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…

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…

Algebraic notation has been bedazzling learners for generations, yet despite research, learned papers, comparative studies, and a great deal of hard work on the part of classroom practitioners the situation remains a stubborn constant. In this article some small-scale research has highlighted some issues that might find a resonance in many…

One original, and continuing, source of interest in large numbers is observation of the natural world, such as trying to count the stars on a clear night or contemplation of the number of grains of sand on the seashore. Indeed, a search of the internet quickly reveals many discussions of the relative numbers of stars and grains of sand. Big…

"The power of two" is a Royal Institution (Ri) mathematics "master-class". It is a two-and-a half-hour interactive learning session, which, with varying degree of coverage and depth, has been run with students from Year 5 to Year 11, and for teachers. The master class focuses on an historical episode--the Josephus…

Operations with zero and concepts associated with the use of zero are examined in some detail. Historical practices concerning zero are discussed. (CT)

A divisibility test for the number 7 is analyzed, and the general method is considered for other numbers. (DT)

A proof is given that for any four digit number, repeated reordering of digits and subtraction will evenutally result in the number 6174. A computer program is included. (DT)

The meaning of International Standard Book Numbers (ISBN) and the mathematics involved in the use of a check digit to catch errors in number transcription are discussed. (JM)

The place of binary arithmetic in the curriculum is discussed, then uses of binary coding for methods of automatic error correction in computers and calculators are analyzed. (DT)

Some proposals on how children may learn the basic multiplication facts through practical activities based on the rectangle. (MM)

Twelve problems which can be proved by the "mailbox principle" are stated and discussed. (DT)