In this article Kay Owens explains how a real-world context can be used to encourage student noticing and deeper analysis of geometric structures when students are asked to draw what they saw. Kay presents examples of students' drawings made during a school trip to the zoo which followed a series of inquiry learning experiences in geometry.

Middle school students need opportunities to craft informal mathematical arguments beyond justification of steps in an algorithm. Pentominoes provide an excellent vehicle for such activity. In this article, the authors describe an exploration with pentominoes that engaged a group of ninth-grade students in proportional reasoning, dilation, and…

Spatial reasoning, which involves "building and manipulating mental representations of two-and three-dimensional objects and perceiving an object from different perspectives" is a critical aspect of geometric thinking and reasoning. Through building, drawing, and analyzing two-and three-dimensional shapes, students develop a foundation…

A Chemistry Concept Reasoning Test was created and validated providing an easy-to-use tool for measuring conceptual understanding and critical scientific thinking of general chemistry models and theories. The test is designed to measure concept understanding comparable to that found in free-response questions requiring explanations over…

Students have difficulties in physics because of the abstract nature of concepts and principles. One of the effective methods for overcoming students' difficulties is the use of analogies to visualize abstract concepts to promote conceptual understanding. According to Iding, analogies are consistent with the tenets of constructivist learning…

While exploring the subject of geometric proofs, boolean logic operators AND and OR can be used to allow students to visualize their true-or-false patterns. An activity in the form of constructing electrical circuits is illustrated to explain the concept.

This article describes a process for increasing the quality of students' thinking through alternating from a quiet intuitive state to rational logical processing. The article provides specific teaching suggestions using guided imagery for students in grades K-2, grades 3-4, and grades 5 through college. (DB)

We have concluded that teaching undergraduate students to use spreadsheet software to analyze, interpret, and communicate spreadsheet data through a graph is an information technology exercise in whole brain thinking. In investigating why our students have difficulty constructing proper graphs, we have discovered that graphing requires two…

A program for teaching children and adults the thinking skills most important in everyday life is described. This program, which has been tried out and evaluated in the United States, France, Germany, England, Australia, Japan, and Israel, is needed in every school and community as a "gymnasium for the mind," to help people fully use their natural…