Summer Intensive · Ages 13–15 · 2026
Reasoning tools to navigate uncertainty.
A six-week summer programme that teaches 13, 14, and 15 year olds the reasoning tools — mathematical and verbal — that allow them to think clearly, model accurately, and act with confidence.
Reserve a placeThe Central Idea
Everything we learn is an attempt to reduce uncertainty.
Every body of knowledge humans have ever created — mathematics, science, language, logic — is an instrument for modelling the world accurately enough to act within it well. This is what the programme teaches: not mathematics as a school subject, but reasoning as a survival capacity.
Students who leave this programme will be able to look at an unfamiliar problem — mathematical or verbal — and construct a path through it. Not by retrieving a memorised procedure, but by reasoning from the tools they have built.
Curriculum
Four interconnected
domains.
Not separate subjects. Four instruments for the same underlying act — building accurate models of the world and reasoning from them.
A flexible, intuitive relationship with numbers at every scale — including the ones that feel uncomfortable. Numbers become navigational tools.
- The number line as a navigational instrument
- Benchmark fractions and percentages
- Decimal and fraction fluency
- Mental benchmark construction
- Min-max and trend reasoning
The visual and structural instruments for representing the world — grids, sets, truth tables, equations — shown visually before being expressed symbolically.
- Grids: visualising percentages and fractions
- Overlapping sets and Venn diagrams
- Truth tables and conditional logic
- Equations as models of real relationships
- Introduction to Bayesian reasoning
Reading and understanding at the level of structure — not just what a text says but how its ideas are connected and what they imply.
- Premise, conclusion, and argument structure
- Cause and effect as an explanatory framework
- Plan and outcome reasoning
- Reading for visual recall and situation modeling
- Identifying common logical fallacies
The integration of all four tools in service of the real challenge: making sound, time-bound decisions when the information available is incomplete.
- Reasoning under time constraint
- When an observation is informative and when it is not
- Metacognitive strategies: knowing when you understand
- Applying Bayesian intuition to real problems
- Structured problem-solving across all domains
Outcomes
What students will have built.
A flexible relationship with numbers at every scale — integers, fractions, decimals, percentages — including the ones that previously felt uncomfortable or illegitimate. Numbers stop being obstacles and become tools that serve the analysis.
Cause and effect. Benchmark construction. Systematic elimination. Premise and conclusion. Plan and outcome. These are structures of thought that transfer across mathematics, sciences, essay subjects, and real decisions.
The ability to construct an accurate mental representation of a described situation — a grid, a number line, a diagram, an equation — rather than processing language at surface level only.
Students will know when they understand something and when they are approximating understanding. They will have specific strategies for identifying where their reasoning breaks down.
The capacity to remain engaged with a problem that does not immediately yield — to keep reasoning rather than guessing or withdrawing. One of the most valuable capacities a student at this age can develop.
Academic Preparation
The foundation for what
comes next.
The programme is not designed as examination preparation. It develops something more valuable: the reasoning capacity that all formal examinations are designed to test.
International Baccalaureate
Theory of Knowledge, Mathematics, Extended Essay
The IB rewards structured reasoning, argument analysis, and movement between abstract frameworks and concrete evidence. These are exactly the capacities this programme develops.
SAT / PSAT
Math, Reading and Writing
The SAT Math section is fundamentally a test of number sense and proportional reasoning — not calculation. The Reading section tests argument structure and inference. Both are core to this programme.
General School Performance
Mathematics, Sciences, Humanities
Students who understand mathematical structure rather than memorising procedures perform more consistently across all subjects and retain knowledge across the academic year.
The Osprey Principle
“Even animals know to act only on informative observations — to follow the bird that returns with a schooling fish, not the one that returns with a flounder.”
When a fishing osprey returns to the nest with a herring, other ospreys will retrace its flight path in search of more. When it returns with a flounder, they will not. The herring is informative — herrings school. The flounder tells you nothing about what else is nearby. Even animals minimise uncertainty through learned pattern recognition. This programme teaches the human equivalent — with far more powerful instruments. The osprey acts on structure. So should we.
The Instructor
A decade spent identifying what actually makes the difference.
The programme was built by Ayham, who has spent more than ten years teaching reasoning to students preparing for the GMAT, GRE, and SAT. His students now study at Harvard, Stanford, Chicago Booth, Berkeley, and Duke, among other leading institutions worldwide.
Much of that work has been with two specific kinds of students: non-native English speakers and students who lacked a solid foundation in math. Helping them perform in timed tests allowed Ayham to identify — with unusual precision — the set of reasoning levers that separate a student who freezes on an unfamiliar problem from one who works through it.
He holds a Bachelor’s in Electrical Engineering from Queen’s University in Canada, and an MBA from IESE Business School. That combination shaped his conviction that mathematical rigour and clear verbal reasoning are not separate disciplines but two expressions of the same underlying capacity — the one this programme is designed to build.
Drillzy exists to ask a simple question: what happens when those reasoning levers are taught not at twenty-five, when habits are already set, but at thirteen — when a student’s relationship with thinking is still being formed?
Reserve a place
Spaces are
limited.
Express your interest and we will be in touch with full programme details, scheduling, and next steps.
All enquiries receive a personal response within 48 hours.