Pedagogy in Action
Diffy Squares
This interactive experience offers one small glimpse of the kind of mathematics The Number Garden wants to cultivate: playful, surprising, rigorous, and genuinely worth thinking about.
Why This Task
A mathematical gem with real room to grow.
Diffy Squares begins with an accessible rule, but it does not stay simple for long. Learners are invited to notice structure, make predictions, and ask whether what they are seeing is accidental or necessary.
That combination matters to me. It is not mere entertainment, and it is not worksheet advancement. It is a problem with enough beauty and depth to sustain genuine inquiry.
Interactive
Try the experience here.
You can open Diffy Squares inline here as part of the About story, or open it on its own page if you would rather give it more room.
Diffy Squares interactive
Start with four numbers, follow the pattern, and see what begins to emerge. The experience includes guided interaction, animated transitions, and room to experiment.
For Parents
What this demonstrates.
Lower floors, higher ceilings
A child can begin with simple arithmetic and pattern recognition, then move toward deeper questions about structure, inevitability, and proof.
Rigorous play
The task feels playful, but it asks the learner to make sense of what is happening rather than merely perform a procedure.
Learning by doing
The mathematical idea is not delivered from above. It emerges through the learner's own noticing, experimenting, and explanation.