for Professional Teaching Standards (NBPTS) proposition 3 states "teachers are responsible for managing and monitoring student learning." They know how "...to organize instruction to meet instructional goals." This article provides 14 organizational patterns for use in organizing instruction in any of the content areas. The 14…

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…

The use of geographic information systems (GIS) in the classroom provides a robust and effective method of teaching the primary spatial skills of identification, description, and explanation of spatial pattern. A major handicap for the development of GIS-based learning experiences, especially for non-GIS specialist educators, is the availability…