Problem-based learning (PBL) has the potential to enhance both cognitive and affective engagement but has been criticised for being unsuitable for learners with low levels of knowledge and skills, such as South African learners from poor backgrounds. In such cases, guided problem-based learning (GPBL), which includes direct instruction and teacher…

This paper is the result of a research done from the Socioepistemological Theory of Mathematics Education, perspective in which we enquire about the reasons to study trigonometric Fourier series in electrical engineering, and what historical and epistemological conditions can be considered to develop more profound meanings when this topic is…

Calculators with computer algebra systems (CAS) are powerful tools when working with equations and algebraic expressions in mathematics. When calculators are allowed to be used during assessments but are not available or provided to every student, they may cause bias. The CAS calculators may also have an impact on the trustworthiness of results.…

Participants were pretrained and tested on mutually entailed trigonometric relations and combinatorially entailed relations as they pertained to positive and negative forms of sine, cosine, secant, and cosecant. Experiment 1 focused on training and testing transformations of these mathematical functions in terms of amplitude and frequency followed…

The purpose of this study was to: (a) investigate the effects of email to enhance learners' use of self-regulation strategies; (b) examine different effects between email list and individually addressed notes on the enhancement of self-regulation; (c) observe and record changes in self-regulation and self-efficacy; and (d) explore the…

Describes the solution to a geometric problem by two ninth-grade mathematicians using The Geometer's Sketchpad computer software program. The problem was to divide any line segment into a regular partition of any number of parts, a variation on a problem by Euclid. The solution yielded two constructions, one a GLaD construction and the other using…

This paper reports upon particular aspects of a study carried out by Delice in 2003, the main aim of which was to compare the performance of students in the 16-19 age group from Turkey and England on trigonometry of "A-level standard" and then to compare the curriculum and assessment provision in each country to seek possible…

Discusses various representations of a curve and the relationships between them. Describes mathematical exercises which use Logo to derive a turtle procedure for graphically representing a cycloid. Provides a proof of the trigonometric series formula to show equality. (RT)