Digital games offer an appealing environment for assessing student proficiencies, including skills and misconceptions in a diagnostic setting. This paper proposes a dynamic Bayesian network modeling approach for observations of student performance from an educational video game. A Bayesian approach to model construction, calibration, and use in…

Learning through meaningful problem solving is integral in any successful mathematics program (Carpenter et al. 1999). The National Council of Teachers of Mathematics (NCTM) promotes the use of problem solving as a means to deepen understanding of all content areas within mathematics (NCTM 2000). This article describes a first-grade lesson that…

Critical thinking is a process that can be taught. It involves "evaluating the accuracy, credibility, and worth of information and lines of reasoning. Critical thinking is reflective, logical, evidence-based, and has a purposeful quality to it--that is, the learner thinks critically in order to achieve a particular goal." The authors have found…

Students frequently have difficulty determining whether a given real-life situation is best modeled as a linear relationship or as an exponential relationship. One root of such difficulty is the lack of deep understanding of the very concept of "rate of change." The authors will provide a lesson that allows students to reveal their misconceptions…

A basic level of literacy and numeracy is essential for full participation in modern societies. While very few people in most of the advanced countries could be regarded as illiterate or innumerate, recent studies have shown that there are, in fact, significant numbers of people with poor skills, and that low levels of skills are associated with…

After waiting over nine months for the results of his PhD thesis the author was motivated to conduct some qualitative research on the reasons why the system of examiners' reports is so slow and goes on to explain how this problem could be improved by the recruitment of retired academics.

In the teaching of physics at upper secondary school level (K10-K12), the students are generally taught to solve problems analytically, i.e. using the dynamics describing a system (typically in the form of differential equations) to compute its evolution in time, e.g. the motion of a body along a straight line or in a plane. This reduces the scope…

We study the greenhouse effect on a model satellite consisting of a tungsten sphere surrounded by a thin spherical, concentric glass shell, with a small gap between the sphere and the shell. The system sits in vacuum and is heated by sunlight incident along the "z"-axis. This development is a generalization of the simple treatment of the…

The author created a lesson in which students successfully practiced reading comprehension skills while developing an understanding of earthquakes. Not only did this lesson help students gain an understanding of the impact of earthquakes, a subject embedded into Missouri's eighth-grade science curriculum, but it also addresses one of the new…

The Common Core raises the bar for states struggling to decide what should be taught or tested. As low-performing schools strive to improve instruction, the blueprint has been defined. The Common Core defines the curriculum in enough detail and specifies ways to teach that content creatively and innovatively, to produce graduates who are problem…

This article presents a lesson that focuses on numeracy. In the lesson, students were tasked to find the best path for a new expressway. The purpose of the activity was for students to gain an appreciation of the complexities associated with designing public infrastructure and to put into practice the mathematical skills. This article also…

Research has shown that students should be given the opportunity to explore mathematical concepts by building on their knowledge and focusing on mathematical reasoning. When students represent ideas, make conjectures, collaborate with others, and give explanations and arguments, they are using mathematical reasoning (NCTM 2000). Certain teaching…

Students may be able to set up a relevant proportion and solve through cross multiplication. However, this ability may not reflect the desired mathematical understanding of the covarying relationship that exists between two variables or the equivalent relationship that exists between two ratios. Students who lack this understanding are likely to…

Transfer is typically thought of as requiring individuals to "see" what is the same in the deep structure between a new target problem and a previously encountered source problem, even though the surface features may be dissimilar. We propose that experts can "see" the deep structure by considering the first-order interactions…

Has technology revolutionised the mathematics classroom, or is it still a device waiting to be exploited for the benefit of the learner? There are applets that will enable the user to solve complex equations at the push of a button. So, does this jeopardise other methods, make other methods redundant, or even diminish other methods in the mind of…