Did you know that replacing a broken thermometer halfway through a class experiment can make a perfectly ordinary temperature change look like a sudden scientific discovery? A graph may jump at the exact moment the replacement arrived. The pupil has not necessarily measured a real jump in the water. The measuring system may have changed.
An instrument-change discontinuity is an apparent break in a sequence of measurements caused partly or wholly by changing the instrument, its setting, its placement or the way it is read. The immediate answer is to preserve the original readings, record exactly when the replacement occurred, compare both instruments on a common stable reference if possible, and avoid claiming a physical change until the measurement change has been investigated.
Diagnose the problem before calculating
Ask a learner to consider this fictional observation: a beaker reads 24.0 °C at minute 12. A thermometer breaks; another is used. At minute 18 the reading is 25.0 °C. What can the pupil state confidently? The recorded numerical readings differ by 1.0 °C, and the instrument changed between them. What cannot yet be stated confidently is that the actual water temperature rose by precisely 1.0 °C. Two unknowns—temperature change and instrument difference—are mixed together.
This is not an invitation to distrust all measurements. It is an invitation to identify what each number represents. A thermometer measures through a physical device with a scale, sensitivity, response time, positioning and possible offset. Different instruments need not produce identical indications for the same sample. A science report becomes more useful when readers can see those conditions instead of receiving a neat but misleading line.
Why a replacement can change the graph
Imagine that instrument A routinely indicates a little below instrument B on the same stable sample. If pupils use A for the first half and B for the second, a higher second-half reading could be a combination of genuine warming and an indication difference. Other changes may also matter: the new thermometer could be dipped deeper, held closer to a heater, allowed less time to settle, or read with a different graduation.
The important distinction is between repeatability (how similar repeated observations are under comparable conditions), offset (a difference in indication relative to a stated reference) and real change in the object studied. Neither a smooth line nor a striking jump identifies its own cause. The US National Institute of Standards and Technology’s discussion of measuring-system characterisation explains why calibration, verification, resolution and operating conditions affect how measurements should be interpreted.
A complete invented worked example: the warming beaker
Record what actually happened
Illustrative classroom exercise, not an actual pupil outcome: A group observes water warming gently under supervised laboratory conditions. Thermometer A reads 24.0 °C at minute 12. It becomes unusable. Thermometer B reads 25.0 °C at minute 18. The replacement is marked in the log, and the exact changeover minute is recorded as unknown between minutes 12 and 18. Pupils also make a reference comparison afterward, with the same stable water sample and similar immersion, waiting and reading conditions.
- Common reference sample near 20 °C: A indicates 20.1 °C; B indicates 20.5 °C. B is 0.4 °C higher than A on that comparison.
- Second stable reference sample near 30 °C: A indicates 30.2 °C; B indicates 30.6 °C. Again, B is 0.4 °C higher than A.
- Original time sequence: minute 12 uses A and reads 24.0 °C; minute 18 uses B and reads 25.0 °C. The recorded difference is 25.0 − 24.0 = 1.0 °C.
- Conditional illustration: If the indication difference really stayed at +0.4 °C through this range under matching conditions, a rough cross-instrument comparison is 1.0 − 0.4 = 0.6 °C. Label this as an assumption-based estimate, not as a proven correction.
Check the arithmetic independently: 20.5 − 20.1 = 0.4; 30.6 − 30.2 = 0.4; 25.0 − 24.0 = 1.0; 1.0 − 0.4 = 0.6, all in °C. The two checks strengthen the specific working assumption in the example, but they do not establish perfect calibration, a constant offset outside that range, or the precise water temperature at any moment. A learner should not erase 25.0 and replace it with 24.6 as though that value had been directly observed.
Show the evidence on the graph without forging continuity
Plot both recorded points faithfully. Mark a vertical dashed annotation or short note between minutes 12 and 18: “Instrument A replaced by B; readings may not be directly comparable.” Where continuous measurement cannot be established, do not draw a confident uninterrupted physical trend across the interval. A graph can show the measured points and their uncertainty without pretending that the gap has vanished.
If the original instrument is broken beyond use and cannot be compared with the new one, the reference check in this illustration is not available. That is a different case: record the discontinuity, retain both readings, and explain that the exact physical difference across the changeover cannot be isolated from instrument differences. Do not fabricate a comparison after the fact.
A straightforward decision routine for students
- Identify the change: write the old and new instrument identities, the time interval, units and reason for replacement.
- Protect the record: keep raw readings with their original labels and do not silently convert, discard or smooth them.
- Check comparability: if safe and feasible, use a common stable sample or standard, identical handling and enough time to settle.
- Calculate with a label: separate the raw indication gap from any explicitly conditional adjustment; state units and assumptions.
- Conclude narrowly: say what the evidence supports and what still needs a repeated or better-controlled test.
