This paper reports on students' understanding of sugar concentration in aqueous solutions presented in two different modes: a visual submicroscopic mode for particles and a verbal mode referring to macroscopic amounts of sugar. One hundred and forty-five tertiary college students studying some form of first-year chemistry participated in the…

All children are born with the gifts of curiosity and creativity--and an insatiable appetite for asking questions to find out about the world in which they live. Fostering these questions and developing inquisitive and investigating minds is one of the essential roles of parent and teacher, and the processes of enquiry are the necessary routes for…

This article confronts the issue of why secondary and post-secondary students resist accepting the equality of 0.999... and 1, even after they have seen and understood logical arguments for the equality. In some sense, we might say that the equality holds by definition of 0.999..., but this definition depends upon accepting properties of the real…

In this article, we present an integer sequence approach to solve the classic water jugs problem. The solution steps can be obtained easily by additions and subtractions only, which is suitable for manual calculation or programming by computer. This approach can be introduced to secondary and undergraduate students, and also to teachers and…

A newspaper numbers game based on simple arithmetic relationships is discussed. Its potential to give students of elementary algebra practice in semi-"ad hoc" reasoning and to build general arithmetic reasoning skills is explored. (Contains 3 figures, 7 tables and 3 notes.)

The ability to solve complex scientific problems is regarded as one of the key competencies in science education. Until now, research on problem solving focused on the relationship between analytical and complex problem solving, but rarely took into account the structure of problem-solving processes and metacognitive aspects. This paper,…

Both exploration and explicit instruction are thought to benefit learning in many ways, but much less is known about how the two can be combined. We tested the hypothesis that engaging in exploratory activities prior to receiving explicit instruction better prepares children to learn from the instruction. Children (159 second- to fourth-grade…

This study analyzed a stratified random sample of 1,707 senior students at 60 four-year universities in South Korea to explore the gender-specific pathways to Korean students' development of generic skills--analytical thinking and problem-solving skills. Multiple regression analyses were performed to investigate the involvement factors…

The present randomized controlled trial examined the effectiveness of the parent training program Parents and Children Talking Together (PCTT) for parents with children in the preadolescent period who experience parenting difficulties. The program is focused on reducing child problem behavior by improving parents' communication and problem solving…

Learning through drama and other art forms enriches children's learning by expanding the possibilities for how children create and express meaning (Adomat, 2009; Berghoff, Egawa, & Harste, 2000). The arts are rarely suggested as a way of opening up broader understandings for young readers; yet drama has been shown to be beneficial in myriad ways…

The blue-eyed islanders puzzle is an old and challenging logic puzzle. This is a narrative of an experience introducing a variation of this puzzle on the first day of classes in a liberal arts mathematics course for non-majors. I describe an exercise that was used to facilitate the class's understanding of the puzzle.

There are, it seems, few instances when "unintended consequences" are regarded as having a positive and beneficial effect. Here a well-used activity takes on a "life of its own" as a result of the enthusiasm of the learners. The outcome provides insights for all those involved, including the "teacher". Maybe it is…

"Probability is a difficult concept to teach, because children and adults find it counterintuitive." This is impetus to consider the detailed planning of a set of lessons with a "mixed", in many senses, group of fourth graders. Can the use of prior experience, and the knowledge associated with that experience, make probability a concept that is…

Learners are all different and teachers are all different, so why do we often ignore this reality when trying to explain, or demystify, some aspect of mathematics in the classroom? Enabling learning can be challenging, demanding of creativity, and needy of alternatives if understanding is the real goal. Here the authors offer ideas that are aimed…

In this study, we seek to understand the beliefs that chemistry faculty hold when grading student solutions in problem solving situations. We are particularly interested in examining whether a conflict exists between the chemistry faculty beliefs and the score they assign to students' solutions. The three categorical values identified in a similar…