A diagnostic probe is useful when different answers lead to different questions from the teacher. Four ticks in a mark book may hide four very different needs. This original ruler-reading probe is deliberately short: it separates placing a strip at zero, counting equal intervals, finding a length when the strip begins away from zero, and naming the unit.
The instrument and learner profiles are fictional classroom examples. They do not establish a diagnosis, fixed ability, official cut score or current grade placement. Use the probe after checking that its ideas have been taught. The aim is to choose the next demonstration or question, rather than to award a total.
Prepare the evidence you want to see
The narrow outcome is: interpret centimetre ruler diagrams with whole-number endpoints and explain how the interval between endpoints gives length. These pictures are schematic. Learners should read their labelled scales, not measure a screen or printed image with another ruler. Every numbered interval represents one centimetre even if the picture is resized.
Read prompts aloud when decoding the wording is not the target. Allow pointing, drawing, speaking or an appropriate communication aid. Make the scale available in a format the learner can perceive; a spoken description of endpoint values can assess calculation from readings, but cannot by itself demonstrate visual ruler reading. Record such changes so the evidence is not overstated.
Ask for an answer and “Show how you decided.” Wait before correcting. If you demonstrate a method during a probe item, label subsequent performance as supported. Do not interpret a taught response as an independent starting point.
The four original tasks
Task 1: find the zero-aligned placement
Strips P and Q are placed above the same centimetre ruler. Which strip is positioned correctly if you want to measure directly from zero? Point to the start you used. Then read the length of that correctly placed strip.
Accessible diagram description: The ruler’s physical left edge is one interval before its zero tick. The scale is marked 0 to 6 cm. P starts at 0 and ends at 3. Q starts at the physical edge and ends at 2. Both strips span three equal intervals, but only P begins at the zero mark.
Answer: P is zero-aligned and its length is 3 cm. Starting at the plastic or wooden edge is not necessarily starting at zero. Q is not correctly positioned for a direct zero-start reading; its endpoint reading of 2 does not give its length.
Task 2: count spaces rather than boundary ticks
The strip below starts at 0 and ends at 4 on a centimetre ruler. How long is it? Show each one-centimetre interval you counted.
Accessible diagram description: Equally spaced ticks run from 0 to 6 cm. The strip spans ticks 0 through 4, covering the four intervals 0–1, 1–2, 2–3 and 3–4.
Answer: 4 cm. There are five boundary ticks including both ends, but only four intervals. A response of 5 cm is a reason to watch the learner count; it is not proof that tick counting caused the answer.
Task 3: separate endpoint reading from length
This strip begins at 2 and ends at 7 on a centimetre ruler. It cannot be moved. Find its length and show how you used both endpoints.
Accessible diagram description: The scale is marked 0 to 8 cm at equal intervals. The strip starts at 2 cm and finishes at 7 cm.
Answer: 7 − 2 = 5 cm. Counting the intervals 2–3, 3–4, 4–5, 5–6 and 6–7 gives the same result. “Always read the number at the end” works only when the other end is at zero.
Task 4: communicate the quantity
Write the strip’s length, including the unit shown on the ruler. Explain what your unit tells another person.
Accessible diagram description: Ticks run from 0 to 8 and the ruler is labelled cm. The strip extends from 0 to 6.
Answer: 6 cm, or six centimetres. The unit identifies the size of the intervals being counted. The number 6 alone does not communicate that unit; 6 m would name a different unit from the one displayed.
Map each response to a testable hypothesis
The tasks overlap: a learner can count intervals in Task 3 as well as subtract endpoints. That is helpful evidence, but it means the four answers are not a validated set of separate psychological measurements. Keep plausible explanations open and use the conversation prompts to distinguish them.
| Item and response | Possible explanation | Conversation prompt | Fresh check and answer |
|---|---|---|---|
| 1: chooses Q | May use the physical edge instead of zero; may have confused the strip labels. | “Point to zero, then point to where each strip begins. Which start did you use?” | A new strip starts at zero and ends at 5 on a cm scale. Its length is 5 cm. Ask the learner to identify zero before answering. |
| 2: gives 5 cm | May count both end ticks as units; may have made a counting slip. | “Show one centimetre, then move that distance along the strip.” | A strip spans 0 to 3 on a cm scale. Three intervals give 3 cm, although four ticks bound them. |
| 3: gives 7 cm | May report the right-hand reading as length; may overlook the stated start. | “What does the 2 tell you? Show the part of the ruler covered by the strip.” | A strip spans 3 to 9 on a cm scale. 9 − 3 = 6 cm; six one-centimetre intervals are covered. |
| 4: gives 6 without a unit | May omit a convention or not understand “including the unit”; unit knowledge remains unconfirmed. | “What does cm mean? Say the whole measurement so another person knows the unit.” | A strip spans 0 to 4 on a scale labelled cm. Report 4 cm or four centimetres. |
The fresh checks above supply all the numerical information needed for discussion. For an independent check of actual ruler reading, draw or provide a readable ruler with those endpoints; merely telling the learner the endpoint numbers changes what is being assessed. Keep that distinction in your notes.
