I report on the findings from research and literature on (a) use of symbols in mathematics, (b) algebraic/trigonometric expressions, (c) solving equations, and (d) functions and calculus. From these, some insights and implications for teaching and learning are derived.

Purpose: The purpose of this paper is to present a discussion of one element of a principal preparation graduate program that uses visualization as a technique to practice decision making. Design/methodology/approach: The author analyzed information collected from participants who created personal case studies using a visualization technique. Data…

When response activities and comprehension strategies are combined, classroom instruction can enhance student engagement and understanding of a text, enrich student response, and improve students' awareness of their own strategic reading. This article presents some activities, adapted from the new IRA book "Children's Literature in the Reading…

Visualization through the use of physical objects is an important method that instructors can use to convey and solidify an understanding of economic principles in their novice students of economics. This paper outlines three simple examples which have been successful in the classroom, each taking a question that students frequently ask--why we…

As a result of attending a course on moving images, the authors consider the balance between visualising and verbalising geometry. In thinking about the balance between visualising and verbalising (and verbal reasoning), the authors began to appreciate more than before that geometric visualisation is greatly aided by what they know--if everyone…

Sex differences in spatial ability are well documented, but poorly understood. In order to see whether working memory is an important factor in these differences, 50 males and 50 females performed tests of three-dimensional mental rotation and spatial visualization, along with tests of spatial and verbal working memory. Substantial differences…

Best-selling author Marcia L. Tate brings her trademark "dendrite-growing" teaching strategies to this practitioner-friendly collection of brain-compatible methods for engaging K-12 students in social studies. Included are 20 proven strategies and more than 200 grade-leveled activities for applying them. Teachers will find concrete ways to…

The paper describes how to conduct guided imagery workshops using slides of paintings, modeling clay, and music in counseling gifted, talented, and creative individuals. (Author/SB)

Describes the contributions of Charles Joseph Minard to statistical graphics, noting the time course of his work and providing background on his famous effort, the flow-map depiction of Napoleon's march on Moscow. Explores some modern re-visions of this famous graphic from an information visualization perspective. (SLD)

Discusses Noetica, a tool that uses a semantic network for structuring knowledge about concepts and the relationships between them. It differs from typical information systems in that the knowledge it represents is abstract, highly connected, and includes metaknowledge. Class hierarchy, visualization, and query tools are also discussed.…

Considers how ideas from document clustering can be used to improve retrieval accuracy of ranked lists in interactive systems and how to evaluate system effectiveness. Describes a TREC (Text Retrieval Conference) study that constructed and evaluated systems that present the user with ranked lists and a visualization of inter-document similarities.…

This article, a play designed around an imaginary conversation between geometric objects, summarizes various approaches to visualizing a tesseract (a.k.a. hypercube--a four-dimensional analog of a cube).

Chemists have used computational science methodologies for a number of decades and their utility continues to be unabated. For this reason we developed an advanced lab in computational chemistry in which students gain understanding of general strengths and weaknesses of computation-based chemistry by working through a specific research problem.…

Virtual Globe software has become extremely popular both inside and outside of educational settings. This software allows users to explore the Earth in three dimensions while streaming satellite imagery, elevation, and other data from the Internet. Virtual Globes, such as Google Earth, NASA World Wind, and ESRI's ArcGIS Explorer can be effectively…