In this paper, we present data from two iterative teaching experiments involving students' constructions of four basic counting problems. The teaching experiments were designed to leverage the generalizing activities of relating and extending to provide students with opportunities to reflect on initial combinatorial activity when constructing…

When learning chemistry, students must learn to extract chemical information from mathematical expressions. However, chemistry students' exposure to mathematics often comes primarily from pure mathematics courses, which can lead to knowledge fragmentation and potentially hinder their ability to use mathematics in chemistry. This study examines how…

Preventing humans from committing errors is a crucial aspect of man-machine interaction and systems of computer assistance. It is a basic implication that those systems need to recognise errors before they occur. This paper reports an exploratory study that utilises eye-tracking technology and automated face recognition in order to analyse test…

This paper presents Lewis Carroll's formula for mentally calculating the day of the week of a given date. The paper concludes that such formulas are too complex for individuals of low intelligence to learn by themselves, and thus "idiots savants" who perform such calendar calculations must be using other systems. (JDD)