We are frequently told that Hong Kong has a model system for learning mathematics. In this article Daniela Vasile notes one short-coming in that the pupils are not taught to problem-solve. She begins with a new class by asking them to write down the craziest equation they can come up with and bases her whole lesson, and the following homework,…

The title is that of a course with the same name, designed for teachers of mathematics. The rational for a course specifically on geometry was that "many of those currently teaching mathematics in school had little geometrical education". Teachers on the course experience geometry through problem solving, and learning to pose geometrical problems.…

Many delegates at "conference" relish the opportunity, and the space, to "do some mathematics". Opportunity and space help to make the experience memorable, but how often is the quality of the starting point, or question acknowledged? Here is a set of starting points or problems that invite the reader to "do some mathematics". Deliberately, no…

Ofsted was asked to provide evidence of effective practice in the teaching of early arithmetic, its report entitled; "Good practice in primary mathematics: evidence from 20 successful schools," was published in November 2011. Did this report pass you by? Unfortunately, as with many other reports not blessed with a "high…

There are, it seems, few instances when "unintended consequences" are regarded as having a positive and beneficial effect. Here a well-used activity takes on a "life of its own" as a result of the enthusiasm of the learners. The outcome provides insights for all those involved, including the "teacher". Maybe it is…

"Probability is a difficult concept to teach, because children and adults find it counterintuitive." This is impetus to consider the detailed planning of a set of lessons with a "mixed", in many senses, group of fourth graders. Can the use of prior experience, and the knowledge associated with that experience, make probability a concept that is…

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…

This author is on a journey--hoping that his expertise might have some small local impact. He shares his experiences that might relate to those who are thinking about volunteering abroad, or trying to modernise a system that is cemented in place. Creating change, developing teaching styles, and working for a charity are some of the challenges he…

During Mathematics Teaching Course-I (MT-I), the author was given the opportunity to teach a primary mathematics class at a Government school in Karachi, Pakistan while on teaching practice. The author was lucky to be able to share the lesson planning with a friend, and they found the sharing of ideas a supportive process. The focus of the lesson…

This article sets out how the author believes mathematics might be taught in creative ways. It is about the author's developing thoughts on how he teaches mathematics, how his class responds to his teaching, and how he adjusts his teaching through assessment of children's learning. Through observations and assessment of learning following his…

For more than one hundred years teachers have paddled beside the great ocean of mathematical adventure. Between them they have taught millions of young people. A few have dived in and kept swimming, some have lingered on the shore playing in pools, but most have dipped their toes in and run like heck in the other direction never to return. There…

Hyperbolic geometry occurs on hyperbolic planes--the most commonly cited one being a saddle shape. In this article, the author explores negative hyperbolic curvature, and provides a detailed description of how she constructed two hyperbolic paraboloids. Hyperbolic geometry occurs on surfaces that have negative curvature. (Contains 11 figures and 4…

Since teachers always teach area and perimeter together--and they are both introduced soon after the definition of a rectangle--it is not surprising that students mix up the notions of area and perimeter. Changing the investigation on maximising the area of a fixed perimeter from the traditional, but boring, "Sheep pens" to the much more…

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…