Singapore School Mathematics Operating Manual · Chapter 52
Stress-test a conclusion by weakening assumptions one at a time, separating results that survive realistic variation from results that depend on one fragile modelling choice.
This chapter is a cross-topic control layer for Primary, PSLE, SEC G1/G2/G3, E-Math, A-Math and JC Mathematics. It complements existing BTT topic owners rather than replacing them.
1. A robust conclusion survives reasonable model changes
The operating principle is to make a robust conclusion survives reasonable model changes explicit. Use a simple numerical example, state the active domain or scale, preserve units and conditions, and verify that the conclusion still matches the original task before passing it downstream.
2. Stress testing changes assumptions deliberately
The operating principle is to make stress testing changes assumptions deliberately explicit. Use a simple numerical example, state the active domain or scale, preserve units and conditions, and verify that the conclusion still matches the original task before passing it downstream.
3. Test one assumption at a time first
The operating principle is to make test one assumption at a time first explicit. Use a simple numerical example, state the active domain or scale, preserve units and conditions, and verify that the conclusion still matches the original task before passing it downstream.
4. Then test interacting assumption changes
The operating principle is to make then test interacting assumption changes explicit. Use a simple numerical example, state the active domain or scale, preserve units and conditions, and verify that the conclusion still matches the original task before passing it downstream.
5. Qualitative conclusions can be more robust than exact numbers
The operating principle is to make qualitative conclusions can be more robust than exact numbers explicit. Use a simple numerical example, state the active domain or scale, preserve units and conditions, and verify that the conclusion still matches the original task before passing it downstream.
6. Bounds often survive when point estimates do not
The operating principle is to make bounds often survive when point estimates do not explicit. Use a simple numerical example, state the active domain or scale, preserve units and conditions, and verify that the conclusion still matches the original task before passing it downstream.
7. Monotonic conclusions can survive parameter uncertainty
The operating principle is to make monotonic conclusions can survive parameter uncertainty explicit. Use a simple numerical example, state the active domain or scale, preserve units and conditions, and verify that the conclusion still matches the original task before passing it downstream.
8. Sign conclusions can survive broad perturbations
The operating principle is to make sign conclusions can survive broad perturbations explicit. Use a simple numerical example, state the active domain or scale, preserve units and conditions, and verify that the conclusion still matches the original task before passing it downstream.
9. Threshold conclusions require margin
The operating principle is to make threshold conclusions require margin explicit. Use a simple numerical example, state the active domain or scale, preserve units and conditions, and verify that the conclusion still matches the original task before passing it downstream.
10. Symmetry conclusions fail when symmetry assumptions break
The operating principle is to make symmetry conclusions fail when symmetry assumptions break explicit. Use a simple numerical example, state the active domain or scale, preserve units and conditions, and verify that the conclusion still matches the original task before passing it downstream.
11. Linear conclusions should be tested against curvature
The operating principle is to make linear conclusions should be tested against curvature explicit. Use a simple numerical example, state the active domain or scale, preserve units and conditions, and verify that the conclusion still matches the original task before passing it downstream.
12. Independence assumptions deserve explicit stress tests
The operating principle is to make independence assumptions deserve explicit stress tests explicit. Use a simple numerical example, state the active domain or scale, preserve units and conditions, and verify that the conclusion still matches the original task before passing it downstream.
13. Constant-rate assumptions deserve range tests
The operating principle is to make constant-rate assumptions deserve range tests explicit. Use a simple numerical example, state the active domain or scale, preserve units and conditions, and verify that the conclusion still matches the original task before passing it downstream.
14. Equal-likelihood assumptions need mechanism support
The operating principle is to make equal-likelihood assumptions need mechanism support explicit. Use a simple numerical example, state the active domain or scale, preserve units and conditions, and verify that the conclusion still matches the original task before passing it downstream.
15. Worst-case tests give guarantees
The operating principle is to make worst-case tests give guarantees explicit. Use a simple numerical example, state the active domain or scale, preserve units and conditions, and verify that the conclusion still matches the original task before passing it downstream.
16. Scenario tests are not proofs of all possibilities
The operating principle is to make scenario tests are not proofs of all possibilities explicit. Use a simple numerical example, state the active domain or scale, preserve units and conditions, and verify that the conclusion still matches the original task before passing it downstream.
17. A conclusion can be robust even if the model is imperfect
The operating principle is to make a conclusion can be robust even if the model is imperfect explicit. Use a simple numerical example, state the active domain or scale, preserve units and conditions, and verify that the conclusion still matches the original task before passing it downstream.
18. Fragile conclusions need conditional language
The operating principle is to make fragile conclusions need conditional language explicit. Use a simple numerical example, state the active domain or scale, preserve units and conditions, and verify that the conclusion still matches the original task before passing it downstream.
19. Stress tests should target plausible alternatives
The operating principle is to make stress tests should target plausible alternatives explicit. Use a simple numerical example, state the active domain or scale, preserve units and conditions, and verify that the conclusion still matches the original task before passing it downstream.
20. A robustness audit
Ask what level of claim is required, which conditions support it, how much detail is justified, and whether the conclusion survives the relevant uncertainty or model variation.
21. Worked examples
Example 1. If a conclusion depends on x>0, test what changes at x=0 and x<0 before calling it universal.
Example 2. If a small term is ignored, compare its maximum possible contribution with the decision margin or required tolerance.
Example 3. If data are grouped, do not claim exact within-group values that the representation no longer contains.
Example 4. If a model conclusion survives several plausible parameter ranges and remains on the same side of every relevant threshold, the qualitative conclusion is stronger than one supported by a single point estimate.
22. Independent practice
1. State one assumption behind a familiar school formula.
2. Give one situation where a smaller term cannot safely be ignored.
3. Explain why a grouped-data summary cannot recover exact raw observations.
4. Give one example of a conclusion that remains true under a range of input values.
5. State the check required before an approximation is used for a threshold decision.
23. Worked answers
1. Example: distance=speed×time under a constant or appropriately averaged speed model.
2. Near cancellation or near a decision threshold, a numerically small term can control the sign or classification.
3. Aggregation maps many possible raw data sets to the same grouped representation.
4. If an entire uncertainty interval lies below an upper threshold, the below-threshold conclusion is robust to every value in that interval.
5. Bound the approximation error and confirm the full plausible result remains on the required side of the threshold.
24. Continue through Batch 13
Return to the BTT Mathematics Hub for Batch 13.