The derivative of a composite function, taken with the chain rule is one of the important notions in calculus. This paper describes a study conducted in Turkey that shows that the chain rule was given with the formula in function notation and/or the Leibniz notation without relating these formulas to life-related problem situations in the…

In this article, the authors investigate how the difficulty of a "set shot" at goal varies with position on the field. By "set shot" they mean a player kicking for goal following a mark or free kick. The analysis begins by defining the "angle of opportunity" as a measure of difficulty for kicks at a given distance and angle from goal, where the…

A well-developed understanding of rate is foundational to conceptual understanding of introductory calculus. Many students achieve procedural competence with the application of rules for differentiation without developing an awareness of the connection between derivative and rate. In addition, rate-related reasoning is needed to make informed…

Many students experience considerable difficulties when they learn and then attempt to construct and communicate proofs of conjectures using the principle of mathematical induction. Although research on the pedagogy of mathematical induction has gained only occasional attention since the 1970s, there has been an increasing interest in this field…

This paper presents a generic method of calculating accurate horizontal and vertical object distances from digital images taken with any digital camera and lens combination, where the object plane is parallel to the image plane or tilted in the vertical plane. This method was developed for a project investigating the size, density and spatial…

Concerns about the importance of variation in statistics education and a lack of research in this topic led to a preliminary study which explored pre-service teachers' ideas in this area. The teachers completed a written questionnaire about variation in sampling and distribution contexts. Responses were categorised in relation to a framework that…

This study was conducted to reveal how students at university level justify their solutions to tasks with various degrees of difficulty. The study is part of a larger study of students' concept formation of limits. The mathematical area is limits of functions. The study was carried out at a Swedish university at the first level of mathematics. The…

Many students have traditionally found the processes of algebraic manipulation, especially factorisation, difficult to learn. This study investigated the value of introducing students to a Vedic method of multiplication of arithmetic numbers to algebra that is very visual in its application. This research considered a possible role of the…

Numeracy in the workplace is much more complex than the simple application of mathematical knowledge and skills learned in school or vocational education. Although the knowledge and skills developed in compulsory education or in formal adult and vocational education and training courses play a foundational role, they are inevitably transformed…

This article reports on the findings of a research project examining participant students' points of view on accelerated programs in mathematics from four state secondary schools in New Zealand. The four participant schools in this research offered a variety of different acceleration designs and philosophies and were different in size location,…

Describes students' written answers that seemed technology-assisted in the 1999 Calculus Tertiary Entrance Examination (TEE). Illustrates how in the 1999 Calculus TEE some students used their calculators in flexible ways. (ASK)

Surveys a group of students who enrolled in a first year university mathematics course to study the impacts of graphing calculators on the Western Australian Tertiary Entrance Examination (TEE). Considers the perceptions of students on their use of and preparation to use graphing calculators. (ASK)

Describes a study that maps the performance of entering undergraduates on secondary school level mathematics items, compares the actual student performance with that estimated by practicing teachers, and identifies the level of agreement demonstrated by the teachers regarding expectations of student performance. (ASK)

Knowledge and understanding of school mathematics enrollment can facilitate planning and identify issues that need to be addressed. Updates earlier research on Australian upper secondary school mathematics trends and examines year 12 mathematics enrollment trends for the period 1980 to 1999. Discusses the implications of these trends. (ASK)

Focuses on the issues of the course advice given to secondary students who were intending to study one of the more demanding mathematics subjects in year 12. Concludes that all students would benefit from studying as much mathematics as they are capable of in terms of the problem-solving skills they would acquire and future course and career…