Procedural and conceptual learning are two types of learning, related to two types of knowledge, which are often referred to in mathematics education. Procedural learning involves only memorizing operations with no understanding of underlying meanings. Conceptual learning involves understanding and interpreting concepts and the relations between…

A problem is discussed which is generated by shadows and which is a generalization of simple harmonic motion.

In this article, we give a brief history of the Feynman's Triangle problem and describe a simple method to solve a general version of this problem, which is called the Routh Theorem. This method could be found useful to school teachers, instructors or lecturers who are involved in teaching geometry.

This article describes one type of mathematical problem, open-start problems, and discusses their potential for use in assessment. In open-start problems how one starts to address the problem can vary but they have a correct answer. We argue that the use of open-start problems in assessment could positively influence classroom mathematics…

In Volume 26, Number 2, we reported on a group case study run for level 3 mathematics students at the University of Brighton. At the core of the study was a quadratic assignment problem, and we reported on attempts by students to use Excel to solve the problem, and on the attendant difficulties. We provided an elegant solution. In this article, we…

Explains an application of mathematical modeling within a school setting as well as progressive use of graphing calculators in mathematical modeling. Analyzes students' performances in the process of problem-solving using the problem of baton-passing in relay races. Discusses students' use of their mathematical knowledge and ideas when they used…

Considers educational aspects of the development of ratio and proportion focusing on the arithmetization undergone by these concepts in light of the relationship between mathematics and music. Investigates the instructional aspects of compounding ratios. Points out features of the differences between identity and proportion which can be…

Poses a practical woodwork problem in which maximizing the perimeter of a square-based pyramid is required. The pyramid is constructed from four identical trapezia to be cut from a given rectangle of wood. A simple mathematical analysis suggests a number of different strategies for the solution of the problem. (Author/NB)

Answers to mathematical problems come in all forms and most come with a variety of questions. Students often forget to ask questions once they have found an answer. This paper suggests that students would always benefit by questioning answers.

In this research paper we discuss how some multiple-choice questions may be used to improve understanding, to develop and to assess modelling capabilities and as an aid to teaching.

To help mathematics educators realise the power of computer-based applications and modelling, this paper deals with four questions: (a) What implications does technology have for the range of applications and modelling problems that can be introduced? (b) In what cases does technology facilitate the learning of applications and modelling? (c) When…

This article conceptualises a real-like model of a mathematical model as an inverse model. The inverse model draws on the un-complexity of concrete real life operations in order to help students to add concrete meaning to mathematical algorithms. The inverse model is described in the context of a pedagogical perception, which grants students in…

A variety of applications of logarithms are presented along with suggestions about how this topic might be made more interesting and relevant in a secondary classroom. In most cases, the treatment is multi-modal using numerical, graphical and algebraic approaches.

Mathematical optimization problems are not typical in the classical curriculum of mathematics. In this paper we show how several generalizations of an easy problem on optimal transportation were solved by gifted secondary school pupils in a correspondence mathematical seminar, how they can be used in university courses of linear programming and…

This paper describes how parametric cubic splines and cubic Bezier curves may be used in designing a two dimensional shape. A simple aerofoil shape is designed using both methods. The mathematics is described and the shape drawn using Excel. The effect of varying parameters is shown in both methods.