Intervention Evidence Registry | Testing Diagnosis to Repair
Finding a likely weakness is only half the job. The teaching response must also improve the learner’s Mathematics.
A repair earns confidence through what happens next
- The student should understand why the correction works.
- The repaired idea should reconnect to the current topic.
- Support should reduce rather than increase indefinitely.
- A changed question should still be manageable.
- The improvement should remain available after some delay.
A correct diagnosis does not guarantee that every teaching method will work. Diagnosis and teaching effectiveness therefore need to be judged separately.
PHASE 4 · INTERVENTION EVIDENCE READER GUIDE
Quick Read: how do we know a Mathematics intervention actually worked?
A repair has worked when the learner understands the corrected relationship, reconnects it to the original problem, needs less support, succeeds on a changed surface and can still use the capability after delay.
Immediate improvement is important, but it is only the beginning. A student can perform well because the tutor has just demonstrated the method, because the worksheet repeats one surface, or because prompts remain visible. The intervention earns stronger confidence only as those supports disappear and the Mathematics remains.
One-sentence answer: judge a repair by what the learner can still do when the tutor, the familiar example and the immediate memory of the lesson are no longer carrying the task.
Diagnosis and intervention are separate claims
A correct diagnosis does not guarantee that the first teaching method will work. If a learner has weak fraction magnitude, a number line, fraction strips, comparison tasks or another representation may each be reasonable interventions. Their effectiveness must be observed rather than assumed.
| Claim | Evidence needed |
|---|---|
| The diagnosis is right | The suspected weakness predicts performance across discriminating probes. |
| The intervention is appropriate | The learner improves after the specific teaching response. |
| The repair is durable | Improvement survives reduced support, changed questions and delay. |
| The repair is useful | The capability reconnects to the learner’s current Mathematics. |
Keeping these claims separate makes it easier to change the intervention without discarding a sound diagnosis—or to revise the diagnosis when no reasonable intervention produces the predicted effect.
The repair ladder: understand → reconnect → fade → transfer → retain
- Understand. The learner can explain what was wrong and why the correction works.
- Reconnect. The repaired capability can be used inside the original current topic.
- Fade. Prompts, worked examples, diagrams or tutor questions reduce.
- Transfer. The learner succeeds when the question looks different or the method is not announced.
- Retain. The capability remains available after time has passed.
For examination goals, a sixth stage can be added: perform under realistic pressure. A capability that exists only in slow supported practice may not yet be examination-ready.
Three interventions that look successful too early
Case 1: success while the model remains visible
A student solves every ratio question using a teacher-provided table but cannot rebuild the table independently. The representation is still carrying too much of the reasoning. The next evidence point is whether the table can be faded or reconstructed by the learner.
Case 2: success only on same-looking questions
A learner completes ten identical algebra questions correctly after a worked example but fails when coefficients, signs or layout change. The intervention produced local procedural fluency but transfer remains unproven.
Case 3: success disappears after a week
The student understood the lesson and performed well that day, then cannot retrieve the idea later. The teaching response may need stronger retrieval, spacing, connection or meaning. Same-day performance should not be recorded as permanent mastery.
Changed-surface verification is essential
A strong verification question preserves the underlying capability while changing features that could have become superficial cues.
| Original repair | Changed-surface check |
|---|---|
| Fraction comparison using a visual model | Compare different fractions on a number line or explain magnitude verbally. |
| Distribution with positive integers | Use negatives, variables or reverse factorisation. |
| Trigonometry in a familiar triangle orientation | Rotate the figure or change the reference angle. |
| Probability using a tree diagram | Represent the same event with a table or sample-space reasoning. |
| Graph transformation with a dynamic tool | Predict a static unfamiliar graph without the tool. |
If the learner succeeds only when the original surface returns, the repair is not yet portable enough.
Support should usually have a fade plan
Support is useful when it opens access to the Mathematics. It becomes a problem when the learner cannot continue without it and no reduction plan exists.
- Full model or explanation.
- Partial prompts.
- Self-generated representation or checklist.
- Independent solution.
- Independent solution under mixed conditions.
Some supports are legitimate permanent tools in the target environment. Others are temporary scaffolds. The tutor should know which category applies rather than fading automatically.
When should an intervention be abandoned or changed?
- The learner repeatedly fails to improve despite accurate use of the intervention.
- Success depends increasingly on prompts rather than decreasing support.
- The repair works locally but does not reconnect to current work.
- Changed-surface questions repeatedly fail.
- The intervention introduces more cognitive load than the problem it is meant to solve.
- New evidence weakens the original diagnosis.
Changing an intervention is not failure of teaching. Persisting with an ineffective intervention because it “should work” is the larger problem.
The intervention must answer to the learner’s subsequent performance, not to the elegance of the teaching idea.
Retention should be sampled, not assumed
Not every repaired idea needs a formal test weeks later. But important gateways should reappear naturally in later mixed work. That creates a low-cost retention check.
- Revisit a repaired algebra edge inside functions.
- Revisit ratio reasoning inside similarity or trigonometry.
- Revisit fraction magnitude inside probability or percentage.
- Revisit graph interpretation inside calculus.
This is stronger than maintaining a separate endless remediation programme because the learner proves that the repair now carries real downstream load.
What parents and tutors can ask after a repair
- Can the learner explain why the correction works?
- Can they use it in the original chapter problem?
- What support can now be removed?
- Does it survive a different-looking question?
- Can the learner choose the method without being told?
- Does the capability remain after delay?
- Has the repair reduced stress or cognitive load in the later topic?
The useful question is not only “Did the student get it right?” but “What now works that did not work before, and how independently?”
Frequently asked questions
How long should an intervention take?
It depends on the capability and learner. The more useful rule is to look for evidence of forward movement and decreasing support. If neither appears, reconsider the intervention or diagnosis.
Is immediate improvement meaningless?
No. It is encouraging first evidence. It simply should not be mistaken for durable mastery until the capability survives stronger checks.
Should every support be faded?
No. A support that is legitimately part of the target environment may remain. Temporary instructional scaffolds should generally reduce as independence grows.
What is the strongest evidence that an intervention worked?
The learner can use the repaired capability independently, in changed and mixed contexts, after delay, and the repair improves the downstream Mathematics that originally motivated the intervention.
The larger idea: the learner—not the lesson—decides whether a repair succeeded
A beautifully explained lesson can fail to produce durable capability. A simple intervention can succeed because it reconnects exactly the missing relationship and then gets out of the learner’s way.
Intervention evidence therefore belongs after teaching, not only before it. The learner’s later independence is the receipt that tells us whether the repair carried load.
Good repair does not end when the student understands with us. It ends when the Mathematics works without us.