The Foil Boat, the Steel Ship, and Fifteen Density Sums
In a Class 8 science class of 36 students, the teacher begins the topic 'floating and sinking' with a probe. He shows a 200 g iron block that sinks and a steel ship of 50,000 tonnes that floats, and asks for an explanation. Twenty-nine students write 'iron is heavy, so it sinks'; six write 'the ship is big, so it floats'; one writes 'there is air inside the ship that pushes it up'. The teacher then takes two identical sheets of aluminium foil from the same roll - the same mass - crumples one into a tight ball and folds the other into a boat shape. The ball sinks, the boat floats. Several students say the teacher 'made the boat lighter', and one asks whether the boat will float in a bucket. The teacher's plan for the remaining four periods is to define density, give the formula d = m/V, and have students solve fifteen numericals.
1. Why will fifteen density numericals fail to change the 'heavy things sink' idea?
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Because the students' idea is a working theory, and the plan never puts it at risk.
- It is not a blank; it is a rule that predicts most everyday cases. A stone sinks, a leaf floats - 'heavy sinks' is confirmed daily. New observations get absorbed into it: the boat floats because 'the teacher made it lighter'. That is the theory protecting itself, and it needs to be confronted, not bypassed.
- The demonstration was dropped too early. The foil pair is exactly the right discrepant event (same mass, different shape, different outcome), but the teacher moved on without collecting predictions, without letting students commit to a wrong answer, and without resolving the contradiction they voiced.
- Numericals build procedure, not a model. A student can compute d = m/V correctly with the formula on the board and still hold that weight decides floating, because the two are stored separately. None of the fifteen sums asks 'will it float?', so the two beliefs never meet.
- The discrimination is never made: mass alone is not the deciding variable; mass per unit volume is; shape changes volume while leaving mass unchanged.
- The ship example is badly chosen. 50,000 tonnes invites weight reasoning. Same-mass and same-volume pairs would be cleaner.
Without prediction, conflict and resolution, the correct formula simply sits beside the wrong belief.
2. Design a two-period sequence that uses the discrepant event properly, and say how you would handle the student who said 'air pushes it up'.
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Period 1 - predict, commit, test.
Before any demonstration, each student writes a prediction and a reason for four pairs: (a) foil ball and foil boat from the same sheet, same mass; (b) two identical sealed bottles, one filled with sand and one with air, same volume; (c) a 500 g block of wood and a 500 g block of iron, same mass; (d) the same egg in fresh water and in very salty water.
Then test each pair, record results in a class table, and put the predictions next to the outcomes without correcting anyone yet. The table itself does the arguing: mass identical, outcome different; volume identical, outcome different.
Period 2 - explain and formalise.
Introduce 'how much water is pushed aside' and then average density of the object against the liquid. Floating occurs when the object's average density is less than the liquid's. Return to the foil pair: same mass, but the boat encloses air, so the same mass now occupies a larger volume and the average density falls below that of water.
The 'air pushes it up' student should not be corrected first - he should be upgraded. His intuition contains the key insight: the air makes the boat-and-air system less dense for its size. Confirm the observation, correct the mechanism, and give him the vocabulary 'average density'. Dismissing it would push a productive idea underground.
Then set the numericals, but pair each one with a prediction ('density 0.8 g/cm³ in water - float or sink?').
3. How would you gather evidence that conceptual change actually occurred, rather than formula recall?
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Use items where the formula cannot be pattern-matched to the answer.
- Novel materials: a sealed tin of air, a piece of camphor, a plastic bottle half-filled with sand - predict and justify before calculating.
- Load it until it sinks: add weights to the foil boat until it goes under, and ask why the same boat changed. This probes whether the student has both mass and volume in play.
- The same object, different liquid: the egg or a plasticine ball in fresh versus saturated salt water. A student with only 'heavy sinks' cannot explain a change of outcome at constant object.
- Explanation writing: 'A ship is made of steel and steel sinks. Explain why the ship floats.' Score on whether mass, volume and displaced water all appear, not on whether the word 'density' appears.
- Listen to language: 'heavy' is not automatically an error - if the student means 'dense' or 'heavy for its size', the concept is in place and only the vocabulary needs fixing. Probe with 'would a big light thing float?'
- Retention check after two weeks with one transfer item, since a correct answer on the day of the demonstration often reflects the demonstration rather than a changed model.