Quillino is built on three long-standing ideas in math education: how children learn a concept (Concrete → Pictorial → Abstract), how they solve a problem once they’ve learned it (Polya’s four steps), and how a tutors guide students when they get stuck (the Socratic method).
CPA.
Concrete → Pictorial → Abstract
Children grasp a concept first by handling it (concrete), followed by seeing it in picture format (pictorial) and finally, working with words and symbols (abstract). Quillino’s visualisations bring math textbooks to life, allowing students to see and learn how math works in real life.
Polya’s four steps.
Understand → Plan → Solve → Check
Many students are able to solve pure math questions but freeze when a question is wrapped in a story, which MOE syllabus commonly asks. Quillino’s AI tutor and word problems are guided by Polya’s four steps, Understand, Plan, Solve, Check. Where students practice breaking down a complex problem.
The Socratic.
Ask → Think → Reason → Discover
When a student is stuck, Quillino’s AI tutor doesn’t hand over the answer. One that gets them unstuck. Students learn by reasoning their way through, not by copying a worked solution, so understanding sticks when they are given a different question which requires the same concepts.
The CPA approach is grounded in Jerome Bruner’s research on how children learn. Polya’s four steps come from George Pólya’s How to Solve It, the book most modern math heuristics trace back to. The Socratic method, teaching by guided questioning, traces back to Socrates and underpins how good tutors have worked one-to-one for centuries.