Learning Science · Using knowledge in a new situation
Recognising when prior knowledge is relevant
Find the relationship that makes earlier learning useful in a new problem.
Use the examples to connect this lesson with the earlier topics. No specialist equipment is needed.
Back to the chapterAfter reading, you can
- Separate possessing knowledge from recognising its relevance.
- State the condition that permits a method to transfer.
A familiar method in unfamiliar clothing
A learner can calculate the unit price of rice but does not think to compare the cost per usable page of two printer cartridges. The quantities look different, yet both comparisons divide a total cost by an amount obtained. Knowing a method and recognising an occasion for using it are separate demands.
Retrieval needs a useful cue
A new problem must bring relevant knowledge to mind. If practice always announces “unit price”, that heading does part of the selection work. Outside the exercise book, the learner must identify the relationship from the situation. Practice should therefore include deciding whether a method applies and explaining why.
Start by describing the goal, quantities and constraints. Ask what earlier problem had the same relationship, not merely similar objects. A method may fit one part of a problem and fail elsewhere: price per page helps with cost, but says nothing by itself about reliability or print quality.
| Cartridge | Price | Estimated pages | Euros per estimated page |
|---|---|---|---|
| A | €24 | 600 | 24/600 = €0.04 |
| B | €30 | 1000 | 30/1000 = €0.03 |
Check the fit before applying
Relevant prior knowledge can be incomplete or misleading. A learner who scales every recipe ingredient by the number of people may use that reasoning appropriately for rice quantity, yet incorrectly assume cooking time must scale by the same factor. Transfer requires conditions, not just a remembered procedure.
Use varied examples and nonexamples. Explain both what carries over and what changes. If a prompt is needed, record that support and later try a case without it. Prompted success can be an instructional step without being evidence of spontaneous recognition.
Worked example
Comparing cartridge costs
Which cartridge has the lower cost per estimated page, and what remains unsettled?
- Cartridge A costs 24 euros for an estimated 600 pages; B costs 30 euros for 1,000 pages. Dividing gives 0.04 euros and 0.03 euros per estimated page. The learner identifies a cost-per-output relationship learned with food prices. The calculation assumes comparable page estimates and does not establish which cartridge is compatible or produces acceptable prints. Recognising those limits is part of using the old method well.
- A useful follow-up asks the learner to invent a case in which cost per unit would not settle the choice. A product that expires before use or fails a required quality standard supplies such a case. Explaining why the calculation is still correct but insufficient develops conditional knowledge: the learner distinguishes a valid subcalculation from a complete decision.
A costs €0.04 per estimated page; B costs €0.03. This comparison assumes comparable estimates and does not decide compatibility, reliability or print quality.
Try it yourself
Think through each question before opening the answer.
A worksheet labels every problem “proportion”. Which transfer demand is hidden?
Show the answer and reasoning
Selecting the method.
The label tells the learner what kind of relationship to use, whereas a new situation may require recognising it.
Why might scaling recipe time with servings be wrong?
Show the answer and reasoning
Cooking time depends on conditions such as geometry, heat transfer and equipment.
The proportional relation for ingredient quantity does not automatically apply to time.
What to carry forward
- Ask which relationship makes prior knowledge relevant.
- Test recognition without a method label and state the conditions of use.
References
Sources supporting the explanations and learning checks in this lesson.