Three contrasting fictional profiles
Profile A: choose a demonstration from observed counting
A selects P and reads 3 cm in Task 1, gives 5 cm in Task 2, gives 7 cm in Task 3 and writes 6 cm in Task 4. In the follow-up conversation A taps every boundary tick from 0 to 4 and counts “one, two, three, four, five”. On Task 3 A says, “The answer is the number at the end.” These observations support two specific instructional needs; the responses alone did not prove them.
Demonstrate a one-centimetre interval by drawing a short arc between adjacent ticks. Move the interval, counting spaces, then compare a zero-start strip with a shifted strip of the same length. Use the fresh 0-to-3 task: the answer is 3 cm. Next use 3-to-9: the answer is 6 cm. If A can solve only while you point to each interval, keep the support in the record and schedule another independent opportunity.
Profile B: clarify the reporting request
B gives P and 3 cm, 4 cm, 5 cm and then simply “6”. Asked what cm means, B says “centimetres” and explains that the strip covers six centimetre intervals. When asked for the “whole measurement”, B says “six centimetres”. This additional evidence supports a clarification of the reporting convention; it does not establish a general language difficulty.
Explain that a measurement needs both a number and its unit. Give the fresh 0-to-4 task without another reminder. “4 cm” supplies the requested information. If B still omits the unit, ask what B thought needed to be written rather than repeating all of ruler measurement.
Profile C: check an apparently successful result
C supplies all four expected answers, including 5 cm for Task 3. However, C says, “I guessed five because it looked about that long.” The correct answer is a false positive for the stronger claim that C can explain a nonzero-start measurement. Do not replace it with an invented incorrect answer; record the correct response and the unsupported explanation separately.
Give the new 3-to-9 task independently. In this fictional continuation C answers 9 cm and again points only to the right endpoint. Demonstrate the uncovered 0-to-3 portion and the covered 3-to-9 portion, then count or subtract to find 6 cm. A later check from 4 to 11 should give 7 cm. If instead C had explained 9 − 3 = 6 correctly at first, the next step would have been another independent application, not automatic reteaching.
A completed decision route
- Can the learner access the picture and prompt? If not, supply a readable or otherwise appropriate version before interpreting the mathematics. Note what changed.
- Does pointing reveal a zero-placement or interval-counting issue? If yes, demonstrate the relevant feature, as with A, then use a fresh unassisted task.
- Are quantities explained correctly but the response convention unclear? Clarify the wording and unit requirement, as with B, then ask for a new measurement.
- Are answers correct but reasons absent or guessed? Seek independent evidence, as with C. Teach only the issue the additional evidence supports.
- Are the method and explanation both sound on a new task? Continue with a suitable application, while retaining opportunities to revisit the skill. Do not infer permanent mastery from one short probe.
Teacher practice and model decisions
- A learner reports 8 cm for a strip from 3 to 8. What is the answer and next question? The answer is 5 cm. Ask how the learner used the 3. The response could reflect endpoint reading, but a copied number is another possibility.
- A learner counts the ticks bounding a 0-to-5 strip and gets six. What should the demonstration show? Show five equal spaces bounded by six ticks. Length is 5 cm on a centimetre scale; counting boundaries and counting intervals answer different questions.
- Two learners have three correct answers each. Should they receive identical support? No. One might omit a unit while the other cannot handle a nonzero start. Compare response patterns and explanations before choosing an action.
Questions about short diagnostic probes
Why not add the four answers into a score?
A total hides which feature needs attention. A response profile and a short explanation are more useful for this narrow teaching decision.
Can I read the questions aloud?
Yes, when reading the words is not the intended outcome. Keep the mathematical demand unchanged and record any explanation or prompting you add.
Does a wrong answer reveal a misconception?
It suggests a hypothesis. A learner’s method and a contrasting fresh task are needed before selecting targeted support.
Is a correct answer enough?
Not for a claim about reasoning. A guessed answer can be correct, so ask for a method without supplying the answer.
Should the learner move every strip to zero?
That is helpful in a placement demonstration. Task 3 deliberately keeps the strip fixed so the learner must use the interval between two readings.
Can I diagnose a learning disability with this probe?
No. Four classroom items cannot establish a disability or a lasting ability label. Use them only to choose and check a small instructional response.
When should I repeat the check?
Use a fresh task after the support, then revisit the idea during later work. Record whether the performance was independent, supported or inaccessible.
Reference for evidence and feedback
The historical KNEC age-based assessment framework, section 4.1, connects tool selection with the evidence sought and the feedback provided. This original probe does not reproduce an official tool or establish current administrative requirements.
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