12responses traced
Class reasoning analysis
Prepared demonstration · deterministic data
Assessment question
A circle has a radius of 3 cm. What happens to its area when the radius is doubled? Explain your reasoning.
4shared learning needs
3secure understanding
3teacher checks
Reasoning topology
Trace Map
Final answers can match while the underlying reasoning diverges.
12 responsesone shared prompt
3Linear scaling18π cm²2Formula confusion12π cm²2Substitution12π cm²2Arithmetic slip112.8 cm²Demonstrated understanding3 learners
same answer ≠ same reasoning
12π cm²formula confusionsubstitution error
18π cm²linear scalingsubstitution error
Learning-need groups
Possible misconception clusters
Ordered by instructional leverage, not score.
attention 3 learners
Area scales linearly with radius
Treats radius and area as directly proportional, missing the squared relationship.
Learning needConnect the visual growth of a circle to the r² term.
Inspect reasoning attention 2 learners
Circumference substituted for area
Uses 2πr while labelling the result as area.
Learning needDistinguish what circumference and area measure, including their units.
Inspect reasoning uncertain 2 learners
Radius substituted inconsistently
Recalls A = πr² but does not preserve the exponent during substitution.
Learning needMake substitution explicit before evaluating the exponent.
Inspect reasoning monitor 2 learners
Sound model, imprecise calculation
Understands the fourfold relationship but introduces a numerical or approximation slip.
Learning needSeparate conceptual understanding from calculation accuracy.
Inspect reasoning Teacher attention
Teacher review requiredThree interpretations to check
How this trace was built
- Responses read12 of 12
- Reasoning traced12 paths
- Needs clustered4 groups
- Review prepared3 flagged
Analysis provenance
Prepared demonstration
- Mode
- Prepared demonstration · deterministic data
- Created
- 7/22/2026, 12:40:27 AM
- Responses
- 12
- Teacher review
- 3
- Run ID
- prepared-demo