# Learning from Kings

Karenann and I were excellently hosted by Dan, headteacher at Kings College Maths School. Every student studies Maths, Further Maths and Physics at A level.

• Every lesson is designed around the principle “Don’t tell the students what to do”. We teach through discussion and questioning. We only break this principle in interventions. Interventions are timetabled in, happen after assessments, and are there to quickly support students.
• While every lesson will involve problem-solving, we also dedicate a session a week specifically to problem-solving. PHD students come in and help run them, we give far less guidance, and focus on encouraging students to fail, to keep on failing, to tenaciously strive for a solution. No lesson objectives, no rush.
• Students are assessed by their teachers on core study skills – collaboration, communication, independence and organisation. Interventions (for example go to board-games club to improve collaboration) are put in place.
• Teachers have a weekly planning meeting, to skill-up those who are new to the Maths, and to ensure teaching is consistent and high-quality.

How do we support the transition from GCSE to A level?

• It is not true that all our students, even though we are a specialist Maths school, are ready for A level. They might lack study skills (see above), might think of maths as a subject where they can easily find “the right answer”, or might have some subject-gaps.
• We start with a topic that is new and impressive, but that also will enable the basics (algebraic manipulation) to be covered. Complex numbers works well – requiring expanding brackets, collecting like terms, while also being something that none of the students will have seen before. Recapping completing the square pales in comparison.
• Students find mechanics particularly hard. This is due to a difficulty separating intuition about forces from the formal modelling. For example, reaction force is equal and opposite to the weight of an object lying on the floor, but this is nothing to do with Newton’s Third Law of Motion.
• Early interventions are key

Lesson Observation: Yr13 Mechanics

Essential Question: “When I push a block, will it slide or topple?”

• 30 minutes of teacher-led exploration of the question. 20 minutes of applying the broad techniques to unfamiliar contexts. The students could have been given the question and nothing else. However, in this lesson the content had to be covered quickly, so more teacher-leading was necessary. Dan guided us through, with constant questioning and time to reflect, talk to each other, and predict. Pacy but still involving students and ensuring we all thought deeply.
• Repeated links to intuition and the physical example (we all had blocks to play with).  “What do you think it might depend on?” , “Intuitvely, should it depend on mu?”, “Translate this into english please”,  “I feel that…”, “Think about the point when it is just starting to happen”. Conscious effort to hone and improve intuition.
• The most difficult part about the lesson was the logical structure.
• If I assume that the block slides, then…
• If I assume that the block topples, then..
• Teacher quickly assesses work on whiteboards. Nothing really written down formally, no huge emphasis on taking good notes. Focus is on the group collectively thinking deeply together.

Counterintuitively, whether the object will slide or topple is not dependent on height of block or mass of block.

Lesson Observation: Yr12 Matrices.

Lesson focus: to use matrices to solve simultaneous equations.

• Excellently clear link between prior knowledge and new method. Students unconvinced for the need for matrices to solve equations that they already have a method for. A possible opportunity for technology here: matrices can solve simultaneous equations in three variables, and an app can split out the inverse (useful if you don’t know how to invert big matrices yet).
• Teacher completes problems on board while students complete on A3 “mini”-whiteboards. Deliberately supportive culture for a class that finds maths hard.
• Usefully uncovered misconceptions – you can divide by a matrix, and matrices commute.

Thank you so much to Dan and Kings Maths School for hosting our visit! We are excited to think how to use some of the exciting things we saw here next year at Six21.