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…

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…

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…

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…

The author tells the story of an exploration he undertook, what he learned, and the questions he was able to answer as a result. Thinking, on the part of the learner, is complex, far from explicit, and some might say intangible. But, by recognising certain "clues" it might be possible to begin to understand how different types of thinking…

As with previous reports of activity at the annual Institute of Mathematics Pedagogy, this does not disappoint. The tasks used to support teaching and learning in mathematics can vary in so many ways, but this variation is compounded when learners begin to access the tasks. A task that really motivates and challenges one learner is likely to…

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"?…

This relationship is omnipresent to those who appreciate the shared attributes of these two areas of creativity. The dynamic nature of media, and further study, enable mathematicians and artists to present new and exciting manifestations of the "mathematics in art", and the "art in mathematics". The illustrative images of the relationship--that…

Designing quality continuing professional development (CPD) for those teaching mathematics in primary schools is a challenge. If the CPD is to be built on the scaffold of five big ideas in mathematics, what might be these five big ideas? Might it just be a case of, if you tell me your five big ideas, then I'll tell you mine? Here, there is…

The Fibonacci series has been studied since it was first described by Leonardo of Pisa--Fibonacci--in 1202. It begins with the sequence 1, 1, 2, 3, 5, 8... Each succeeding number is the sum of the previous two. In number theory courses, students are introduced to the concept of modulo arithmetic, sometimes called "clock" arithmetic. In modulo…

The Institute of Mathematical pedagogy meets annually--the theme for 2010 was: "Mathematical Friends & Relations: Recognising Structural Relationships". Here one participant documents her reflections on the experience of working with a group of mathematics educators at the Institute. The challenges, the responses--both the predictable and the…

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…

Many learners still struggled to appreciate, and understand the difference between, the concepts of fractions and ratio. This is not just a UK phenomenon, which is demonstrated here by the use of a resource developed by the Wisconsin Centre for Education, in association with the Freudenthal Institute of the University of Utrecht, with a group of…

In this article, the authors explore the reasons why some mathematical functions are referred to as odd, and others as even. They start by recalling the definitions of both functions. Simply stated, the value of an even function is the same for a number and its opposite, whereas the value of an odd function changes for the opposite number when the…

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…