Make the mathematics clear enough to think about
Learning Through Doing is built on a simple idea: pupils are more likely to understand mathematics when they can see it, represent it, talk about it and connect it with symbols. The teaching remains explicit and purposeful, but pupils are active participants in making sense of the idea.
A close or medium shot showing pupils physically representing an idea while discussing their thinking with a teacher or partner.
- Dimensions:
- 16:9 landscape, 2400px wide minimum
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- ltd-uk-our-approach-hero-01.webp
Production note: Confirm written school and parent or carer permission before uploading identifiable pupil media.
Confirm written school and parent or carer permission before uploading identifiable pupil media.
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Start with the concept, not the worksheet
Every lesson begins by identifying the mathematical idea that needs to be understood. From there, the teacher chooses examples, representations, tasks and questions that will make that idea visible.
This keeps the lesson focused. Pupils may be busy, but the activity is never the point on its own. The point is what the activity helps them notice and understand.
Concrete and visual representations
Manipulatives and visual models give pupils a way to represent relationships that are difficult to hold mentally. A part-part-whole model can show composition. An array can show equal groups and factors. A place value chart can show the relationship between units.
Pupils should not stay dependent on equipment. The aim is to use representations well enough that pupils can connect them with language, diagrams and notation, then call on those connections when solving unfamiliar problems.
A consistent visual gallery showing ten-frames, part-part-whole models, number lines, arrays, place value tools and fraction strips. Each image should show the model being used rather than photographed in isolation.
- Dimensions:
- Six square images, 1200px wide minimum each
- Upload as:
- ltd-uk-our-approach-visual-models-01.webp
Production note: Confirm written school and parent or carer permission before uploading identifiable pupil media.
Confirm written school and parent or carer permission before uploading identifiable pupil media.
Upload guidance: replace this placeholder with the final media. Keep the same aspect ratio and recommended filename so the page layout does not shift.
Explicit teaching with active thinking
Teachers need to be clear about what they are teaching and pupils need clear explanations. Explicit teaching does not require pupils to sit passively while every step is demonstrated for them.
LTD combines teacher modelling with carefully planned prompts, partner talk and investigation. The teacher directs attention to important features while preserving enough thinking for pupils to do.
Strategy before speed
Fluent recall becomes more reliable when it grows from relationships. For addition and subtraction, pupils can use number bonds, make ten, doubles and compensation. For multiplication, they can build from known facts, use commutativity and connect multiplication with division.
Practice still matters. LTD uses repetition with variety so pupils revisit an idea through changing examples, representations and questions. This supports automaticity without stripping the practice of meaning.
Talk is part of the mathematics
Pupils refine ideas when they have to describe what they made, justify a choice or compare two methods. Mathematical talk also gives the teacher valuable information about what pupils understand and where a misconception may be forming.
The strongest questions are often simple: What do you notice? What stayed the same? What changed? How does your model show that? Is there another way? Will it always work?
Reasoning and problem solving are not add-ons
Reasoning is developed inside the lesson, not saved for a final challenge question. Pupils explain representations, predict results, test claims and make connections as they work.
Problem solving also becomes more accessible when pupils have a strong bank of concepts, strategies and representations to draw on.
Build from what pupils already know
New learning is easier to understand when it is connected with an established idea. LTD sequences lessons so teachers can activate useful prior knowledge and trace backwards when a class needs an earlier concept.
This matters for whole-class teaching and intervention. A gap is more likely to close when the underlying idea is addressed directly.
Teacher knowledge changes the lesson
The quality of a resource matters, but the teacher remains central. Knowing why a representation works, which misconception to expect and what question to ask next makes the lesson more responsive.
That is why LTD includes teacher background and professional learning alongside classroom materials.
Ready to bring Learning Through Doing into your classroom?
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