"It's so difficult to improve in A level math"
THe following are some barriers to achieve a better grade in A level Math:
1. Missing "link" between theory and problem solving
Based on my past experiences, there are students who can "memorise and recite" theories and formulas very well, but they are clueless when it comes to applying them for problem solving on their own.
Even in school, the focus will be on explaining the provided solution. Hence the crucial part of how to interpret the question and devising a plan before solving could be missing.
2. Misconception: Getting A = "DRILL & DRILL"
A significant portion of students adopted "memorise and drill" approach to get A1 or A2 for O level Mathematics but will soon find themselves "stuck" at D or E grade for A level, no matter how hard they drill and practice.
This is because A level questions are not all routine and a number of questions require students to solve a problem using "non-routine" methods. This means that students have to think how are the various parts of a question are linked together. In fact, students who do not follow the question's instructions and use "routine methods" may end up scoring 0 for that question.
In fact, some students just memorise the steps to solve certain problems and have no idea on what they are doing. Hence, they will face problems when the question is modified slightly.
3. Dependent on answers provided by others
Nowadays it is very easy to source for answers by asking people to help solve math problems. This has a negative impact on grades as students are dependent on answers being spoon-fed to them. Ultimately, examination is all about self survival, so students should "crack their brains" to solve math problems.
It is a painful and slow process to come out with own solution but this is the training that A grade students go through to earn them that grade.
4. Unhealthy Revision methods
It is common that students face the problem of "short term memory" due to the fast pace of teaching in school and the lack of consistent practice. Many students will only revise a particular topic when a test is near and often realise that they fall into the cycle of always have to start from scratch. Hence they find it difficult to make a breakthrough since time is spent on "recovery" rather than "improving".
It is very common for schools to provide topical revision to prepare students and students who do topical practice only tends to perform poorer than students who prepare through mock exams. Here's why:
Suppose there are 22 topics to revise and 1 week a student covers 5 topics (which is alot), hence the student will need more than 4 weeks to cover the syllabus. However by the time the student reaches the 22nd topic, it will be more than a month ago since the first topic has been revised, so the "short term memory" problem kicks in and the student will need to restart the vicious cycle again.
The students lack the skill to identify the topic that a question is testing because it is written in the topical revision package while it is not written in the exam paper.
Doing questions in the same topic repeatedly, students will find the later questions easier as they are similar to the questions at the front. However in exam, many topics are only tested once and students will need to get that question correct at the first try.