Different technological artefacts may offer distinct opportunities for students to develop resources and strategies to formulate, comprehend and solve mathematical problems. In particular, the use of dynamic software becomes relevant to assemble geometric configurations that may help students reconstruct and examine mathematical relationships. In…

The electrochemical synthesis of transition-metal acetylacetonates described here can form the basis of assisting in the transformation of an entry-level laboratory course into a research-like environment where all members of a class are working on the same problem, but where each member has a personal responsibility for the synthesis and…

In Experiment 1, students received an illustrated booklet, PowerPoint presentation, or narrated animation that explained 6 steps in how a cold virus infects the human body. The material included 6 high-interest details mainly about the role of viruses in sex or death (high group) or 6 low-interest details consisting of facts and health tips about…

Organic chemistry students typically struggle with the retrosynthetic approach to solving synthesis problems because most textbooks present the chemistry grouped by "reactions of the functional group". In contrast, the retrosynthetic approach requires the student to envision "reactions that yield the functional group". A second challenge is the…

Mutational inactivation of a specific gene is the most powerful technique to analyze the biological function of the gene. This approach has been used for a long time in viruses, bacteria, yeast, and fruit fly, but looked quite hopeless in more complex organisms. Targeted inactivation of specific genes (also known as knock-out mutation) in mice is…

Reversing is the notion of thinking or working in reverse. Computer science textbooks and tutors recognize it primarily in the form of recursion. However, recursion is only one form of reversing. Reversing appears in the computer science curriculum in many other forms, at various intellectual levels, in a variety of fundamental courses. As such,…

This note generalizes the formula for the triangular number of the sum and product of two natural numbers to similar results for the triangular number of the sum and product of "r" natural numbers. The formula is applied to derive formula for the sum of an odd and an even number of consecutive triangular numbers.

In this article we consider an example suitable for investigation in many mid and upper level undergraduate mathematics courses. Fourier series provide an excellent example of the differences between uniform and non-uniform convergence. We use Dirichlet's test to investigate the convergence of the Fourier series for a simple periodic saw tooth…

Three elementary students with autism were taught single-digit addition problem-solving skills using number and touch-point strategies. Prior to the study, all students were unable to correctly calculate single-digit addition problems. An alternating-treatments design was used to compare the acquisition performance of single-digit addition…

This study investigated the influence of informational complexity and working memory capacity on problem-solving efficiency. We examined two predictions of the "situational efficiency hypothesis," which states that the efficiency of problem solving varies as a function of situational constraints. One prediction is that informational complexity…

Despite its importance in mathematical problem solving, verification receives rather little attention by the students in classrooms, especially at the primary school level. Under the hypotheses that (a) non-standard tasks create a feeling of uncertainty that stimulates the students to proceed to verification processes and (b) computational…

Recently in many Canadian schools, escalated violence presents an evident threat. Rates of severe youth violence are considerably lower than sensational media coverage would have people believe, but at the same time, many young people, as well as adults, do not feel safe, respected, or constructively engaged as they should be. While schools cannot…

We solve exactly the problem of calculating the electromagnetic fields produced by a finite wire with a constant current, by using two methods: retarded potentials and Jefimenko's formalism. One result in this particular case is that the usual Biot-Savart law of magnetostatics gives the correct magnetic field of the problem. We also show…

Background: Collaborative learning is recognized as an effective learning tool in the classroom. In order to optimize the collaborative learning experience for children within a collaborative partnership, it is important to understand how to match the children by ability level, and whether assigning roles within these dyads is beneficial or not.…

This article investigates the potential of fMRI to test assumptions about different components in models of complex cognitive tasks. If the components of a model can be associated with specific brain regions, one can make predictions for the temporal course of the BOLD response in these regions. An event-locked procedure is described for dealing…