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 that 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.
When watching a series, it seems like common sense to start from the beginning and watch at our own pace. But in a classroom, students don't always have that choice.
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, learning without deeper understanding can still feel a little hollow. It is like someone who has a knack for socialising — funny, engaging, easy to talk to — but has not often turned those encounters into deep and genuine friendships.
Survivorship bias behind mental acrobatics
But students differs 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 — especially if we overlook those who struggle with the same approach.
When deeper exploration is not welcome
For some students, opportunities for deep conceptual exploration are music to their ears. But for various complex reasons, not every student welcomes them.
The paradox of motivation
When students have examinations to prepare for and a syllabus to complete, deeper exploration can feel like a distraction from more immediate goals.
For some students, we may only have the opportunity to engage them in deeper exploration after major examinations, such as the PSLE or O-Levels.
But this creates a narrow window of opportunity.
When examinations are approaching, students may be highly motivated to study, but reluctant to explore beyond what seems immediately useful.
When examinations are over, they may finally have the freedom to explore, but their motivation to attend additional lessons may diminish.
Despite all this, some students stay curious
It is easier for a student with high ability to stay curious. When necessary, they may perform mental acrobatics to keep up. But they still have enough capacity to pursue questions that interest them. 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 struggle to keep pace with the lesson and fall short of expected benchmarks in checkpoint exams.
Our affinity for curious students
Our founder, Mr Lim, was himself a curious student. But at the time, his abilities were not sufficient to satisfy many of his curiosities and goals.
He knows what it is like to have questions and goals that exceed one's present abilities.
While School of Mathcraft now caters to students with a wider range of profiles, our central focus remains the same: helping students learn, think and explore mathematical ideas deeply.