This article describes how teachers address issues and tensions that students meet in learning division of fractions. First, students must make sense of division of fractions on their own by working individually and in small groups, using concrete or pictorial representations, inventing their own processes, and presenting and justifying their…

This study concerns pupils' experience of unit and non-unit fractions of a discrete quantity during specially designed lessons. The aim was to explore pupils' understanding of operations such as "b/c of a" in lessons where the teachers were aware of some pupils' difficulties beforehand and what needed special attention.…

This research explores the emergence of student creativity in classroom settings, specifically within two content areas: science and social studies. Fourteen classrooms in three elementary schools in Korea were observed, and the teachers and students were interviewed. The three types of student creativity emerging in the teaching and learning…

This study aims at knowing how students experience wikis while they are involved in a problem solving science activity. The study took place in a physics and chemistry 8th grade class (13 years old), where teacher implemented a problem solving activity about acid-base reactions, using a wiki. Participants were 20 students, of which 12 were female…

Researchers have suggested that teachers use a specialized type of knowledge specifically attributed to the work of teaching. One aspect of this specific type of knowledge is the ability to analyze children's work. With continued emphasis on a teacher's ability to analyze their students' thought processes, teacher candidates will need to develop…

This research study investigates how pre-service teachers integrate statistical content, students' thinking, and pedagogy as they examine how 11- to 12-year olds develop mathematically. The findings provide insights into: a) how pre-service teachers identify some of the difficulties that students commonly have, and b) what pedagogical approaches…

This study examined how toddlers gain insights from source video displays and use the insights to solve analogous problems. Two- to 2.5-year-olds viewed a source video illustrating a problem-solving strategy and then attempted to solve analogous problems. Older but not younger toddlers extracted the problem-solving strategy depicted in the video…

Individuals who have difficult-to-understand speech and minimal reading skills are often limited to icon or picture-based augmentative and alternative communication (AAC) strategies. However, basic phonemic awareness skills could make strategies such as alphabet supplementation, in which the speaker selects the first letter of words they are…

Managing disruptive behaviors in schools is a high-ranking concern in communities across the country (Rose & Gallup, 2006). Unfortunately, the practice of instituting tougher and more severe consequences for increased discipline problems has not resulted in a decrease of disruptive behavior (Lewis & Garrison-Harrell, 1999; Safran &…

Dodgson's method of computing determinants is attractive, but fails if an interior entry of an intermediate matrix is zero. This paper reviews Dodgson's method and introduces a generalization, the double-crossing method, that provides a workaround for many interesting cases.

Generations have been inspired by Edwin A. Abbott's profound tour of the dimensions in his novella "Flatland: A Romance of Many Dimensions" (1884). This well-known satire is the story of a flat land inhabited by geometric shapes trying to navigate the subtleties of their geometric, social, and political positions. In this article, the authors…

This article presents the author's response to Yan Ping Xin and Dake Zhang's recent critical evaluation of her and colleagues' work in "Exploring a Conceptual Model-Based Approach to Teaching Situated Word Problems," published in "The Journal of Educational Research" in 2009 (Vol. 102, No. 6). Most critiques of prior research are written in a fair…

1This article describes how, by incorporating NASA's Students' Cloud Observations On-Line (S'COOL) project into a problem-based learning (PBL) activity, middle school students are engaged in authentic scientific research where they observe and record information about clouds and contribute ground truth data to NASA's Clouds and the Earth's…

The emphasis on problem solving and problem solving courses has become a standard staple of most teacher preparation programs in mathematics. While opinions differ on whether problem solving should be integrated throughout the preparatory courses or teachers should also have a dedicated course for it, everybody agrees that problem solving skills…

We generalize a standard example from precalculus and calculus texts to give a simple description in polar coordinates of any circle that passes through the origin. We discuss an occurrence of this formula in the context of medical imaging. (Contains 1 figure.)