In this article, the authors would like to look at a range of solutions submitted by Year 4-5 teams in the 2003 "Naturally Mathematical Challenge" to a question that involves no more than the numbers 1 to 6 and possible arrangements of them. In the context of other competition questions and in their elaboration of mathematical process,…

This study investigated how tacit knowledge was used by expert and novice principals during problem-solving situations. Through the use of a phenomenological, qualitative approach, novice principals were compared with expert principals as both went about their daily tasks of school leadership. Results of the study contribute to the research on…

This article discusses an approach designed for mathematics educators. Maria Montessori intended this knowledge to be shared with other teachers, increasing the Montessori community's understanding of children's thinking. A group of Montessorians has even tried to formalize this process with a program called Teachers' Research Network. Similarly,…

My fellow teachers and I took a look at the use of tape and scissors in our 3-6 classroom. We had noticed children's over-reliance on these tools and wondered what would happen if we simply removed them. We decided to initiate a classroom research project in which the students worked for a while without scissors or tape. One goal of the project…

This research focuses on eliciting bilingual students' problem-solving reasoning by providing mathematical tasks designed to involve the students in the action described in the problem by making connections to contexts familiar to them. Results showed these tasks allowed children to articulate their mathematical reasoning through gestures and…

Many researchers have described cognitive differences between gifted and average-performing children. Regarding strategy use, the gifted advantage is often associated with differences such as greater knowledge of strategies, quicker problem solving, and the ability to use strategies more appropriately. The current study used microgenetic methods…

The contradiction between equity and efficiency is an important issue common to the development of higher education worldwide as well as a problem that many thinkers, politicians, pedagogues, sociologists, and economists, both past and present and in China and abroad attempted to solve. There is an abundance of expositions on equity and efficiency…

This pilot study investigated the capacity of eye-gaze tracking to identify differences in problem-solving behaviours within a group of individuals who possessed varying degrees of knowledge and expertise in three disciplines of science (biology, chemistry and physics). The six participants, all pre-service science teachers, completed an 18-item…

This paper presents affect as an essential aspect of students' self-reflection and self-regulation. The introduced concepts of self-system and self-system process stress the importance of self-appraisals of personal competence and agency in affective responses and self-regulation in problem solving. Students are viewed as agents who constantly…

A socio-constructivist account of learning and emotions stresses the situatedness of every learning activity and points to the close interactions between cognitive, conative and affective factors in students' learning and problem solving. Emotions are perceived as being constituted by the dynamic interplay of cognitive, physiological, and…

This study describes and contrasts theoretically and empirically problem solving of situated problems in school and the real world at the macro level as a social-cultural activity system and analyzes the process of solving situated problems by high school students at the micro level as an activity. Three potentially experiential problem tasks were…

Reform in geography education, as reflected in "Geography for Life: National Geography Standards" (1994) for the U.S.A., favors a constructivist approach to learning. This study examines the acceptance of this approach among students in two upper secondary schools in China. A lesson was developed to illustrate interactive problem solving…

Quilts are an integral part of the North American culture. Most households in North America have quilts with intricate geometric patterns. These patterns symbolize different things to different groups of people in this part of the world. It is important for students to see how mathematics comes from what is done in day-to-day life, not from the…

This article describes the Mathematics Investigation Center (MIC), a tool to help elementary teachers differentiate the curriculum for their gifted mathematics students. Using the same mathematical theme that the rest of the class is studying, the activities provide depth for the gifted students by shifting from a computation level to a problem…

Undergraduate biology programs are currently undergoing reform to involve students in biomedical research. Engaging students in more active, hands-on experiments allows students to discover scientific principles for themselves, and to develop techniques of critical thinking and problem solving. This models the world of real scientific research,…