Early years practitioners know what parents are reminded of every Christmas Day--it does not matter how long families spend carefully selecting the presents, the children are likely to spend longer playing with the empty boxes! Children are fascinated with boxes and practitioners can capitalise on this and support early mathematical development…

The authors see mathematics as an endless source of surprise, which excites and motivates them. Many writers have exploited this characteristic of the subject to nurture learning. The challenge is to create conditions for learners so that they too will experience a surprise. The authors tend to see surprise as a positive emotion; mathematics as…

Polish students learn about Platonic solids in the final year of secondary grammar school, but in such a way that few perceive the beauty of this branch of mathematics. An average student associates polyhedra with calculating lengths and angles in a cube, cuboid or pyramid. But for the author, 3-D geometry is the branch of mathematics that shows…

In this article, the author presents a lesson on rotational symmetry which she developed for her students. The aim of the lesson was "to identify objects with rotational symmetry in the staff car park" and the success criteria were "pictures or sketches of at least six objects with different orders of rotation". After finding examples of…

There have been calls for at least 30 years in American education for a return to basics in mathematics instruction. The problem lies in defining what is basic. Mathematics is more than arithmetic. It is a fabric of ideas, relationships, principles and procedures. But all too often the emphasis in classroom instruction is on static facts and…

General Certificate of Secondary Education (GCSE) mathematics assessment previously included a piece of coursework that required learners to develop a general equation to describe the relationship between two groups of numbers on a number grid. In this author's experience, it became clear that Year 10 students often struggled to form a link…

In this article, the authors talk about transformation geometry being treated as little more than a set of tricks rather than as a mathematically rigorous topic. This appears to lead to pupils seeing little point in studying "reflections, rotations and translations" as other than examinable items in some future test. Following the argument…

In this article, the authors describe a free interactive circular geoboard environment that can lead learners to pose mathematical questions. They list three major ways in which one can imagine the environment and problems being used by teachers. Among other things, they discuss how the environment could support teaching and learning, and how the…

Last year, the author worked with a group of Key Stage 3 (KS3) consultants at a regional roadshow devoted to the topic of information and communications technology (ICT), "Embedding ICT in mathematics teaching." The roadshow was organized by the Association of Teachers of Mathematics (ATM) and the Mathematical Association (MA), and the…

In this article, the author shares some of the activities for the classroom invented by Gill Hatch. One of those activities is the activity for older students, which is for the five-year-olds through to post-graduates. Card-sorting game, geometry games, algebra games, and loop games are also some of those activities for the classroom invented by…

Alf Coles and Barry Orr reflect on what it looked like when Alf taught a year 7 lesson. In this article, Alf was asked by Barry (student) if he would take a lesson with the Y7 class that he had taken over from another teacher in the department in order to see what someone else might do with his lesson plans. Alf describes what some moments with…

Having used the DfES "Problem Solving" pack in a variety of school and centre-based applications, the author taught some of the lessons to classes of children and also observed lessons from the pack being taught to classes from Y1 to Y6. The lessons are part of a series of materials from the Primary National Strategy designed to help…

Discussion in maths lessons has always been something encouraged by ATM but can be difficult to initiate for non-specialist and inexperienced teachers who may feel they need material in books to get them going. In this article, the author describes resources aimed at encouraging discussion among primary mathematicians. These resources include: (1)…

In this article, the author believes that a visual image of the number system is helpful to everyone, especially children, in understanding what is, after all, an abstract idea. The simplest model is the number line, a row of equally spaced numbers, starting at zero. This illustrates the continuous progression of the natural numbers, moving to the…