Learners are all different and teachers are all different, so why do we often ignore this reality when trying to explain, or demystify, some aspect of mathematics in the classroom? Enabling learning can be challenging, demanding of creativity, and needy of alternatives if understanding is the real goal. Here the authors offer ideas that are aimed…

Has technology revolutionised the mathematics classroom, or is it still a device waiting to be exploited for the benefit of the learner? There are applets that will enable the user to solve complex equations at the push of a button. So, does this jeopardise other methods, make other methods redundant, or even diminish other methods in the mind of…

In this article, the author explores her personal views on mathematics and how she solves problems. She experiences some personal revelations while attending a "Mathsjam". Organised by some of the more prominent names in the popularisation of mathematics, "Mathsjam" was billed as the UK's first Gathering for Gardner, an event…

In this article, the author explores what Assessing Pupils' Progress (APP) is about. He contends that the predilection for testing is a catastrophe as far as the teaching and learning of mathematics is concerned; it is an outcome of the drive for collecting so-called "data" on pupils. What those people, who should know better, either choose to…

Solving true problems requires persistence. The National Council of Teachers of Mathematics (NCTM) states that "problem solving means engaging in a task for which the solution method is not known in advance. In order to find a solution, students must draw on their knowledge, and through this process they will often develop new mathematical…

Two problem-solving strategies involved in finding the area of a particular square formed on a geoboard are described in detail. (MP)

An inconsistency between American and British accounting methods led the author to this problem whose solution involves linear equations and geometric series. (SD)

The relationships between arithmetic, geometric, and harmonic means and the root mean square of two numbers are examined. The problem of generalizing these relationships to three variables is discussed. (SD)

Students were given the problem: Given a deck of cards in a certain order, after how many shuffles will it return to its original order? They worked with small decks of cards to develop a general formula, but were unhappy with the results. (SD)