From Imaginary Numbers to Collapsing Bridges: Encouraging Year 11 students to consider taking Further Mathematics A level

Thursday 14th November 2019

Long ago, there was the Further Maths Network. Then there was the Further Mathematics Support Programme. Now there is the Advanced Mathematics Support Programme

The organisation has changed and evolved over time, but one thing has remained the same: our commitment to encouraging more students to see the interest and value inherent in the Further Mathematics A level qualification. Although it is increasingly challenging, in the current climate of ‘3 A levels’, to sell the case for two of those A levels to be maths, nevertheless entries have more or less held up, and students and schools continue to choose the subject in good numbers. Universities value the qualification and undergraduates regularly report on the relevance of Further Mathematics to their 1st Year studies.

To encourage students to continue to think in these positive terms, I make a point of visiting schools in my region as often as possible to work with students and teachers. In any presentation, I always include some brief factual messages about how Further Mathematics can help with the study of a range of undergraduate courses, and how Further Mathematics can contribute to students’ wider appreciation of maths in all its manifestations. But above all, I want students to experience Further Mathematics, rather than hear about it. 

To this end, I regularly use an hour-long activity that involves complex numbers and their place in the Further Mathematics curriculum and more widely in maths, science and engineering. Many, many presentations have been given extoling the virtues of these magnificent numbers. However, it is perfectly possible for students to experience their many intricacies for themselves, armed only with the property \(i^2=-1\). The algebra is straightforward; iterating and graphing points is elementary with the ClassWiz and (optionally) a graph-plotter. And when students see the finished version of their work (courtesy of my colleague Ben Sparks’ wonderful animation of the Mandelbrot Set) their mouths drop open. It is a winner every time. And it’s a short step from there, via an oscillation equation, to the spectacular video of the collapsing Tacoma Narrows Bridge.

If your school is interested in the AMSP working with your students to promote post-16 pathways, please get in touch.

By Martin Bamber

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