Multiple Representations

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Why it works

Research, especially in mathematics and science education, shows that representing a concept in multiple forms, concrete or physical, visual or graphical, symbolic or numerical, and verbal, and crucially helping students connect and translate between them, builds deeper, more flexible, more transferable understanding than any single representation. Each representation highlights different aspects; moving among them reveals the concept more fully and supports different learners. The key is not just showing multiple representations but explicitly connecting them, so students see they are the same idea in different forms, which is where deep understanding lives.

The research: Research on multiple representations in math and science.

The run-of-show

Choose your slot. The agenda, timings, and length update to match.

The core activity: represent a concept multiple ways, and connect them

Teachers leave with a concept represented multiple ways and explicitly connected.

Pick a concept students grasp shallowly.
Represent it in multiple forms (concrete, visual, symbolic, verbal).
Explicitly connect and translate between the representations.
Help students see they are the same idea in different forms.

Multiple forms, explicitly connectedA concept understood one way is shallow. Represent it concretely, visually, symbolically, and verbally, and explicitly connect the forms, where deep understanding lives.

Facilitator notes

Use multiple representations, and explicitly connect them.
Each highlights different aspects.
Connection is where understanding forms.

One representation gives shallow understandingA single representation reveals only part of a concept. Use multiple forms and explicitly connect them to build deep, flexible understanding.

Adapt it

Elementary: concrete, visual, verbal, connect.
Secondary: symbolic, graphical, verbal, concrete, connect.
All settings: multiple forms, explicitly connected.

Participant handout

One page for every teacher. Print it, or save it as a PDF.

K12 Academics · Professional Learning

Multiple Representations: connect the forms

Deep, flexible understanding: concrete, visual, symbolic, and verbal forms, explicitly connected as one idea.

The concept students grasp shallowly:
The multiple forms I represent it in (concrete, visual, symbolic, verbal):
How I explicitly connect and translate between them:
How I help students see they are the same idea:
A concept to represent multiple ways:

Make it stick

Connect the forms:

Use multiple representations.
Connect them explicitly.
Bring a concept you taught multiple ways to the next PLC.

Common questions

Isn't one clear representation enough?

One representation gives a partial, shallow grasp. Representing a concept in multiple forms, concrete, visual, symbolic, verbal, and connecting them reveals it more fully and builds flexible, transferable understanding.

What are the forms?

Concrete or physical, visual or graphical, symbolic or numerical, and verbal. Each highlights different aspects of a concept; moving among them deepens understanding.

What's the key move?

Explicitly connecting the representations, helping students see they are the same idea in different forms, not just showing several. The connections are where deep understanding forms.