A facility with signed numbers forms the basis for effective problem solving throughout developmental mathematics. Most developmental mathematics textbooks explain signed number operations using absolute value, a method that involves considering the problem in several cases (same sign, opposite sign), and in the case of subtraction, rewriting the…

While most scientists agree that laboratory work is an important part of introductory science courses, there is scant evidence for the relationship between laboratory work and student learning, particularly at the college level. This work reports the quantitative component of a mixed-methods study of the effect of cooperative problem-based…

Students who are preparing to study science and engineering need to understand equation solving but adult students returning to study can find this difficult. In this paper, the design of an online resource, Equations2go, for helping students learn to solve linear equations is investigated. Students learning to solve equations need to consider…

Five high-school chemistry teachers were asked to enact a lesson in which they posed a problem for which students were likely to generate solutions based on reasoning that was not aligned with accepted principles of chemistry. Four teachers selected a problem related to the stoichiometry of a reaction; the fifth chose a problem associated with…

The basis of this intervention study is a distinction between numerical calculus and relational calculus. The former refers to numerical calculations and the latter to the analysis of the quantitative relations in mathematical problems. The inverse relation between addition and subtraction is relevant to both kinds of calculus, but so far research…

Teachers of gifted students often are challenged to find ways to stimulate critical thinking and problem-solving skills. School chess clubs are one way of meeting that challenge. This article poses how games such as chess affect learning and gifted students. Two detailed strategies for teaching chess to students beginning in kindergarten are…

Ofsted was asked to provide evidence of effective practice in the teaching of early arithmetic, its report entitled; "Good practice in primary mathematics: evidence from 20 successful schools," was published in November 2011. Did this report pass you by? Unfortunately, as with many other reports not blessed with a "high…

The author identifies higher order thinking as an essential component of dance training for students of all ages and abilities. Weaving together insights from interviews with experts in the field of dance education with practical pedagogical applications within an Improvisation and Composition class for talented and gifted youth, this article…

Many traditional science curricula explore human body systems separately, paying little attention to how the systems interact. For example, the textbooks "Biology" (Miller and Levine 2006) and "Biology: An Everyday Experience" (Kaskel, Hummer, and Daniel 2003) detail the structure and function of each system and individual organs but offer little…

The purpose of this study was to introduce problem posing activity to third grade students who have never met before. This study was also explored students' metaphorical images on problem posing process. Participants were from Public school in Marmara Region in Turkey. Data was analyzed both qualitatively (content analysis for difficulty and…

Anne Roche and Doug Clarke discuss the importance of developing students' persistence in relation to problem solving during the use of challenging tasks. They provide a useful list of strategies that teachers can use to encourage persistence amongst their students.

Error-based simulation (EBS) has been developed to generate phenomena by using students' erroneous ideas and also offers promise for promoting students' awareness of errors. In this paper, we report the evaluation of EBS used in learning "normal reaction" in a junior high school. An EBS class, where students learned the concept…

Using errors as a method of learning has been made explicit through a two-staged peer review and discussion. During organic chemistry discussion sessions, quizzes are followed by a structured peer review designed to help students identify and discuss student errors. After the face-to-face discussion, a second stage of review involves analyzing and…

This article describes a follow-up analysis of findings from a randomized study that tested the efficacy of a blended version of Enhanced Anchored Instruction (EAI) designed to improve both the computation and problem-solving performances of middle school students with disabilities. The goals of the secondary analysis were to track overall error…

Engaging learners in exploratory problem-solving activities prior to receiving instruction (i.e., explore-instruct approach) has been endorsed as an effective learning approach. However, it remains unclear whether this approach is feasible for elementary-school children in a classroom context. In two experiments, second-graders solved mathematical…