Discover
Probe prior knowledge. Ask the learner to solve and explain before offering assistance.
02 / THE PROXIMAL MATH STRATEGYThe next step
The next step
is teachable.
A strategy for discovering what a learner understands, guiding the next reachable challenge and building independence.
LEARNING THAT MOVES WITH YOU ✦
WHAT IS PROXIMAL MATH?More understanding.
More understanding.
Less guessing.
Proximal Math™ is a proposed numeracy teaching strategy drawing inspiration from Vygotsky's Zone of Proximal Development, formative assessment and responsive instruction. It begins with what the learner has demonstrated, not with an assumption about what they should already know.
A teacher then chooses a manageable next challenge, uses suitable models or questions, and gradually withdraws assistance as the learner's understanding becomes secure.
Importantly, scaffolding and the ZPD are connected ideas, but they are not the same concept; the educational framework deserves scholarly scrutiny and practical testing.
Start with something the learner understands.UNDERSTAND · PRACTISE · PROGRESSA five-stage
A five-stage
instructional journey.
Each phase serves a teaching decision, not just a task to complete.
Explore
Introduce concrete objects, visual representations and meaningful contexts to clarify the relationship.
Guide
Model useful reasoning, ask targeted questions and respond to misconceptions when support is needed.
Practise
Offer supported and independent tasks, then fade prompts as understanding strengthens.
Transfer
Check whether the learner can apply the idea to unfamiliar numbers or situations independently.
A TEACHING EXAMPLEFrom one quarter
From one quarter
to new reasoning.
First, a learner shows one quarter of 12 counters independently. The teacher asks them to form four equal groups and explain the grouping. If that idea is secure, the teacher introduces three quarters of 12, offering a timely clue only if needed.
The learner then practises with other quantities, gradually moving from counters to diagrams and symbols. A new problem, such as three quarters of 20, checks whether the relationship can be used without a prompt.
12 ÷ 4 = 33 × 3 = 9¾ of 12 = 9
Explore a worked demonstration ↗
Visual → verbal → symbolic → independent.THE STRATEGY IS THE INTERVENTIONIt does not need
Discuss an institutional pilot ↗
It does not need
a new device.
Print, counters, manipulatives, group discussion, teacher explanation and digital displays can all support the approach. A pilot would test feasibility, competence, learner engagement and transfer—not assume results.
Discuss an institutional pilot ↗