Reasoning transferred to a new scale factor.
Back to analysis
Transfer check complete
Most learners revised the model.
Evidence from a new radius scale shows where understanding held—and where teacher follow-up still matters.
Prepared demonstration · deterministic data9 of 12 resolved
Assessment question
A circle has a radius of 3 cm. What happens to its area when the radius is doubled? Explain your reasoning.
Before and after
Possible misconception load
Before intervention9learners in possible misconception clusters
→
After transfer check3uncertain or requiring follow-up
9Resolved
2Uncertain
Correct answer with incomplete evidence.
1Teacher follow-up
The original reasoning pattern persisted.
Response evidence
What changed in their thinking
Synthetic student labels
01
Learner 01Transfer answer: 9×
resolvedExplains that tripling radius gives 3² = 9 times the area.
02
Learner 02Transfer answer: 9×
resolvedUses 25π and 225π to verify the factor.
03
Learner 03Transfer answer: 9×
uncertainCorrect answer, but explanation only says ‘square it’.
04
Learner 04Transfer answer: 9×
resolvedContrasts circumference ×3 with area ×9.
05
Learner 05Transfer answer: 3×
follow-upReturns to 2πr in the transfer question.
06
Learner 06Transfer answer: 9×
resolvedWrites π(15)² ÷ π(5)² = 9.
07
Learner 07Transfer answer: 9×
uncertainCorrect factor with an incomplete substitution step.
08
Learner 08Transfer answer: 9×
resolvedLeaves the ratio symbolic and avoids premature rounding.
09
Learner 09Transfer answer: 9×
resolvedUses exact π terms and states the factor clearly.
10
Learner 10Transfer answer: 9×
resolvedGeneralises with k².
11
Learner 11Transfer answer: 9×
resolvedAccurate visual and symbolic reasoning.
12
Learner 12Transfer answer: 9×
resolvedChecks the result numerically.