Definitions and problems together
Students meet concepts in the setting where those concepts are needed. This makes abstract language concrete and keeps formal work connected to purpose.
Methodology
The post-USSR method
Our lessons are built around carefully designed sets of problems that reveal a topic step by step. Instead of giving students a finished explanation and asking them to imitate it, we guide them through a route where the ideas become visible through use, comparison, and discussion.
Difficulty rises with intention
A sequence should feel climbable. Early problems establish footing, middle problems expose structure, and later ones stretch independence without turning the topic into guesswork.
Extensions are built in
Students rarely move at the same speed. Optional branches and richer variants let faster students keep growing while others consolidate the core path properly.
Discussion completes the method
The written sheet is only part of the lesson. Instructor questions, board conversations, and feedback turn the sequence into a live mathematical dialogue.
Why problems come first
Deep understanding grows when students have to act on an idea before they can summarise it perfectly. Problems force attention onto the essential distinctions: what is known, what is assumed, what needs proving, and which tools are actually relevant.
This is especially important in mathematics, where fluent language can create the illusion of understanding. Working through a sequence makes understanding visible because the student has to use it.
How the sequence is designed
A strong sequence does more than sort problems by difficulty. It chooses a route. The order of tasks should expose the shape of a topic, create opportunities for pattern recognition, and prepare the student for later abstraction.
We also use branching material. Some tasks deepen the core path; others widen it. That flexibility allows us to preserve a common lesson while still giving individual students the right level of challenge.
What instructors add
Good materials are necessary, but they are never enough on their own. Instructors decide when to intervene, when to let a student persist, which partial idea is worth developing, and how to turn a mistaken attempt into a useful step.
That human judgement is what keeps the method alive. The sheet provides structure; the lesson provides interpretation, pressure, and encouragement.
Where this tradition comes from
This approach is influenced in part by the post-USSR problem-school tradition, where mathematical culture was often transmitted through carefully built sequences, written solutions, and close discussion rather than lecture-heavy teaching.
What matters to us is not the label but the method itself: students remember ideas better when those ideas have been built rather than delivered, and over time that gives them a model for how mathematics can be learned independently.
Ready to find the right starting point?
Book a trial lesson and we will recommend the most suitable next step.