Wojciech Kowalczyk

The focus is on the very first lesson. The student is provided a diagnostic test (based on what they are studying; GCSE, A level maths, further maths and their modules etc). They are given a mid range difficulty question for each topic they should know. For each topic, I can thus mark their ability down and write any additional notes on the way they think. From this, I will know whether this topic needs to be approached in more detail or only lightly glossed over.
After the lesson 1 diagnostics test is completed, I will ask the student what they are hoping to achieve. Whether it is to just generally improve in maths, reach a certain grade pass an interview and so forth. From this, I can then plan a full skeleton of what their lessons should look like. Of course, the tutoring does not stop once I think that they are capable of reaching their target; this is just a minimum.
To me, mathematics is not about memorising formulations; it is about understanding the material and the confidence to approach it. With these two key factors, I believe any student can do well, regardless of starting point.
During the lesson, we now use this diagnostics test and work on their weak spots in particular. Learning maths is about solving problems that are slightly above your level. This may seem difficult at first, but this is the best way to improve, but also provides immense satisfaction to learning. Too much content and you don't have experience or confidence with solving the problems. Too many problems and you fail to learn enough content. There is thus a perfect balance in both, with a large focus on problems. This way, I can see the way the student thinks, and then tell them what needs improvement. While learning is improving from your mistakes at its core, if one only experiences failure, it does not bring motivation. Thus, the student is also told what is going right.
I have been tutoring for 7 years and each student was satisfied with the result.