The Tutor Handbook Vol No.0089 | The Diagnostic Probe

The Tutor Handbook · Volume 0089 · Series ID THB-0089

Series route: The Tutor Handbook — Complete Series Index.

A learner gets the answer wrong.

The tutor can immediately think of five explanations.

Perhaps the learner does not know the concept. Perhaps the concept is understood but cannot be retrieved without a cue. Perhaps the question language is hiding the relevant relationship. Perhaps the learner knows two methods and is choosing the wrong one. Perhaps the method is correct but one execution step is unstable. Or perhaps the learner has simply made a one-off slip that deserves correction but not a new intervention.

The dangerous move is to choose the first explanation that feels plausible and start teaching it. A tutor who assumes missing knowledge may explain a concept the learner already understands. A tutor who assumes carelessness may prescribe checking when the real problem is representation. A tutor who assumes weak memory may add flashcards when the learner can retrieve the fact perfectly but cannot recognise when it applies.

The alternative is not a giant diagnostic test. Often the tutor needs something much smaller: one carefully chosen question, comparison, changed condition or follow-up task designed to make two competing explanations behave differently.

A Diagnostic Probe is a small, deliberately designed learning task whose main purpose is not practice or grading, but discrimination: it changes one meaningful condition so the learner’s response helps the tutor decide which of several plausible explanations for the difficulty deserves more confidence.

This is one of the central crafts of diagnostic tutoring. The probe should reveal more than it teaches. It should be small enough that the tutor can interpret it, fair enough that failure is meaningful, and narrow enough that the result changes the next decision.

Quick Answer

Begin with at least two plausible explanations for the observed difficulty. Ask what result would look different if explanation A were true rather than explanation B. Then design the smallest task or condition change that exposes that difference while keeping unrelated demands as stable as possible. Preserve the learner’s first response before teaching. Interpret the probe as evidence, not a verdict. If the result does not separate the explanations, redesign the next probe rather than forcing a conclusion.

Good probes often change one of seven things: wording, representation, support, delay, method choice, task familiarity or execution demand. A diagnostic probe becomes especially valuable when the proposed interventions differ. If both explanations lead to the same sensible next action, elaborate diagnosis may not be worth the cost.

1. What This Volume Owns

Volume 0004 | Diagnostic Tutor owns the broad job of finding the first useful weak link. Volume 0036 | The Differential owns the problem of keeping old, new and mixed causes separate. Volume 0037 | The Branch Point owns intervention choice once the cause is sufficiently separated.

This volume owns the instrument between those stages: the construction of a small question or task that increases information about the cause without becoming a whole new teaching programme.

Its central question is:

What is the smallest fair change to the task that would make two competing explanations predict different learner behaviour?

2. A Wrong Answer Is an Outcome, Not a Cause

Consider the Mathematics question: “A shirt costs $80 after a 20% discount. What was its original price?” A learner calculates $64.

Several stories fit the same visible answer. The learner may think the original price is reduced by 20%. The learner may understand the relationship but apply the percentage to the wrong base. The learner may misread “after a 20% discount” as “take 20% off 80.” The learner may know reverse percentage in isolation but fail to identify it when the question does not name the method. Or the learner may simply have rushed into a familiar calculation.

If the tutor immediately explains reverse percentage, the explanation may correct the answer while destroying evidence about which explanation was actually true. The learner becomes better informed, but the tutor becomes less informed about the original cause.

That is why diagnosis and teaching sometimes need a brief separation. The tutor first asks enough to understand what kind of help is needed. Then the tutor helps.

3. Formative Assessment Gives the Larger Educational Logic

AERO’s current Monitor Progress guidance describes checking for understanding as a way to determine what students know and can apply, identify gaps, and adjust instruction, guidance or feedback. Its classroom examples emphasise varied checks for understanding, active participation and responding to student struggles. EEF’s Embedding Formative Assessment programme likewise includes questions and tasks that elicit evidence of learning as one of its central strategies.

A Diagnostic Probe is a tutoring-scale application of that larger formative logic. It does not claim that one tiny question can fully diagnose a learner. It uses a carefully chosen response to decide what deserves to be checked or taught next.

The distinction is important because formative assessment is not “test the learner more.” It is “gather the evidence that improves the next instructional decision.” Sometimes that evidence comes from one question. Sometimes it comes from an explanation, comparison, gesture, diagram, rewritten prompt or delayed return.

4. Start With Competing Explanations, Not a Favourite Diagnosis

The quality of the probe depends on the quality of the competing explanations.

“The learner is weak at fractions” is too broad. “The learner may not understand equivalence” and “the learner may understand equivalence but be unable to retrieve a common-denominator procedure” are more useful because they predict different responses.

