Milad Khajapoor

Every student I work with will be asked to complete a short diagnostic test that I have personally designed. This isn’t a traditional exam, and it’s not about getting every question right or wrong. Instead, it serves as a starting point, a valuable tool that helps me gauge each student’s current level of understanding, problem-solving approach, and overall confidence with the material. I pay close attention not just to the answers, but to how they arrive at those answers, which gives me insight into their thought processes, reasoning strategies, and any common misconceptions they may have. This allows me to identify both their strengths and the specific areas where they may need extra support or practice.

Using the results of this initial assessment, I then create a tailored learning plan that is adapted to the student’s needs and academic goals. This plan can take the form of a weekly or even daily structure, depending on how many lessons the student would like and how intensively they wish to study. My aim is to build a solid foundation first and then gradually stretch and challenge the student as their confidence grows.

As we move forward and cover a number of topics, I will also provide follow-up tests or checkpoints. These are not meant to cause pressure, but rather to check understanding and retention of the material covered so far. They help highlight whether a student is truly comfortable with the concepts or whether we need to revisit anything before moving on. In this way, the learning process remains flexible and responsive to the student’s progress.

A typical lesson follows a structured yet adaptable format. We usually begin with a brief recap of the previous session to reinforce memory and clear up any lingering doubts. If the student has had homework, we’ll spend a few minutes reviewing one or two questions they found particularly tricky — encouraging them to ask questions and explain where they got stuck. After that, I’ll introduce a new topic or concept for the day. I break it down clearly, often using step-by-step explanations and visual examples to ensure it’s easy to follow. Then we’ll go through one or two worked examples together, highlighting important techniques or common pitfalls.

Following this, the student will attempt similar problems independently, with me guiding them when needed but gradually stepping back to allow them to develop their own approach and confidence. This practice phase is crucial for consolidating understanding, and it also gives me further feedback on how well they’re grasping the material.

The majority of my students, around 90%, are taught online. I have learners joining from all over the country, and the convenience of online learning means they can access high-quality tuition from the comfort of their own home. To ensure clarity, everything I write or draw during the lesson is displayed on their screen in real time, just like a virtual whiteboard. Students don’t need any specialist equipment, just a stable internet connection and a willingness to learn.

For A-Level students in particular, the focus goes beyond simply solving maths questions. These lessons are also about deepening their understanding of the reasoning behind each method. I place a strong emphasis on building analytical thinking and mathematical communication, helping them to explain their methods, justify their steps, and interpret the meaning behind the results. This dual focus on problem-solving and reasoning not only improves their exam performance, but also strengthens their overall mathematical mindset, preparing them for further study or application of maths in real-world contexts.