Teachers are implementing flipped instruction in an increasing number of mathematics classes but the research base is not yet well developed on this topic. Many studies of flipped instruction in mathematics have involved a small number of classes utilizing flipped instruction being compared to classes with non-flipped instruction, but this study…

In this study, we aim to explore the extent of mathematics pre-service teachers' ability to apply their procedural understanding combined with spatial perception for drawing conceptual conclusions related to angles in a pyramid. The participants are 16 pre-service high school mathematics teachers. They have studied solid geometry during one…

Access to advanced study in mathematics, in general, and to calculus, in particular, depends in part on the conceptual architecture of these knowledge domains. In this paper, we outline an alternative conceptual architecture for elementary calculus. Our general strategy is to separate basic concepts from the particular advanced techniques used in…

Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)

Argues that the history of mathematics may be an efficient element to provide students with flexibility, open-mindedness, and motivation towards mathematics. Illustrates examples, one of which concerns an historical presentation of 'definition' that was developed with mathematics students who will become mathematics teachers. (Contains 19…

Most introductory textbooks on simple linear regression analysis mention the fact that extreme data points have a great influence on ordinary least-squares regression estimation; however, not many textbooks provide a rigorous mathematical explanation of this phenomenon. Suggests a way to fill this gap by teaching students the concept of breakdown…

The author discusses the use of the duality principle in combination with the hierarchy of algebraic operations in helping students to retain and use definitions and rules for arithmetic and geometric sequences and series. (MN)

Describes the results of part of a study into mathematical problem solving in secondary schools. Concludes that positive results were achieved, in part, as a consequence of the time that was spent in problem-solving lessons which allowed students to practice reading and working with word problems and working on basic material, particularly…

The effects of nonexamples on the acquisition of the geometrical concept of semiregular polyhedra were examined. Results favored the treatments containing both examples and nonexamples. (TG).

Discusses the initial purposes of the National Curriculum assessment. Argues that pupils and teachers could benefit from a better analysis of assessment data by considering a system of assessment used in France. Suggests that the use of information technology would enable formative, diagnostic, summative, and evaluative assessment to take place…

Proposes that the style and format of questions used by lecturers and tutors profoundly influence students' conceptions of what mathematics is about and how it is conducted. Use of questions depends on both scaffolding and fading their use in front of students so that students internalize questions for their own learning and practice of…

A syllabus is proposed for a course in statistics at the secondary level. Brief comments are given on each topic, indicating how they may be presented to students. The overall approach to teaching statistics from an interdisciplinary point of view is discussed. (Author/SD)

Attention is drawn to an ancient Greek method for finding the least common multiple (LCM) of two numbers. A link is established between this method and a well-known method of obtaining the highest common factor (HCF) numbers. This leads to consideration of some relationships between HCF and LCM. (Author/MK)

Presents the equations of motion governing the trajectory of a cricket ball subject to a linear drag force. Uses a perturbation expansion technique to solve the resulting trajectory equation for the range of a cricket ball struck into the outfield. (Author/ASK)

Adopts several strategies for successful teaching and learning of linear algebra, which consist of a set of computer projects allowing students to explore new concepts, make conjectures, apply theorems, and work on applied projects of their choice. The resulting improvement in student learning has been remarkable. (Contains 12 references.)…