Mistakes that make a science report look cleaner but less accurate
The first mistake is inventing the value the broken thermometer “would have given”. That is not an observation. The second is deleting inconvenient values because the new line does not join the old one. That removes the very clue a reader needs. The third is automatically subtracting a single difference measured at one condition from every subsequent reading; offsets may change with temperature, sensor type or placement. The fourth is treating a replacement model’s printed precision as guaranteed accuracy.
There is also a practical distinction between instrument error and scientific disagreement. If the temperature rises across a gap in the record, the water may truly have warmed. The claim is not that the increase is imaginary; it is that the design cannot tell how much of the observed jump belongs to warming without further comparison. That measured humility is part of careful scientific reasoning.
Progressive practice: guided, paired, then independent
Guided: spot the break before finding the difference
Give the learner a table: 10 min, A, 21.2 °C; 15 min, A, 22.0 °C; 20 min, B, 23.1 °C. Ask for the measured change between 15 and 20 minutes and one reason not to interpret it immediately as true warming. The numerical gap is 1.1 °C; the instruments differ. The diagnostic is whether the learner mentions the change of instrument spontaneously.
Paired: decide whether an adjustment is justified
Now add a stable-sample check: A reads 22.4 °C and B reads 22.7 °C under comparable conditions, so B indicates 0.3 °C higher on that sample. Ask two pupils to explain what extra assumption is needed before making a tentative 1.1 − 0.3 = 0.8 °C cross-instrument estimate. They should mention that the 0.3 °C difference would need to hold under the experimental conditions and range. A pupil who states “the true rise was 0.8 °C” without qualification needs a lesson on evidence language.
Independent: write a two-sentence laboratory conclusion
With no surviving A for a stable comparison, supply readings 26.1 °C (A, 8 min) and 27.0 °C (B, 14 min). The student should write: “The recorded indications increased by 0.9 °C between the readings. Because a different thermometer was used after the first reading and no direct comparison was possible, the exact change in water temperature is not established by these two points alone.” An acceptable answer can be shorter, but must preserve both facts.
What parents and teachers can observe
Rather than rewarding a pupil for a graph without gaps, ask what changed in the method and whether the graph tells the truth about that change. A teacher can observe three behaviours over successive practicals: instrument names and change times appear in the log; raw values survive into the report; and conclusions distinguish recorded indications from physical interpretations. A parent can use a home thermometer comparison or an invented worksheet scenario, without needing specialist equipment, to ask “Which sentence is a measurement, and which sentence is an assumption?”
A four-week teaching sequence can move from highlighting changes in provided tables, to annotating graphs, to making conditional calculations, and finally to explaining an unfamiliar instrument swap independently. Score the explanation against a simple checklist rather than claiming a guaranteed exam mark. Improvement means more accurate statements of evidence and fewer unexplained adjustments.
Limitations and responsible practice
A classroom reference comparison does not replace professional calibration. Instrument safety and the teacher’s laboratory instructions come first. Certain sensors take time to respond, and a fixed offset found for two illustrative samples may not apply at other values. If the replacement differs greatly in range or resolution, a common reference may be insufficient. When measurements inform safety, health or formal compliance, use the appropriate qualified process, not a school exercise.
NIST’s engineering statistics guidance on calibration problems notes the importance of systematic instrument and operator effects. Here, the general lesson is simple: evidence should remain traceable to the tool and method that produced it.
Frequently asked questions
Should we delete all measurements from the first thermometer?
No. Preserve the record, label which instrument produced which values, and assess whether the parts can be compared. Deleting an entire segment without justification destroys useful evidence.
Can we use the replacement thermometer immediately?
Only according to the relevant safety and method instructions. Allow appropriate response time, record placement and instrument identity, and check suitability for the range. Do not assume readings are comparable merely because both display °C.
Does a 0.4 °C offset prove every result is wrong by 0.4 °C?
No. It describes the difference in the illustrated reference comparisons. Wider use requires checking whether that relationship is stable across the conditions of interest.
Is it better to stop the experiment?
That depends on safety, the experiment’s aim and what must be measured. A controlled restart can be best when continuity is essential. Continuing with a clearly documented limitation may be useful for an exercise about evidence.
Continue learning and transfer the habit
For related checking skills, see how sensor response delay can mimic change and how to measure when a ruler’s zero edge is damaged. For chemistry graph reasoning, explore data-based science explanations. The wider eduKate Education Hub and the diagnosis-to-independent-checking approach in Secondary 1 Mathematics show how the same habits transfer across subjects.
The core aim is not to make every graph perfect. It is to teach pupils to notice when a conclusion outruns the evidence, preserve what they truly observed, and design a better check the next time. That is a skill they can carry into science, mathematics and everyday decision-making.