In this blog, Tolly suggests some excellent learning resources for students who are working towards their Maths A-Level whilst studying at home.
Mathematics is a subject with two key elements: the individual topic skills, and the overarching problem-solving techniques. In terms of solving a challenging top-grade standard problem, it is vital to be completely secure with the relevant basic skills. This is not because they are necessarily the challenging element of the problem, but rather if a student is allocating a significant proportion of their mental processing capacity to applying the basic techniques, they will not have much left to concentrate on the overall problem. They will end up feeling like they have reached a dead-end in the problem, struggling to see the overall picture.
The second element, the general problem-solving techniques, can be practised and developed just like any other skill. This needs to happen over time, learning which techniques work well for which types of problems. This is where a teacher can have a huge impact on the development beyond what they can self-learn, as the teacher can make those lines of thought explicit and they can model the problem-solving process for the student.
When you look back at a previous level of mathematics it looks so simple. An A-level student will look back at a GCSE paper and wonder why they found it so challenging. This is not necessarily because they have become a dramatically better mathematician since, but rather because they have become much more familiar with applying those basic skills when using them alongside the more advanced A-level processes. The key to preparing for an A* (or equivalent) at any level is to mimic this process. A student should not just be practising previous A* questions, they should be applying their knowledge to more advanced problems, which in turn makes the A* questions seem relatively elementary in comparison.
Dr Madas has provided a wonderful service to mathematics education by providing the resources on this website. There are packs of original questions sorted by topic which are graded by difficulty, and the more challenging questions really do help to develop the necessary skills. He has also provided sets of original A-level practice papers which are generally challenging, which have a fantastic quality of question, and he has provided useful worked solutions for all of them.
These are positioned in difficulty just above the A-level A*, and requiring the same content knowledge, making them ideal practice material. These are available on their website.
These are the Oxford University mathematics entrance test papers. They only require basic content, but the questions are more challenging than A-level questions.
These are the entrance tests which are used primarily by Cambridge University. These generally only require A level Mathematics knowledge, but they are great for developing problem solving skills.
These archived papers are fantastic for the new A-level syllabus, offering practice questions which contain a lot of contextual and modelling-related examples.
This was a project that aimed at creating resources to help develop problem solving skills and deeper understanding in A-level mathematics.