Learning Science · Remembering and making sense
Connecting a new idea with what you already know
Connect a new idea to relevant knowledge while checking whether the connection is accurate.
Use the examples to connect this lesson with the earlier topics. No specialist equipment is needed.
Back to the chapterAfter reading, you can
- Build a meaningful connection
- Identify a misleading analogy
A place for a new idea
A learner knows that a balance scale compares quantities. When learning equations, that experience can help explain why changing both sides in the same way preserves equality. Relevant prior knowledge supplies relationships with which to interpret a new idea.
A connection helps when it preserves what matters. It can mislead when superficial similarity hides a different mechanism. An electrical circuit is sometimes compared with water flow, but the comparison needs explicit limits. A familiar analogy is a teaching tool, not proof that every property transfers.
Make the relationship explicit
Ask what is shared, what differs and what prediction follows. For an equation, identify the equal quantities and explain why the same operation is applied to both. Do not stop at “It is like a balance.” Naming an analogy without mapping its relations leaves the explanatory work undone.
If the assumed prior idea is missing or mistaken, introduce it with a small case. Otherwise the new explanation builds on a gap. A brief starting question can reveal what the learner actually brings, rather than what the teacher expects them to know.
Check beyond the familiar case
Use a new example whose surface details differ but whose relationship is the same. Then use a contrasting case in which the relationship does not apply. Together these checks help distinguish understanding from copying one example’s appearance.
A connection should be revisable. As knowledge develops, a simple analogy may need refinement rather than total rejection. Say which part remains useful and which part must change. This helps learners see a model as a bounded tool for reasoning rather than a story that must be either perfectly true or worthless.
In the loaf model, equal pieces are equal relative to one stated whole. Comparing a piece across different wholes requires keeping both the absolute amount and the fraction in view.
Worked example
From sharing food to fractions
Two loaves have different lengths. Can two equal-looking pieces represent different fractions of their own whole?
- Assume each loaf has uniform thickness and width, and compare length as a simple model of its amount. Loaf A is 12 cm long and loaf B is 18 cm long.
- Half of A is 12 ÷ 2 = 6 cm. One third of B is 18 ÷ 3 = 6 cm. The selected pieces have equal lengths under the model.
- The fraction compares each piece with its own whole. Six of twelve equal length units is one half; six of eighteen is one third. Equal absolute lengths do not make those relative fractions equal.
Yes. The pieces are both 6 cm in this authored model, but they are one half and one third of different wholes. State the whole before comparing fractions.
Same piece length, different fractions
Try it yourself
Think through each question before opening the answer.
Why ask what differs in an analogy?
Show the answer and reasoning
It marks where the familiar model stops making reliable predictions and prevents extending it too far.
An analogy preserves selected relationships. Identifying a difference prevents importing a property that was never justified by the comparison.
A learner lacks the experience used in an example. What should change?
Show the answer and reasoning
Introduce the needed relation directly or choose an accessible shared example, then check understanding rather than repeating the same analogy louder.
A familiar story cannot help if its essential relationship is unfamiliar to the learner. Teach the relation directly or choose a more accessible case, then check a new example.
What to carry forward
- Link relationships, not just words.
- Check the knowledge a connection assumes.
- Use examples and contrasts to test the link.
References
Sources supporting the explanations and learning checks in this lesson.