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…

Games are for playing, more often than not playing a game is a social experience, it is fun, and we all enjoy playing games. Play and playing are ways in which we learn, so how often are games part of the normal activity of the mathematics classroom? The answer, in most cases, has to be--not often. Is it that games just don't seem to fulfil the…

Symbolism is an important element within mathematical notation. Symbolism enables unambiguous communication of mathematical ideas and forms. Current mathematical symbolism is the result of much evolution and acceptance by those working in the field. When is it appropriate to challenge accepted norms and suggest alternatives or "changes"?…

What is it that makes learners "think"? What geometrical problem, simply posed, can switch on the thinking processes of students? The author describes one such starting point that worked in a real classroom with Year 9 students. A group of learners for whom "mathematics comes easy" experience being stuck, they learn to handle this unfamiliar…

The minus sign is a mathematical symbol that is multi-functional. Yet, how often is its use explicit to the non-mathematician, or more importantly the learner, who is expected to interpret the symbolism appropriately, when often the "meaning" stems from context of its use. From the perspective of the learner, such nuances of use simply…

Mathematical proof is a strange concept; it is ironical that there is no precise definition of what constitutes a mathematical proof since without definitions there can be no proof--Dreyfus, 1999. Proof can be divided into many different categories. In this article, the author discusses these categories. She looks first at the background of proof…

Symmetry is found in the visual arts, architecture and design of artefacts since the earliest time. Many natural objects, both organic and inorganic, display symmetry: from microscopic crystals and sub-atomic particles to macro-cosmic galaxies. Today it features strongly in higher mathematics such as Linear and Abstract Algebra, Projective and…

"Project work" is far from being a new phenomenon in the mathematics curriculum. Students reporting their findings of the "project" in a scrapbook format may be a novel approach. Asking learners to assess their "effort rating" is unusual self-assessment. But, there is far more detail in this account of project work.…

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 article outlines an extension exercise that is based on the elementary geometrical constructions in the National Curriculum. The challenge for students is to organise and execute an extended construction. The hidden, parallel agenda is proof, for the teacher's role is to convince students that they "must" succeed and that doing so is a…

Having decided to spend some time looking at one's understanding of numbers, the author was inspired by "Alex's Adventures in Numberland," by Alex Bellos to look at one's innate appreciation of number. Bellos quotes research studies suggesting that an individual's natural appreciation of numbers is more likely to be exponential rather…

The author states her belief that mathematics is a human construct based on axiomatic systems, and that these constructs are both personal and social. She argues that to succeed in mathematics, learners' personal constructs need to be aligned with formal globally agreed mathematical conventions. Put more simply, she informs her students that…

In this article, the author describes what his students are doing following the ATM Easter conference in Telford, where he was inspired by a workshop entitled "Vitamin D Maths," conducted by Jocelyn D'Arcy. He describes an activity that allows his Year 11 students to walk through angles drawn on the floors. This topic will now literally…

The author conducted a workshop with colleagues in which awareness of Pythagoras' theorem was raised. This workshop was an unforgettable event in the author's life because it was the first time that she had interacted with teachers from a different school system, and it allowed her to develop presentation skills and confidence in her own…

Action research is demanding, and often unpredictable. In this article, the author first introduces the context of her research on "Cultural Mathematics" and briefly describes the preparation for the course, with minimal comment on the methodology. She presents some of the challenges that arose during the course, using the categories…