“The learner is careless” is usually too vague. What did the learner fail to control? Did they copy the number wrongly, skip a condition, change a sign during manipulation, misread a unit, or stop checking because the first answer looked familiar? Each produces different evidence.

Before designing the probe, write two short hypotheses in behaviour language. For example:

Hypothesis A: Beatrice understands the inference but chooses evidence that is merely related rather than directly supporting the claim.
Hypothesis B: Beatrice has not formed a defensible inference and is selecting evidence only after committing to an unsupported answer.

Now the tutor can ask what task would make these stories separate.

5. The Best Probe Changes One Meaningful Condition

Diagnostic clarity increases when the tutor changes one useful condition while leaving other demands relatively stable.

If the question language might be the problem, simplify the wording while preserving the mathematical relationship. If the representation might be the problem, move from words to a diagram without changing the underlying concept. If retrieval might be the problem, compare performance with and without a cue. If method selection might be the problem, remove the chapter label while keeping the procedure familiar. If timing might be the problem, compare a short untimed sample with a comparable timed one.

This is not experimental control in a laboratory sense. Real educational tasks contain many interacting features. The discipline is simply to avoid changing five things when one would answer the question.

6. Seven High-Value Probe Families

Many tutoring probes fall into seven practical families.

Wording probe: preserve the concept, simplify or change the language.
Representation probe: preserve the relationship, change the form: words, diagram, table, equation, graph or physical model.
Support probe: add or remove one bounded cue, worked step, prompt or reference.
Delay probe: repeat an appropriately comparable demand after time has passed.
Selection probe: remove labels so the learner must choose the method or concept.
Variation probe: preserve the rule while changing surface features or context.
Execution probe: provide the method or representation so the tutor can test whether the remaining difficulty lies in carrying it out.

The family matters less than the causal question. A good tutor does not collect probes as tricks. The tutor chooses the one that best separates the live hypotheses.

7. Mathematics Case: Representation or Algebra?

This and the later cases are fictional composites for teaching, not claims about real students.

Alicia struggles with a word problem: “The sum of two consecutive integers is 47. Find the integers.” She writes several numbers but never forms an equation.

The tutor keeps two explanations alive. Perhaps Alicia does not understand what consecutive integers mean. Perhaps she understands the relationship but cannot represent it algebraically.

Probe one: “Give me any two consecutive integers.” Alicia immediately says 12 and 13. That weakens the vocabulary explanation.

Probe two: “If the first integer is n, what could you call the next one?” Alicia says n + 1 only after a long pause and a hint. Now the representation explanation gains support.

The tutor has learned more with two tiny tasks than with another page of word problems. The next intervention can target algebraic representation rather than reteaching the meaning of consecutive integers or drilling equation solving after an equation has already been given.

8. English Case: Inference or Evidence Selection?

Beatrice reads a short passage and answers that a character is nervous. She selects a sentence saying the character entered the room. The evidence is related to the scene but does not justify nervousness.

Hypothesis A: Beatrice has a reasonable inference but weak evidence discrimination. Hypothesis B: the inference itself is a guess.

The tutor asks, “Without choosing a line yet, what two details made you think she was nervous?” If Beatrice can point to trembling hands and repeated checking of the door, the inference exists before evidence selection. If she cannot identify any supporting detail and instead changes the emotion repeatedly, the inference itself may be unstable.

A second probe can present three candidate lines and ask which one most directly supports the inference and why. That separates constructing an inference from selecting evidence for it. The tutor now knows whether to teach inference formation, evidence discrimination or both.

9. Science Case: Knowledge or Question Interpretation?

Ciara gives a weak answer to a question asking why a metal spoon feels colder than a wooden spoon in the same room.

The tutor suspects either a missing heat-transfer idea or a question-interpretation problem. Instead of immediately explaining conduction, the tutor asks a narrower oral prompt: “If both spoons have been in the same room for hours, do you expect their temperatures to be very different before you touch them?”

If Ciara says they should be about the same temperature but one draws energy from the hand faster, the scientific mechanism is substantially present. The weak written answer may reflect difficulty turning that mechanism into the exact explanation the question requires. If she believes the metal spoon must actually be at a much lower temperature because it feels colder, the conceptual repair is more fundamental.

The probe prevents the tutor from confusing poor expression with missing science—and from confusing correct terminology with actual mechanism.

10. The Support Probe Must Not Become the Answer

Support probes are powerful and easy to misuse. The tutor wants to know whether a learner can select a method with a light cue. The tutor says, “Remember, this is a simultaneous-equations question.” The probe has failed because it performed the selection for the learner.

A useful support probe adds the minimum information necessary to test the competing explanation. Instead of naming the method, the tutor might ask, “What quantities are unknown?” or “Can you write one relationship before deciding how to solve it?” If the learner can proceed, the evidence says something about how much orientation was needed without giving away the central decision.

