Trigonometry is an important section in mathematics that links algebraic, geometric and graphical reasoning. Many secondary school learners are not familiar with these types of reasoning; thus, trigonometry presents a challenge for these learners. The traditional 'chalk and talk' method of teaching trigonometry is used by many teachers; however,…

Increasing pressure is mounting from all areas of society to maximise technology use within educational domains. Whilst curriculum documents call for the utilisation of technology as a teaching tool in the mathematics classroom, the benefits of exploring forms of dynamic mathematical software, such as GeoGebra, are often introduced in the senior…

There is a recognised need in mathematics teaching for new kinds of tasks which exploit the affordances provided by new technology. This paper focuses on the design of prediction tasks to foster student reasoning about exponential functions in a mathematics software environment. It draws on the first iteration of a design based research study…

Educational material often includes engaging perceptual information. However, this perceptual information is often extraneous and may compete with the deeper to-be-learned structure, consequently hindering either the learning of relevant structure or its transfer to new situations. This hypothesis was tested in 4 experiments in which 6- to…

The article illustrates how statistical content and pedagogical reasoning were taught in tandem in an undergraduate course. A typical day in the course is described. It is also suggested that practising teachers can benefit from strategies used in the course. (Contains 1 table and 3 figures.)

In light of the prosperity of online social media, Web users are shifting from data consumers to data producers. To catch the pulse of this rapidly changing world, it is critical to transform online social media data to information and to knowledge. This dissertation centers on the issue of modeling the dynamics of user communities, trending…

Communities, also called clusters or modules, are groups of nodes which probably share common properties and/or play similar roles within a graph. They widely exist in real networks such as biological, social, and information networks. Allowing users to interactively browse and explore the community structure, which is essential for understanding…

The purpose of this study was to determine the extent to which performance on the TOEFL iBT speaking section is associated with other indicators of Japanese university students' abilities to communicate orally in an academic English environment and to determine which components of oral ability for these tasks are best assessed by TOEFL iBT. To…

When conducting item reviews, analysts evaluate an array of statistical and graphical information to assess the fit of a field test (FT) item to an item response theory model. The process can be tedious, particularly when the number of human reviews (HR) to be completed is large. Furthermore, such a process leads to decisions that are susceptible…

The least squares method of fitting a line is not one that naturally occurs to students. We present three tasks to understand student views on how lines may be fit.

In mathematics, as in baseball, the conventional wisdom is to avoid errors at all costs. That advice might be on target in baseball, but in mathematics, avoiding errors is not always a good idea. Sometimes an analysis of errors provides much deeper insights into mathematical ideas. Certain types of errors, rather than something to be eschewed, can…

We describe an example of learning with multiple representations in an A-level revision lesson on mechanics. The context of the problem involved the motion of a ball thrown vertically upwards in air and studying how the associated physical quantities changed during its flight. Different groups of students were assigned to look at the ball's motion…

A partially unusual behaviour was found among 14 sophomore students of civil engineering who took a pre test for a free fall laboratory session, in the context of a general mechanics course. An analysis contemplating mathematics models and physics models consistency was made. In all cases, the students presented evidence favoring a correct free…

Chat conversations and other types of online communication environments are widely used within CSCL educational scenarios. However, there is a lack of theoretical and methodological background for the analysis of collaboration. Manual assessing of non-moderated chat discussions is difficult and time-consuming, having as a consequence that learning…

This is a guide to using Maple in teaching fundamental calculus of one, two and three variables (limits, derivatives, integrals, etc.), also suitable for Maple beginners. It outlines one of the ways to effective use of computers in the teaching process. It scans advantages and disadvantages of using Maple in relation to students and teacher. The…