Within his classroom, the author is often confronted by students who fail to see, or accept, the relevance of mathematics both to their lives and the world around them. One topic which is regularly perceived as being disconnected from people's daily lives is that of circle theorems, especially among less motivated students. In this article, the…

While there is evidence for an association between the development of reading and arithmetic, the precise locus of this relationship remains to be determined. Findings from cognitive neuroscience research that point to shared neural correlates for phonological processing and arithmetic as well as recent behavioral evidence led to the present…

Mentoring is an effective method of helping inexperienced individuals develop and progress in their profession. Extension staff have many opportunities to mentor volunteers and other community partners. The keys to establishing a successful mentoring relationship include creating a relationship of trust, clearly defining roles and…

The problem of youth violence has become a national priority given both the cost and repercussions to youth, to the school systems, and to society. Over the past two decades there has been increasing research examining gender differences in the expression of aggression. This research has suggested that boys typically display their aggression…

Can children genuinely create new knowledge, as opposed to merely carrying out activities that resemble those of mature scientists and innovators? The answer is yes, provided the comparison is not to works of genius but to standards that prevail in ordinary research communities. One important product of knowledge creation is concepts and tools…

This paper reports on the results of an observational parallel study conducted simultaneously at 2 universities--one each in New Zealand and Germany. It deals with university engineering students' difficulties in the formulation step of solving a typical application problem from a first-year calculus course. Two groups of students (54 in New…

When teaching mathematics with technology, the author does so in the belief that technology enables students to experience mathematical ideas in a way that might not otherwise be possible. However, teachers must be careful: Sometimes technology does not produce results in the way that they or their students expect. Rather than allowing unexpected…

The purpose of this study was to determine the perceptions of violence among youths, specifically as it relates to problem solving and conflict resolution or retaliation. I conducted a qualitative study with adolescents from fourteen to nineteen years old who completed age- and sex-based scenarios involving a peer conflict. The results indicate…

This study investigates how the beliefs and values of physics faculty influence their choice of physics problems for their students in an introductory physics course. The study identifies the goals these instructors have for their students, the problem features they believe facilitate those goals, and how those features correspond to problems they…

Individual creativity is ubiquitous. New technologies both enable and urge fresh approaches to creativity in the context of education. University-level education offers a natural place to adjust pedagogical structures in favor of a more individual approach to learning that organizes the intellectual community into new patters of interaction and…

This article examined, through a Cultural Historical Activity Theory lens, how immersive- or pervasive environments and pedagogical agents could more easily support social collaboration as foundation of contemporary learning theory. It is argued that the fundamentalism-liberationism contradiction (learn "from" versus learn "with" technology) is no…

Prior research has shown that tutored problem solving with intelligent software tutors is an effective instructional method, and that worked examples are an effective complement to this kind of tutored problem solving. The work on the expertise reversal effect suggests that it is desirable to tailor the fading of worked examples to individual…

To help fifth- through eighth-grade students develop their deductive reasoning skills, the author used a ten-week supplementary curriculum so that students could answer logic questions. The curriculum, a series of lessons built around language-independent logic puzzles, has been used in classrooms of fifth through eighth grades. In most cases,…

The author introduces the birthday problem in this article. This can amuse willing members of any birthday party. This problem can also be used as the motivational first day lecture in number theory for the gifted students in high schools or in community colleges or in undergraduate classes in colleges.

Minds-on engagement in active learning is explored through the experiences of Margaret Sanders, a general music teacher. Minds-on learners think about their experiences. They are actively involved as questioners and problem solvers while they complete musical tasks and reflect on their work after it is completed. Minds-off learners focus on their…