I recently received an enquiry from a client asking for tuition for the King's Scholarship at Eton College. He had some specific questions including:

• whether you would recommend an initial diagnostic assessment;
• how you would distinguish between syllabus gaps, lack of fluency and deeper problem-solving weaknesses;
• what you would envisage focusing on during the first six weeks;
• your recent experience specifically preparing pupils for Eton King’s Scholarship Mathematics

Here's my response:

• An initial diagnostic assessment is always useful. If you don't want to waste lesson time, we could have your son complete a baseline test (usually a 13+ CE paper) which we can then review during our first session to establish any particular areas for attention beyond the concepts and topics you have already identified.

• How I distinguish between syllabus gaps, lack of fluency and deeper problem-solving weaknesses: in a sense, this is the most important thing that takes place during the sessions.
  • I will have your son complete a series of exercises (steadily building in complexity from a suitable baseline level up to KS past papers in the time immediately before the exam) in between sessions.
  • We can then start each lesson by reviewing any mistakes or omissions (and any other questions that he may have about the paper) and then practice similar questions together.
  • Much of the analysis comes from looking at a student's working (both written down from homework and emerging in real-time during sessions) and from conversation with the student: from something as simple as "have you covered this topic at school?" to more searching questions about problem-solving strategies etc.
  • My approach during the lessons tends to be to determine and offer the minimum prompting required by the student in order to complete the problem and to note any patterns in support required (e.g. particular topics or question formats, any common pitfalls etc.)

• Focus during the first six weeks, I expect would be on the topics you've identified plus any problems identified in the initial assessment. Starting from a baseline 13+ CE level and moving up to more challenging problem-solving questions as appropriate.

• Over the past ten years, I have taught, I believe six boys for Eton KS, four of whom gained a scholarship plus one Proxim Edit. Also, several boys for similar scholarships such as the Westminster Challenge, Winchester Election & St Paul's John Colet Academic Scholarship (actually, the most recent student was already so well-versed in the St Paul's papers that we spent most of the sessions tackling Eton Maths B papers to challenge him!)