Critical to constructing and interpreting graphs is an individual's understanding of the underlying coordinate systems, yet coordinate systems are often overlooked or taken-for-granted in both mathematics education research and curricula. In this paper, we foreground coordinate systems and present a distinction between two uses of coordinate…

Linear algebra students are typically introduced to the problem of how to convert from one coordinate system to another in a very abstract way. Often, two bases for a given vector space are provided, and students are taught how to determine a transition matrix to be used for changing coordinates. If students are successful in memorizing this…

Using an interactive map-based PDF, students learn key concepts related to biodiversity while developing data-analysis and critical-thinking skills. The Bird Island lesson provides students with experience in translating geospatial data into bar graphs, then interpreting these graphs to compare biodiversity across ecoregions on a fictional island.…

One measure of the impact of a new idea in geography education is how well it is incorporated into teachers' everyday practice. "Spatial thinking" is not really a new idea in geography education; spatial analysis has long been one of its core traditions, but the use of the term is novel and only beginning to be widely used. By spatial thinking the…

In this article, the authors present a laboratory exercise in data collection and statistical analysis in biological space using clustered stomates on leaves of "Begonia" plants. The exercise can be done in middle school classes by students making their own slides and seeing imprints of cells, or at the high school level through collecting data of…

Static, animated, and interactive visualizations are frequently used in electronic learning environments. In this article, we provide a brief review of research on visuospatial cognition relevant to designing e-learning tools that use these displays. In the first section, we discuss the possible cognitive benefits of visualizations consider used…

Presents a distance and time map exercise designed as a crime scenario. Explains that students must determine whether one individual could have committed a series of crimes in a given time period. Includes graph production that gives practice in interpreting and expressing aspects of spatial information. (DK)

This report is part of a long-term research on the construction of mathematical meanings through the interaction with various technologies. The research involved a set of teaching experiments based on body motion with sensors and calculators at different school levels, from kindergarten to secondary school. Here I refer to the one developed in a…

Integrating mathematics with family and consumer sciences (FCS) has enabled youth to pass the Minnesota 8th Grade Math Basic Skills test. The test focuses on the eight content areas: (1) problem solving with whole numbers and fractions; (2) problem solving with percentage/ratio; (3) number sense; (4) estimation; 5) measurement; (6) tables and…