Investigates the thinking process underlying students' improper linear reasoning and how this process is affected by their mathematical conceptions, beliefs, and habits. Explores the actual process of problem solving from students falling into the linearity trap and the mechanism behind it. Discusses specific mathematical conceptions, habits, and…

Analyzes student performance on solution calorimetry problems in an introductory university chemistry class. Includes data from written classroom exams for 207 students and an extensive longitudinal interview with a student. Indicates learning difficulties, most of which appear to originate from failure to understand, that net increases and…

Analyzes the cognitive processes and kinds of knowledge needed to work in a scientific domain like physics. Discusses the processes needed to interpret scientific concepts, uses of quantitative and qualitative descriptions, hierarchical ways of organizing scientific knowledge, and processes facilitating problem solving. Describes the use of these…

Describes the activities of the Physics Teachers Action Research Group in which college physics teachers work together in planning, revising, and evaluating student projects that foster greater conceptual understanding and address student misconceptions. Presents the details of a project in which students were asked to build an accelerometer. (JRH)

America 2000 presents an educational reform agenda that neglects the arts. Prevailing misconceptions of the arts are based on a massive misunderstanding of their role in human development and education. The arts contribute significantly by celebrating the value of multiple perspectives and nuances in problem solving, relating form to content, and…

Discusses a misconception about the cycloid that asserts the final point on the path of shortest time in the "Brachistochrone" problem is at the lowest point on the cycloid. Uses a BASIC program for Newton's method to determine the correct least-time cycloid. (MDH)

Presents a problem in which the incorrect application of the Law of Sines leads to an erroneous solution. Demonstrates that the commission of this error by an ophthalmologist using laser trabeculoplasty could lead to patient injury. (MDH)

Analyzes three widely-held conceptions of critical thinking: as one or more skills, as mental processes, and as sets of procedures. Considers each a misconception and offers alternative proposals for teaching critical thinking. (CMK)

Social studies educators advocate discussion as an influential instructional method to encourage students to apply knowledge and develop higher-order thinking and understanding. The classroom reality, however, is that teachers only use the discussion method sparingly. Instead, teachers predominantly use a quasi-discussion form called recitation to…

The authors investigated whether guidance and reflection would facilitate science learning in an interactive multimedia game. College students learned how to design plants to survive in different weather conditions. In Experiment 1, they learned with an agent that either guided them with corrective and explanatory feedback or corrective feedback…

Background/Context: The theoretical framework of the paper comes from research on problem solving, considered by many to be the essence of mathematics; research on the importance of oral language in learning mathematics; and on the importance of the teacher as the primary instrument of learning mathematics for most students. As a nation, we are…

In this article, the author describes a week of "timely" open-ended lessons with a high ability Y9 group of boys. He gives lessons that would give the students some sense of purpose, as they try to generate a mathematical entity to represent something they used regularly. He states that understanding metric time is something his students…

Traditionally, students learn arithmetic throughout their primary schooling, and this is seen as the ideal preparation for the learning of algebra in the junior secondary school. The four operations are taught and rehearsed in the early years and from this, it is assumed, "children will induce the fundamental structure of arithmetic" (Warren &…

The purpose of this study was to investigate the effects of a problem solving based instructional model on earth science students' achievement and alternative frameworks. Students' opinions toward the instructional method were also investigated. The investigations employed a pretest/posttest control group design to detect any significant change.…

Twelve linear algebra students were interviewed about the concept of a Solution of a System of Equations. The interviews were analyzed using APOS tools, in particular the ideas of Action, Process, Object and Schema, and Genetic Decomposition. The analysis of the interviews revealed several misconceptions of Solution. The analysis also revealed…