Evidence before labels
Describe what the learner did, said, represented, or checked before making any interpretation.
LEARNING PHILOSOPHY
Do not rush to answer.
Stay with the thinking.
WHYLO treats mathematics as a connected practice of understanding, fluency, strategy, reasoning, representation, and reflection. Every interaction is designed to reveal one useful piece of that practice.
WHAT DID YOU NOTICE?HOW DO YOU KNOW?CAN YOU SHOW IT ANOTHER WAY?
SIX DESIGN PRINCIPLES
The rules we use when making every lesson.
These are product rules, not marketing lines. A feature that conflicts with them should be changed or removed.
Understanding and fluency together
Accurate, efficient calculation matters. So does knowing why a method works and when to use it.
Explanation is part of learning
A learner’s words reveal connections that a final answer alone cannot show.
More than one representation
Objects, diagrams, tables, equations, graphs, and speech each make different relationships visible.
Challenge without overwhelm
Make a task smaller, switch the expression mode, or pause—without turning support into a judgement.
Human-centred AI
AI asks and organises evidence. It does not diagnose, rank, or replace the learner, family, or educator.
A STAGE IS NOT A GRADE
Five depths of thinking, flexible by concept.
Age helps recommend a first experience, but observed thinking decides what kind of question should come next. A learner can be at WHYLO 4 in data and WHYLO 2 in fractions without either being a failure.
Explore
Notice quantity, shape, pattern, and change through concrete action and simple language.
Connect
Show one idea in more than one way and connect strategies and representations.
Apply
Carry a relationship into an unfamiliar everyday problem and check whether it still holds.
Reason
Build a model, compare alternatives, and justify a decision with mathematical evidence.
Argue
Test assumptions and limitations, revise a model, and defend a conclusion.
Movement rule
Do not move a learner because of one correct answer. Look for the idea again in another context, representation, or day.
THE SHAPE OF A LESSON
A short cycle that leaves room to think.
Discover
Begin with a story, object, pattern, or decision worth making.
Explore
Try a method before receiving an explanation.
Explain
Name the relationship in the learner’s own language.
Extend
Change one condition or compare another strategy.
Apply
Use the idea in a practical situation or create a new problem.
WHEN A LEARNER IS STUCK
Wait→Offer one small hint→Change representation→Pause or finish successfully
WHAT AI MAY AND MAY NOT DO
The AI is bounded on purpose.
A fast answer generator is not the goal. The AI should create room for the learner’s thinking, then organise only the evidence actually present.
AI MAYAI MAY NOT
Ask one age-appropriate follow-upReveal the complete answer immediately
Refer to a strategy visible in the responseInvent intent, emotion, or understanding
Record observable evidence for the next lessonDiagnose ability, intelligence, attention, or health
Suggest a smaller step or another representationLock a learner into a permanent stage
Admit uncertainty and return to the taskPretend confidence when evidence is weak
FROM PRINCIPLE TO PRACTICE