Learning Science · Reading, representing and explaining
Text, diagrams and symbols as complementary tools
Choose representations for the relationships they make visible and explicitly connect their meanings.
Use the examples to connect this lesson with the earlier topics. No specialist equipment is needed.
Back to the chapterAfter reading, you can
- Explain complementary roles for prose, diagrams and symbols.
- Translate between representations without changing quantities or conditions.
Three ways to express the same relationship
A journey can be described in words, listed in a table, or represented by a graph of distance against time. Prose can state conditions: the traveller maintains a steady speed during this interval. A table gives exact recorded pairs. A graph makes a pattern visible. A formula can express the relationship compactly across many possible values. Each format supports some questions more directly than others.
A diagram is not automatically understandable because it is visual. Learners must know what its lines, arrows, positions and labels represent. An arrow might mean movement, force, sequence or causation. Read its meaning from the legend and surrounding explanation, rather than from appearance alone. Symbolic notation also requires introduction: in d = vt, d is distance, v is constant speed and t is elapsed time.
Map the correspondence
Choose one specific case and locate it in every representation. At constant speed 3 metres per second, a 4-second journey covers 12 metres. Find the pair (4, 12) in the table, the corresponding point on the graph, and the substitution 12 = 3 × 4 in the formula. Mapping one case makes abstract correspondences inspectable.
Then identify what remains constant and what changes. On a distance–time graph, a steeper straight line means a higher constant speed, rather than a taller hill. Confusing the drawn line with a picture of the route is a representational error. Text can prevent that error by saying precisely what each axis measures and why slope represents the relevant rate.
| Elapsed time (s) | Distance (m) | Correspondence |
|---|---|---|
| 0 | 0 | d = 3 × 0 |
| 2 | 6 | d = 3 × 2 |
| 4 | 12 | d = 3 × 4 |
| 5 | 15 | d = 3 × 5 |
The same constant-speed journey
Add a format only when it serves a purpose
Research frameworks for multiple representations emphasise their functions and the work learners must do to interpret and connect them. Offering many formats can create extra tasks, especially when links are left implicit. Start with the formats needed for the learning goal and teach how they correspond.
Check accessibility as well as correctness. A colour-only distinction can disappear for some readers; labels and line patterns preserve meaning. A written equivalent can describe an essential spatial relationship for a learner who cannot inspect the image. The representation should reduce unnecessary search while retaining the quantities, assumptions and uncertainty that matter.
Worked example
A tank represented three ways
How do a tank’s words, values and formula preserve the same conditions?
- A tank starts empty and receives 2 litres per minute with no outflow. The text states those assumptions. A table records 0 minutes/0 litres, 1/2 and 3/6. The formula V = 2t expresses volume V in litres when t is in minutes. A straight graph through these pairs would show a constant rate.
- If the tank initially contains 5 litres, the formula becomes V = 5 + 2t, and the graph starts at 5. If there is outflow, the original relationship may fail. Translation must preserve these conditions; reusing the first graph after changing the story would communicate a different system.
Keep initial volume, units, rate and outflow assumptions attached to every representation. Changing a condition changes the relationship, not just its wording.
Tank values preserve the stated conditions
Try it yourself
Think through each question before opening the answer.
Why is an unlabelled rising line insufficient to show learning over time?
Show the answer and reasoning
The axes, units and measurement are unknown.
It could show performance, cumulative attempts or something else; shape alone cannot establish the claim.
At 3 metres per second, what distance corresponds to 5 seconds?
Show the answer and reasoning
Fifteen metres, assuming speed stays constant.
The table entry, graph point and formula substitution should all express that same pair.
When would a table be preferable to a diagram?
Show the answer and reasoning
When comparing exact values or categories is the central task and spatial layout adds little.
Choose the form by the relationship to be inspected.
What to carry forward
- Teach the code of a representation before expecting interpretation.
- Use explicit correspondences when combining formats.
References
Sources supporting the explanations and learning checks in this lesson.