This connects to Volume 0038 | The Dose. Diagnostic support must still preserve the operation being measured.

11. Preserve the First Response Before Teaching

A probe has an evidence phase and a teaching phase. Confusing them weakens both.

Ask the question. Allow appropriate wait time. Record enough of the first response to remember what happened. Then teach.

This does not require a clinical transcript or a surveillance system. A compact note may be enough: “Could explain ratio verbally, could not map it to 3x = 18 without representation cue.” The note preserves the distinction the tutor needed.

The learner should not be left struggling for diagnostic purity. Once the needed evidence has been gathered, return to instruction. A diagnostic tutor is still a tutor.

12. Wait Time Is Part of Probe Validity

A learner who needs several seconds to formulate an answer can look like a learner who does not know the answer when the tutor interrupts too quickly. The probe then measures the adult’s tolerance for silence as much as the learner’s capability.

Appropriate wait time depends on the task. A simple retrieval item and a multi-step reasoning explanation should not have the same expectation. The key is to give the learner a realistic opportunity to perform the target operation before interpreting non-response.

This connects to Volume 0068 | The Opportunity Check. A failed probe is informative only when the learner actually had a fair opportunity to demonstrate the relevant skill.

13. Accessibility Is Not Noise

A diagnostic task can become invalid when access barriers interfere with the target skill. A learner who uses enlarged text, text-to-speech, approved notation support or another legitimate accommodation should not have that support removed merely because the tutor wants an “independent” response.

The relevant question is whether the support performs the target intellectual operation. Volume 0073 | The Access-Support Boundary owns that distinction.

A probe of algebraic reasoning should not become a reading-speed test unless reading speed is intentionally part of the question. A probe of inference should not become a handwriting test. Diagnostic elegance begins with measuring the job you actually care about.

14. One Probe Should Not Become a Verdict

A well-designed probe can sharply change the tutor’s confidence. It still samples one performance under one set of conditions.

If Alicia fails to represent one word problem after a vocabulary check, the representation hypothesis becomes stronger. It does not become a permanent label: “Alicia has a representation weakness.” The tutor should look for recurrence across appropriately varied tasks, especially before reorganising a whole learning route.

This connects to Volume 0076 | The Evidence Sample. The probe changes the next question. Repeated evidence changes the learner model.

15. Negative Results Are Useful

A tutor designs a wording probe expecting simplified language to improve Mathematics performance. The learner still fails.

That is not a failed probe. It weakens the language explanation.

A representation cue also fails. That weakens the representation explanation. A provided method allows correct execution. Now the problem appears closer to method selection than execution.

Good diagnosis progresses partly by eliminating attractive wrong stories. A probe earns value when it changes the probability of the competing explanations, not only when it confirms the tutor’s first idea.

16. When No Probe Is Needed

Diagnosis has a cost. It uses lesson time and learner attention. If two plausible causes would lead to the same low-cost, reversible intervention, elaborate discrimination may not be necessary.

Suppose a learner sometimes forgets a vocabulary word and sometimes fails to retrieve it quickly enough in writing. A brief spaced retrieval routine may sensibly address both. The tutor can begin the routine and observe the receipts rather than spending half a lesson separating two explanations that do not yet change action.

Diagnostic sophistication should improve decisions, not become an intellectual hobby.

17. When a Larger Diagnostic Sequence Is Needed

One probe is not always enough. If the learner’s difficulty is high consequence, repeated across contexts, or responsive to several interacting supports, the tutor may need a sequence.

A useful sequence might move from the least supported task to one carefully chosen cue, then a changed representation, then a fresh transfer item. The order should answer a causal question, not simply increase help until the learner becomes correct.

If the tutor finds themselves administering a long battery with no clear decision attached to each item, return to the hypotheses. What exactly will the next response change?

18. The Diagnostic Probe Card

Observed difficulty: What exactly happened?
Hypothesis A: What is one plausible explanation?
Hypothesis B: What competing explanation would lead to a different intervention?
Predicted difference: If A is true, what response should differ from B?
Probe: What is the smallest fair task that exposes that difference?
Held stable: What important conditions should stay similar?
Allowed support: What access support or bounded cue is legitimate?
First response: What did the learner do before teaching?
Interpretation: Which hypothesis gained or lost support?
Uncertainty: What still cannot be concluded?
Next action: Teach, probe again, collect another sample, or leave the learner model unchanged?

19. Three-Student Tutorials Make Probe Design More Valuable

In a three-student room, a tutor cannot repeatedly run long individual diagnostics without turning the class into serial one-to-one tuition. Small probes allow the tutor to learn while keeping the group moving.

