7th October 2010 9:00
By Blue Tutors
One of the first things new tutors learn is that with one-to-one tuition students generally ask many more questions than you would expect them to in a lesson at school. Obviously this is because students tend to feel much more confident when sitting with their tutor, than in a classroom with 20-30 of their peers. However, it’s common for tutors to begin to notice something about the way that students are taught, and it creates criticisms about the way that many modern qualifications are laid out.
We’re going to look at the Maths A-level specifically, but that shouldn’t deter non-maths tutors from reading this article, because it applies to many subjects, and hopefully it won’t sound too technical.
Something introduced very early on in the Maths A-level is the exponential function. This is a number, e ( = 2.7181....) set to the power of x (ex). Now this isn’t a particularly complicated idea, by A-level students are used to using powers, and although e2 is quite a difficult calculation to do on a piece of paper, generally students are happy with their understanding of the idea, and can work out different powers of e on their calculator. However, a real concern is that A-level Maths students are never told where this seemingly arbitrary value of e (2.7181...) comes from. They’re just told what it is, and are asked to begin using it in calculations.
Another early concept in C1 (core mathematics 1) is differentiation, and differentiation can help students to understand where the exponential function comes from, but it’s not until C3, which most students are taught roughly a year after learning about e and differentiation, when students are told why the exponential function is special.
Very simply the exponential function is the only function where the rate at which it’s changing is equal to the value of the function itself (it differentiates to give itself). This is a relatively easy thing to explain to a student, and yet the examination boards have considered it reasonable to ask students to accept certain ideas with no explanation. It also constrains school-teachers to teach in the order the examining boards use, because of the modular nature of the Maths A-level.
One of the lovely things about being tutors is that we can take time to tutor ideas and concepts which are so often taught poorly at school, and this will help our students to understand their subject properly – not simply understand well enough to tick boxes in an exam.