More is known now than ever about the range and nature of alternate conceptions that children hold, but educators are not yet sure of the best way to support effective development of children's scientific understanding. The coherence of science as perceived by the student matters in learning. That is, what the child brings to a learning task can…

An industrial-type distillation column, including appropriate pumps, heat exchangers, and automation, was used as a unit operations experiment to provide a link between classroom teaching and real-world applications. Students were presented with an open-ended experiment where they defined the testing parameters to solve a generalized problem. The…

The skills of communication, critical thinking, and problem solving are essential to thriving as a citizen in the 21st century. These skills are required in order to contribute as a member of society, operate effectively in post-secondary institutions, and be competitive in the global market. Unfortunately they are not always intuitive or simple…

Researchers have documented difficulties that elementary school students have in understanding volume. Despite its importance in higher mathematics, we know little about college students' understanding of volume. This study investigated calculus students' understanding of volume. Clinical interview transcripts and written responses to volume…

This article responds to Henry Tam's article in this issue of FORUM by exploring opportunities for co-operative problem-solving for staff and students of the Royal Docks Community School in the London Borough of Newham. Becoming a co-operative trust helped the school move out of special measures and develop a strategy of participation and…

The notion of temporal range is introduced and discussed in this paper. Two dimensions of temporal range are identified: mathematical temporality relating to mathematical ideas, their precursors and horizons; and a mathematical learning temporality where what students say/do provides the ground on which future learning can be built. These…

In this article, we share our learning experience as a Lesson Study team. The Research Lesson was on Figural Patterns taught in Year 7. In addition to helping students learn the skills of the topic, we wanted them to develop a problem-solving disposition. The management of these two objectives was a challenge to us. From the lesson observation and…

This paper demonstrates, following Vygotsky, that language and tool use has a critical role in the collaborative problem-solving behaviour of school-age children. It reports original ethnographic classroom research examining the convergence of speech and practical activity in children's collaborative problem solving with robotics programming…

I discuss a pedagogical strategy in which we ask students to write about science. Such writing is to be done regularly and often, in class and out of class, in the format of brief "letters to a friend" and longer essays. The goal of this technique is not to teach students how to write; it is to use their writing to help them learn the science.…

Knowledge sharing and transfer are essential for learning in groups, especially when group members have different disciplinary expertise and collaborate online. Computer-Supported Collaborative Learning (CSCL) environments have been designed to facilitate transactive knowledge sharing and transfer in collaborative problem-solving settings. This…

There are at least five different equivalent definitions of the absolute value concept. In instances where the task is an equation or inequality with only one or two absolute value expressions, it is a worthy educational experience for learners to solve the task using each one of the definitions. On the other hand, if more than two absolute value…

Means-end actions are an early-emerging form of problem solving. These actions require initiating initial behaviors with a goal in mind. In this study, we explored the origins of 8-month-old infants' means-end action production using a cloth-pulling training paradigm. We examined whether highlighting the goal (toy) or the means (cloth) was more…

The focus of the article is the validation of an instrument to assess gifted students' affect after mathematical problem solving tasks. Participants were 225 students identified by their district as gifted in grades four to six. The Chamberlin Affective Instrument for Mathematical Problem Solving was used to assess feelings, emotions, and…

This paper explores the relation between problem solving learning environments (PSLEs) and assessment concepts. The general framework of evidence-centered assessment design is used to describe PSLEs in terms of assessment concepts, and to identify similarities between the process of assessment design and of PSLE design. We use a recently developed…

Intellectual engagement is an absorbing, creatively energized focus resulting in a deep personal commitment to exploration, investigation, problem-solving and inquiry over a sustained period of time. In this article, the authors argue that participatory learning environments with a focus on knowledge building offer clear learning benefits to…