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Case study 15: Extension activities for GCSE Mathematics

This case study shows how a school raised the standards and motivation of its most able GCSE Mathematics students. The same approach could also be used in other subjects.

Background

large mixed comprehensive with some gifted mathematicians

Implementation

sharing extension and stimulation ideas and activities across the department

Impact

exciting mathematics lessons with a feeling of fun

better exam results

more students taking AS/A levels in the subject

Background

The school is a large mixed 11 to 18 comprehensive in which mathematics classes are setted from the end of year 7.

The GCSE Mathematics results were a little above the national average, but the school thought it could improve them by using additional resources and ideas to stimulate and stretch gifted students.

Two years ago, following a comment from an inspection report, the school made a concerted effort to provide extension activities for key stage 3 pupils in the top two sets, both in class and for homework. It did this by pooling ideas from all mathematics staff. Many of the activities were based on increasing the everyday relevance of material and making mathematics more fun. Master classes after school proved very successful because of the problem-solving and games approach to the subject.

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Implementation

The school realised that extension activities were also needed at key stage 4, to stretch and stimulate the more able students. Ideas were pooled and a range of activities were added to the schemes of work, particularly for the top two sets. Gifted students were encouraged to enter the European Kanga Competition and the UK Mathematics Challenge, several emerging triumphantly with gold certificates. This raised the self-esteem of the whole cohort and made many feel that mathematics could be a passport to lifelong success. 'Mathematics can make you fly' was the catchphrase.

Two members of staff with an interest in the history of their subject encouraged students to research the lives of famous mathematicians. They started with a quiz giving clues about the mathematicians, which got students on the trail using books, encyclopedias and the internet.

Two teachers who taught application of number at levels 2 and 3 in the sixth form found some interesting and relevant everyday examples of mathematics in the worked activities on the market and also in the key skills test papers. The department agreed to introduce some of these key skills scenarios in key stage 4 mathematics lessons, where appropriate to the syllabus. This stimulated and motivated all the sets and improved the overall response to homework and coursework completion. It also led to a much higher number wanting to progress to AS Mathematics the following year.

Knowing that some gifted mathematicians develop a passionate interest in one part of the subject, the department encouraged pairs of students to prepare a visual and oral presentation on any aspect of mathematics that interested them. This gave scope for their independent learning skills. Deadlines were set for the presentations and topics chosen included:

• representing relative sizes on log graphs, from the mass of the universe down to the mass of a hydrogen atom;
• extended calculations, like estimating the number of people who have ever lived;
• representing time scales from the dawn of time in an imaginative way, illustrating famous events;
• researching the life spans of 50 well-known animals and presenting the results;
• investigating the study of mathematical patterns and their impact on society;
• studying ways of estimating the size of crowds at events, such as concerts, sports fixtures and demonstrations;
• investigating the effect of sample size on the accuracy and reliability of statistical information.

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Impact

Although the preparation and delivery of the presentations took time, it resulted in some very stimulating question-and-answer sessions. A number of the students gained confidence from their presentations and enjoyed the teamwork involved in a pair presentation.

The school found that there is no limit to the topics that could be chosen. The most able students were able to:

• show their originality of thought;
• in some cases, impart their enthusiasm for the subject;
• use a variety of methods to obtain their findings, with a good explanation of what they were doing;
• leave no stone unturned in their quest for truth and accuracy;
• enjoy playing with the results and making sense of them;
• show great precision in their measurements or calculations;
• create and test their own hypotheses.

The best students showed a repertoire of high-level intellectual skills. Others were then able to recognise some of these skills in themselves, which proved inspirational.

The overall outcomes included:

• more stimulating mathematics lessons;
• happier, more focused teachers;
• better GCSE results in the subject;
• a substantial increase in numbers entering the sixth form to take AS/A level Mathematics;
• early indications that the first cohort are interviewing with more panache at universities.

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