During the last decades of the twentieth century, changes in school curricula have resulted in proof-free or proof-lite curricula. In this article, the author argues that proof is, and should be seen to be, a central component in the school curriculum--from at least the middle of the primary years and upwards. He identifies proof with problem…

This paper examines the way two 10th graders cope with a non-standard generalisation problem that involves elementary concepts of number theory (more specifically linear Diophantine equations) in the geometrical context of a rectangle's area. Emphasis is given on how the students' past experience of problem solving (expressed through interplay…

For the last five years, the Higgins School of Humanities has worked to develop a culture of dialogue at Clark University through its Difficult Dialogues Initiative. People know that genuine communication, creative collaboration, and effective problem solving are necessary to address the challenges they face as a nation and world; a renewed…

A major goal of education is to help learners store information in long-term memory and use that information on later occasions to effectively solve problems (Vockell 2010). Therefore, this author began to use the Rubik's cube to help students learn to problem solve. There is something special about this colorful three-dimensional puzzle that…

There are few conversations about teaching these days that do not include talk about teacher quality. Yet, within the conversations about improving teacher quality, the dialogue is often political--consumed with one-dimensional solutions for improving teacher quality, such as linking teacher pay to student performance. Absent from the pervasive…

A station-based laboratory practical exam for first-year high school chemistry students is described. Students move individually through six stations meant to authentically assess both basic lab skills and problem-solving skills utilized throughout the year. The exam can be completed in an approximately 85 min lab period and can be easily adapted…

Research (Fish, 2004) suggests that everybody should be taught how to freehand sketch and utilise it as a tool for supporting the visualising instinct. A fundamental shift in philosophy of the technology education system in Ireland towards design driven subjects brought with it a need to develop practising teacher's technological capabilities.…

This article distills a discussion about the goals, mechanisms, and effects of three environments which aim to support the acquisition and development of computing concepts (problem solving and programming) in pre-University and non-technical students: Alice, Greenfoot, and Scratch. The conversation started in a special session on the topic at the…

Complex dynamic control (CDC) tasks are a type of problem-solving environment used for examining many cognitive activities (e.g., attention, control, decision making, hypothesis testing, implicit learning, memory, monitoring, planning, and problem solving). Because of their popularity, there have been many findings from diverse domains of research…

As part of an integrative learning experience at the end of a sophomore Calculus II course at the United States Military Academy, this project served as a multidisciplinary problem-solving exercise that explored the connections among mathematics, biology, and other fields of study. During a seven-lesson block of instruction, this module was…

A survey of business people, Victoria University business studies alumni and business academics revealed a strong preference for curricula, learning activities and assessments that develop professional skills and personal attributes, adding value to the student learning experience and developing graduate capabilities beyond discipline and…

Case studies pertaining to the health benefits of foods can be particularly effective in engaging students and in teaching core concepts in science (Heidemann and Urquart 2005). This case study focuses on the chemistry of curcumin, the health-promoting ingredient in turmeric. The case was developed to review core concepts in organic chemistry and…

We propose to mine temporal patterns in Intelligent Tutoring Systems (ITSs) to uncover useful knowledge that can enhance their ability to provide assistance. To discover patterns, we suggest using a custom, sequential pattern-mining algorithm. Two ways of applying the algorithm to enhance an ITS's capabilities are addressed. The first is to…

In this study, the researchers examined the relationship between residential treatment staff members' use of cognitive and behavioral disputations and problem-solving skills just prior to discharge for 59 youths with emotional and behavioral disorders. The researchers also assessed the direct and indirect effects of engagement in treatment on…

For more than one hundred years teachers have paddled beside the great ocean of mathematical adventure. Between them they have taught millions of young people. A few have dived in and kept swimming, some have lingered on the shore playing in pools, but most have dipped their toes in and run like heck in the other direction never to return. There…