Learning Science · Concepts and changing explanations
Concepts as organised relationships
Build a concept by linking its meaning to properties, causes, examples and neighbouring ideas.
Use the examples to connect this lesson with the earlier topics. No specialist equipment is needed.
Back to the chapterAfter reading, you can
- Distinguish knowing a word from understanding a concept.
- Construct and check meaningful relationships between ideas.
A word can hide a missing relationship
A learner says that density means heaviness. This seems reasonable when comparing a stone with a sponge, but it fails when comparing a tiny stone with a large bale of sponge. Density relates mass to volume: how much mass is present for each unit of volume. Understanding requires keeping both quantities in view. A correct word alone cannot show whether that relationship is understood.
A concept is an organised way of identifying and reasoning about something. Some concepts have precise defining conditions, such as an even integer. Others, such as a fair explanation, require several criteria and judgments about context. Learning a concept includes recognising cases, explaining relevant relationships, and noticing when the concept does not apply.
Give each connection a meaning
A list reading mass, volume, density contains relevant vocabulary but says little about its organisation. A labelled relationship is more informative: density equals mass divided by volume. Another relationship states that doubling mass while holding volume constant doubles density. These connections let a learner generate answers rather than retrieve three isolated definitions.
A small concept map can externalise such connections. Read every arrow as a sentence with a subject, a linking phrase and an object. Different arrows can mean different things: is a kind of, causes under these conditions, is measured by, or contrasts with. An unlabelled arrow between heat and temperature leaves the reader guessing whether the connection is identity, cause or association.
Check the organisation by using it
Try changing one part of an example while holding another fixed. Ask which relationship predicts what happens next. This reveals weak links more directly than asking whether the map looks familiar. Research on knowledge integration describes learning as establishing relationships across experiences; it does not imply that every attractive map causes better learning.
Begin with a few useful connections and inspect them against definitions or evidence. A larger network can contain more errors and be harder to navigate. Facts still matter: relationships cannot substitute for knowing what the connected terms mean. Revisit the network after solving a problem, adding a condition or correcting a link when the problem reveals a gap.
| Parcel | Mass (g) | Volume (cm³) | Density (g/cm³) |
|---|---|---|---|
| A | 200 | 100 | 2 |
| B | 200 | 400 | 0.5 |
Worked example
Two parcels with the same mass
Parcel A has mass 200 g and volume 100 cm³. Parcel B also has mass 200 g but volume 400 cm³. Which is denser, and what relationship explains it?
- Keep both quantities visible and identify their roles. The masses are equal, so calling one parcel heavier cannot explain a density difference.
- Calculate mass per unit volume: A has 200 g ÷ 100 cm³ = 2 g/cm³. B has 200 g ÷ 400 cm³ = 0.5 g/cm³. These are invented instructional values for the parcels’ average densities.
- Compare equal volumes: A contains four times as much mass per cubic centimetre as B because 2 ÷ 0.5 = 4. Link density to mass divided by volume rather than to mass alone.
A is denser even though the parcels have equal mass. The calculation tests the concept’s relationship: average density uses both the mass and the occupied volume.
Try it yourself
Think through each question before opening the answer.
Why does a map with many connected words fail to prove understanding?
Show the answer and reasoning
Connections may be vague or false. Ask the learner to read a labelled connection as a claim and use it to predict a new case.
More links create more claims to inspect, not automatic evidence of understanding. Ask the learner to explain a labelled relation and use it when a quantity or condition changes.
Both mass and volume double. What happens to density?
Show the answer and reasoning
It stays the same because the numerator and denominator increase by the same factor. The relationship, rather than either quantity alone, determines the answer.
If mass m and nonzero volume V both double, the ratio becomes 2m divided by 2V, which equals m divided by V. Looking at the increase in mass alone would miss the matching volume increase.
Improve the connection "triangle — three".
Show the answer and reasoning
A triangle has three straight sides forming a closed plane figure. The revised statement explains what three counts and includes relevant conditions.
“Three” needs a role and conditions. In ordinary plane geometry, the revised connection specifies three straight sides enclosing a figure rather than three objects or an open path.
What to carry forward
- Learn relationships as well as labels.
- Label connections precisely and test them in a changed case.
References
Sources supporting the explanations and learning checks in this lesson.