We have a particular affinity for curious students.
We design our programmes to engage them in deep conceptual exploration.
But aren't all children curious?
Children are curious in general. But staying curious in a classroom can be difficult.
Curiosity has a window of opportunity
Asking questions is a skill that needs practice. It is easier to ask when the ideas are still simple.
Much later, when ideas have become entangled with each other, a student may not even know what to ask or how to ask it.
Even when they can frame the question, a proper explanation may depend on earlier ideas the student does not understand, leading to more questions further and further back.
At that point, pursuing the question in class may no longer be productive.
Catching up competes with keeping up
Curiosity often reveals gaps in our previous understanding. But classrooms have to move forward. There is a syllabus to cover, a test next week, an assignment due. There is rarely enough time for students to pause and investigate those gaps, because that takes time away from what they are expected to learn now.
Mental acrobatics can work well in exams
Self-motivated students may sometimes keep up by memorising procedures, recognising examination patterns and learning to apply the “right” rules.
Very talented mental acrobats can go surprisingly far through the syllabus this way. But to us, that can still feel a little hollow. It is like someone who is very good at talking to strangers, but rarely takes the time to turn some of those encounters into deeper relationships.
Survivorship bias behind mental acrobatics
Students differ in their ability to manipulate abstract rules without fully understanding what lies underneath.
Those with particular talent for this kind of mental acrobatics can navigate many examinations successfully by memorising steps, recognising patterns and cleverly using plug-and-chug methods.
When we see these students succeed, it can appear as though curiosity and deeper understanding were never necessary.
Despite all this, some students stay curious
When a student with high ability is also curious, their curiosity may not conflict strongly with progress. When necessary, they may perform mental acrobatics to keep up. But they still have enough capacity to wander and explore questions. Often, they can also postpone a question without losing their curiosity.
However, a curious student may not have high ability. When their attention is drawn towards something they want to understand or explore, they may lose pace with the lesson and fall short of expected benchmarks in checkpoint exams.
What to expect from our lessons
We take pride in creating the best lessons we can for students who need greater breadth and depth.
More than mental acrobatics
We model what it looks like to treat mathematics as something that can be understood, questioned and connected, rather than just a set of mental acrobatics.
For some students, this can be a refreshing view of the subject.
Understand enough to keep going
Some students, by habit or necessity, will gravitate back towards mental acrobatics.
We do not insist that they understand every detail before moving on. Instead, we help them build a working "vocabulary" of ideas they understand well enough for mathematics to remain a coherent story.
Growing into the kind of student who can be confident in math
We curate problems that students can solve by creatively using what they already know. When they get stuck, we negotiate how much help to give and strategise with them about what to try next.
When learning a new topic, we also explore how its anchor problems can be worked out from first principles using ideas from previous topics.
Customised curriculum for individual progress
We allow students to accelerate when they are ready, and slow down when something underneath needs strengthening. Whether accelerating or catching up, our approach is the same: start with the simplest idea the student does not yet know.
School curriculum support
Enrichment is not always the immediate priority.
When schoolwork requires more attention, we may temporarily put broader exploration aside to catch up, strengthen foundations and address gaps.
Problem-solving and Math Olympiad
How do people who are naturally strong at problem-solving approach unfamiliar problems? Our benchmark is whether, over time, our students' approaches become less distinguishable from those of naturally strong problem-solvers.
We use Math Olympiad problems as a training ground for this.
For our purposes, competency at around the lower-secondary competition level is often enough to support future curiosity, goals and academic demands.