The clarity of the argument, and the detail in the mathematics, make this a real piece of "mathematics in context". However, while this might be not described as "mathematics for the faint hearted", there are classroom implications for application, interest, and motivation. "All things solar" have seen a rise in popularity through the serious…

Pattern can be identified in many forms. Mathematicians appreciate pattern and its ability to describe, to explain, to determine, to create a sense of security--"I can see a pattern...", and pattern is part of the sense making process for learners, from a very early age. Number squares exhibit a multiplicity of patterns that may vary according to…

The use, and misuse, of statistics is commonplace, yet in the printed format data representations can be either over simplified, supposedly for impact, or so complex as to lead to boredom, supposedly for completeness and accuracy. In this article the link to the video clip shows how dynamic visual representations can enliven and enhance the…

The first word of this item is "imagine". This instruction has the potential to signal a journey through a world of geometry that might leave you spellbound. On the other hand, it could be the start of a roller-coaster ride through three dimensions that will tax both your imagination, and your powers of visualisation. It is likely that you will…

As with much in life the term "investigative", when used to describe an approach to teaching and learning, can have many interpretations. Some might consider that the term "investigations" is somehow "mired in the past", others might consider "investigations" to be a "credo" that sustains their own mathematics teaching and learning. With…

It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…

This is mathematics in action, in context, in real life, and in detail. Begin the journey with Archimedes, and travel alongside the likes of Fermat, Fibonacci, Coxeter, and Adler. There is much to consider and opportunities to make links to things that might be "known", but maybe not well appreciated. On the way you will come across an angular…

As with so many aspects of mathematical enquiry, there is little that is "original", or "brand new", but that does not diminish the outcome of work that borrows from "those who have gone before". In this piece the author "borrows" from the work of Desargues, Monge, Ceva, Menelaus, van Aubel, and Gergonne. This novel approach to providing a proof…

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,…

Of the four mathematical operators, division seems to not sit easily for many learners. Division is often described as "the odd one out". Pupils develop coping strategies that enable them to "get away with it". So, problems, misunderstandings, and misconceptions go unresolved perhaps for a lifetime. Why is this? Is it a case of "out of sight out…

Does the term "learning journal" readily conjure up an image of something that is part of the normal mathematics classroom? Personally, do you ever use a journal of some form to help you organise your thoughts? Or, put quite simply--what is a learning journal? It might be that you are unfamiliar with the label, but journals are one type of…

This is the story of a real problem, not a problem that is contrived, or invented for the convenience of the appropriate planning tool. This activity by a group of students, defined simply as "8FN", might be likened to an "end of term concert". If you just happened to be a delegate at the ATM Conference 2003 you might remember…

To most children in primary school role-play is just something you do, and something you enjoy. It is part-and-parcel of being at school, part of the normal classroom activity. So, why can it not just be a normal part of learning mathematics? Can we study learners "in role", and make judgments about what they learn, and how they learn? This is the…

The notion of "understanding", and its place in the learning process, is often placed in sharper focus when considered in the context of learning and teaching algebra. There are tensions between "doing" algebra, following algorithms, using "rules", or "tricks", and understanding "what you are doing". How does this impact the "way" that algebra is…

What does "to be a mathematician" mean? What is implied, and what image is created of "a mathematician"? Are "mathematicians" members of an exclusive club? Are mathematicians different to "other people"? Are mathematicians different because they are able to mathematize? These might not be the most oft asked questions, but are they questions to…