A common task can contain different probes. Alicia may receive the same mixed Mathematics item without a topic label because method selection is under question. Another learner may receive the method but explain why it applies because conceptual understanding is the live uncertainty. A third may complete the full item under moderate timing because performance is the current job.

The shared content does not require identical evidence conditions. What matters is that each variation answers a real question about that learner.

20. Parent Communication: “I Am Not Testing More; I Am Trying to Avoid Teaching the Wrong Thing”

Parents can understandably worry when tuition appears to spend time on diagnosis instead of teaching. A concise explanation helps:

She is losing marks on reverse-percentage questions, but there are two plausible reasons: she may not understand the percentage base, or she may understand it but fail to recognise when reverse percentage is needed. One short changed question will help me choose whether to reteach the concept or train method selection. I would rather spend five minutes separating those causes than spend five weeks practising the wrong one.

This is diagnosis in service of efficiency.

21. Learner Communication: Make the Probe Low-Stakes

A probe works better when the learner understands its purpose.

“I’m going to change the question slightly because I want to know which part I should teach, not because I am trying to catch you.”

This reduces the temptation to perform for the tutor rather than reveal the current route. It also models a powerful idea: mistakes can be used to choose better help rather than to label the learner.

22. Tutor Professional Learning: Practise Designing Probes, Not Only Explanations

Tutor training often emphasises how to explain a topic. Diagnostic tutoring requires an earlier skill: knowing what to ask before deciding which explanation belongs.

Stanford’s National Student Support Accelerator recommends practice-based tutor professional learning, including analysing live or video models, rehearsals and feedback. Its coaching guidance also recommends observations tied to specific goals and evidence. Probe design is well suited to that kind of rehearsal. Give tutors a learner response. Ask them to generate two competing explanations, predict what each would produce, and design one fair discriminating question.

The quality test is not whether the probe sounds clever. It is whether the result would actually change the next teaching decision.

23. Common Failure: The Leading Probe

“You know this is about conservation of energy, right?”

The learner agrees and solves the problem.

The tutor concludes that the learner knew the principle.

But the probe supplied the central selection. It answered the question it was supposed to measure.

When selection is the target, the prompt must leave selection with the learner.

24. Common Failure: The Probe Changes Too Much

The tutor changes the wording, numbers, representation, time limit and amount of help. The learner succeeds.

Which change mattered?

Sometimes a large change is necessary for teaching. It is weak as a discriminating probe because too many explanations remain possible.

25. Common Failure: The Probe Becomes Repeated Testing

The tutor keeps designing clever diagnostic questions but never returns to instruction.

This is especially risky for anxious or struggling learners. Tuition should not become an endless audition of weaknesses. Gather the minimum evidence needed to choose the next useful teaching move. Then teach, practise, revisit and reduce help as appropriate.

26. Common Failure: The Tutor Diagnoses a Person Instead of a Performance

“He cannot infer.”

“She is a visual learner.”

“He has poor memory.”

These statements outrun most ordinary tutoring evidence. The probe should update a local educational hypothesis: “On these unfamiliar passages, she formed plausible inferences when asked orally but selected weak textual evidence independently.” That description is more useful and less likely to become a permanent label.

27. Common Failure: Only Testing the Tutor’s Favourite Explanation

A tutor believes the problem is retrieval. Every probe tests retrieval. Eventually the learner looks like a retrieval problem because no competing cause is given a fair chance.

Good differential diagnosis includes a real alternative. Ask what observation would embarrass the current hypothesis. If no possible learner response could make the tutor change their mind, the probe is not diagnostic.

28. Research Boundary

AERO and EEF provide strong practical and research-informed foundations for formative assessment, checking for understanding and adapting instruction to student evidence. These sources support the broader principle that teaching should respond to evidence gathered during learning. They do not validate every specific probe designed in this handbook, nor do they establish a universal sequence of diagnostic questions for private tutoring.

The examples here are instructional applications. Their quality depends on subject knowledge, task validity, fair access, appropriate interpretation and repeated evidence where the claim is consequential. A probe is a disciplined question, not a psychometric instrument.

29. Evidence and Connected Reading

30. Final Principle

A skilled tutor does not become diagnostic by asking more questions. The tutor becomes diagnostic by asking a question whose possible answers have different implications.

Observe the difficulty. Keep more than one explanation alive. Change one meaningful condition. Preserve the first response. Let the evidence weaken as well as strengthen your favourite hypothesis. Gather more only when the decision requires it. Then return to teaching.

The best Diagnostic Probe is small enough to disappear after it has done its job. Its purpose is not to label the learner. Its purpose is to stop the tutor from confidently teaching the wrong problem.

That is the Diagnostic Probe.

Small Group Tutorials

The Tutor Handbook Vol No.0089 | The Diagnostic Probe — How a Tutor Designs One Question That Separates Competing Explanations Without Teaching the Answer