This study examined an International Baccalaureate school that has been able to perform at a high level on state accountability measures while integrating 21st Century skills into the curriculum through a clearly defined organizational model. This study was designed to examine the manner and extent to which an International Baccalaureate School…

Many types of visual representations are used in math textbooks but not all of them contain mathematically relevant information. Little research directly addresses the effects of different types of representations on mathematics performance. Theories offer differing perspectives about how visual representations such as illustrations influence…

Gestures are profoundly integrated into our communication. This study focuses on the impact that gestures have in a mathematical setting, specifically in an undergraduate calculus workshop. There was strong correlation between diagramming and the two types of gestures identified in this study (i.e., dynamic and static gestures). Dynamic and static…

The purpose of this study is to assess students' conceptual learning of electricity and magnetism and examine how these conceptions, beliefs about physics, and quantitative problem-solving skills would change after peer instruction (PI). The Conceptual Survey of Electricity and Magnetism (CSEM), Colorado Learning Attitudes about Science Survey…

It has been well-documented that many students do not understand the meaning of the equal sign. Thus, researchers have called for instruction that specifically addresses misconceptions about the equal sign, and have indicated that such work must start at the elementary level. In response to these recommendations, some state curriculums require…

There are a variety of technologies that are increasingly being integrated into mathematics classrooms for their potential to increase student engagement, motivation, understanding, and achievement. YouTube can be an especially useful technology for students to create, share and interact with others, and learn more about mathematics. However, the…

This article discusses an instructional strategy which explores eventual similarities and/or analogies between familiar problems and more sophisticated systems. In this context, the Atwood's machine problem is used to introduce students to more complex problems involving ropes and chains. The methodology proposed helps students to develop the…

"Self-diagnosis tasks" are aimed at fostering diagnostic behavior by explicitly requiring students to present diagnosis as part of the activity of reviewing their problem solutions. Recitation groups in an introductory physics class of about 200 college students were distributed into a control group and three intervention groups in which different…

"Self-diagnosis tasks" aim at fostering students' learning in an examination context by requiring students to present diagnoses of their solutions to quiz problems. We examined the relationship between students' learning from self-diagnosis and the typicality of the problem situation. Four recitation groups in an introductory physics class…

In two experiments, participants studied two types of word lists. Direct lists were taken from the Deese-Roediger-McDermott (DRM) paradigm (e.g., "water", "bridge", "run") and contained words directly related to a nonpresented critical item (CI; e.g., "river", Roediger & McDermott, 1995). Mediated lists (e.g., "faucet", "London", "jog") contained…

The problem of communication between observers in the vicinity of a black hole in a Schwarzschild metric is considered. The classic example of an infalling observer Alice and a static distant mother station (MS) is extended to include a second infalling observer Bob, who follows Alice in falling towards the event horizon. Kruskal coordinates are…

The Solution Circle (SC) approach is a flexible tool which encourages participants to maintain a positive, creative approach to problem-solving. This project focussed on the introduction of this approach to staff in a primary and a secondary school. The rationale was to implement a problem-solving/discussion tool that would allow staff to utilise…

Purpose: The purpose of this paper is to develop a conceptual model that uses dialectical inquiry (DI) to create cognitive conflict in strategic decision-makers for the purpose of improving strategic decisions. Activation of the dialectical learning process using DI requires strategic decision-makers to integrate conflicting information causing…

In a companion study, eye-movement analyses in the Tower of London task (TOL) revealed independent indicators of functionally separable cognitive processes during problem solving, with processes of building up an internal representation of the problem preceding actual planning processes. These results imply that processes of internalization and…

The ability to represent numerical quantities in symbolic form is a necessary foundation for mathematical competence. Variables are particularly important symbolic representations for learning algebra and succeeding in higher mathematics, but the mechanisms of how students link a variable to what it represents are not well understood. Research…