The Pendulum Data That "Proves" the Wrong Thing
A 4th-grade class investigates pendulums. Each group changes one variable: Group A changes string length, Group B changes bob mass, Group C changes release angle. The teacher reminds them to change only one thing at a time. Group B's data show almost no difference in swing time across masses and they conclude "mass doesn't matter." Group A's data are noisy-one trial used a 20 cm string and recorded a time close to the 40 cm trials-and they conclude "length doesn't matter either." The teacher must decide which conclusions to accept, how to handle Group A's outlier, and what the class should do next.
1. Evaluate each group's conclusion and identify the specific problem, if any, in Group A's investigation.
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Group B's conclusion is well supported; Group A's is not.
- Group B: They controlled variables (only mass changed) and found consistent results across masses. Concluding "mass doesn't affect swing time" is a reasonable inference from their data-though the teacher should have them say "in our tests," modeling appropriate tentativeness.
- Group A: Their conclusion is undermined by a procedural/measurement problem, not by the physics. A 20 cm trial producing a time near 40 cm trials signals a likely error: mis-measured length, mistimed swings, or inconsistent release. With one anomalous trial, they cannot conclude length doesn't matter-they have a data-quality problem that must be resolved before any conclusion.
The key distinction to teach: a surprising result is not the same as a wrong result, but you must rule out error before trusting an anomaly.
2. What should the teacher have Group A do next, and how does this fit the practice of planning and carrying out investigations?
Read the worked answer
Group A should re-run the anomalous trial and check their procedure before concluding.
Steps:
- Re-measure the 20 cm string and re-time several swings (time multiple swings and divide to reduce timing error).
- Check consistency: does the repeat match the other short-length trials, or does it still look like the 40 cm time?
- Decide: if repeats are consistent with a trend by length, revise the conclusion; if the anomaly persists, investigate why (measurement, release, timing) rather than discard it.
This is the core of planning and carrying out investigations: controlling variables, taking repeated measurements, and treating outliers as information to be explained. The teacher should also have Group A compare their length data as a graph-if time rises with length, the single bad point stands out visually, reinforcing that conclusions follow patterns in reliable data, not single trials.