Computational thinking is the capacity of undertaking a problem-solving process in various disciplines (including STEM, i.e. science, technology, engineering and mathematics) using distinctive techniques that are typical of computer science. It is nowadays considered a fundamental skill for students and citizens, that has the potential to affect…

In these times, described as an ´post-truth´ era where we are faced with information overload, it is a challenge to help students find relevant information, support their knowledge building and engage them in thinking critically about information and knowledge from different perspectives. This study investigates how a visual analytics interface…

We report our qualitative study of twenty-four students enrolled in the second-semester of a second-year undergraduate (sophomore-level) organic chemistry course, Organic Two. We asked the research participants to propose the product and electron-pushing mechanism of elementary mechanistic steps in the absence and presence of the corresponding…

Building from the evidence-based learning progression in geometric reasoning from the RMFII project, this paper presents data from students' solutions to three problems in geometry and measurement situations to identify key components needed to nurture reasoning. To show emerging analytical reasoning students must coordinate multiple pieces of…

The teaching and learning fractions is one of the most problematic areas in primary school mathematics. A large number of studies have engaged paper-and-pencil test to measure students' instrumental understanding about fractions but few have sought to learn about children's fraction sense. This paper reports a study that investigated fraction…

Proving in school geometry is not just about validating the truth of a claim. In the school setting, the main function of the proof is to convince someone that a claim is true by providing an explanation. Students consider proving to be difficult; in fact, they find the very concept of proof demanding. Proving a claim in planar geometry involves…

Submicrorepresentations (SMRs) are a powerful tool for identifying misconceptions of chemical concepts and for generating proper mental models of chemical phenomena in students' long-term memory during chemical education. The main purpose of the study was to determine which independent variables (gender, formal reasoning abilities, visualization…

Presents problems designed to focus student attention on the visual representations that accompany the verbal statements of problem situations involving motion over a period of time. Shows that as a result of engaging in these activities, students gain a better understanding of a given problem situation before they apply procedures to answer…

Presents a problem of tetras made with four cubes, mathematical ideas involved in this problem, and guiding questions for teachers. (KHR)

Protocols of people attempting to solve syllogistic problems and explaining how they reached their conclusions were examined. Two main groups of subjects were identified. One group represented the relationship between classes in a spatial manner supplemented by verbal representation. The other group used a primarily verbal representation. A…

Two types of instruction were emphasized in the solution of insight problems. One study directed subjects to reformulate their initial view of the problem to avoid unnecessary assumptions about it; another required visualization of problem components. Results indicated that reformulation instructions contributed to performance, but visualization…

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…

This paper presents a historical overview of visualization as a human problem-solving tool. Visualization strategies, such as mental imagery, pervade historical accounts of scientific discovery and invention. A selected number of historical examples are presented and discussed on a wide range of topics such as physics, aviation, and the science of…

Investigates gender differences and the role of spatial visualization in problem solving in high school geometry. Reports that, whereas males and females differed in spatial visualization and in their performance, they did not differ in logical reasoning ability or in their use of geometric problem-solving strategies. (Author)

The purpose of this report is twofold. The first is to deliver an accurate portrayal of students' achievement in geometry and measurement as gleaned from the results of the 1986 Massachusetts Educational Assessment Program (MEAP). The second is to provide K-12 teachers of mathematics with activities that have proven to be helpful in encouraging…