By Andrew B. Raupp, Founder & Executive Director, STEM.org Educational Research™
Short answer: before students reach for an exact answer, they should know roughly what kind of answer would make sense. Estimation is not a lesser form of mathematics. It is a way to create an independent benchmark against which a calculator, spreadsheet, sensor, simulation or AI-generated result can be judged.
One of the most useful habits in STEM takes only a few seconds:
Before calculating exactly, predict the neighborhood of the answer.
That habit sounds elementary. It is not.
It is a form of independence.
When a learner estimates first, the calculator is no longer the authority. The spreadsheet is no longer the authority. The sensor is no longer the authority. The software becomes a tool whose output can be compared against a prior model of what reality should approximately look like.
That distinction matters more as STEM tools become easier to use and harder to inspect.
A machine can be precise without being right
In a 2019 PLOS ONE study, researchers gave college students an onscreen calculator that was secretly programmed to return incorrect answers on selected problems. The errors ranged from modest numerical distortions to conceptual mistakes.
The striking result was not merely that students could be fooled. It was how rarely many of them became suspicious.
Across the studies, higher numeracy predicted a greater likelihood of noticing implausible calculator output. Presenting problems in concrete, familiar contexts also increased suspicion in some conditions. But numeracy did not make students less likely to use the calculator in the first place.
That is an important distinction. Skilled learners may use the same tools as everyone else. What changes is whether they possess enough independent understanding to challenge the output.
The study involved calculators and college students, so it should not be treated as direct evidence about every modern technology. But the pedagogical question travels well: what does a learner know before the tool answers?
Estimation is not just rounding
School estimation is sometimes reduced to a ritual: round the numbers, perform an easier calculation, move on.
Real estimation is broader.
It asks whether an answer should be positive or negative. Whether the magnitude should be closer to 10, 100 or 10,000. Whether doubling an input should roughly double the output. Whether a percentage can exceed a logical boundary. Whether the units are consistent. Whether a measurement is physically plausible. Whether the direction of change fits the model.
Research on approximate calculation shows that this kind of reasoning develops over time and is distinct from exact arithmetic. In other words, being able to compute precisely does not automatically guarantee strong estimation skill.
An experimental study by Jon Star and Bethany Rittle-Johnson makes another useful point. Fifth- and sixth-grade students learned computational estimation either by comparing alternative strategies or by reflecting on strategies one at a time. Students who compared strategies became more flexible problem solvers, and students who already knew some estimation strategies also developed stronger conceptual knowledge.
The lesson is not that there is one correct way to estimate. Quite the opposite. Estimation becomes powerful when learners can choose among several ways to get a reasonable benchmark.
The Plausibility Loop
A simple routine can turn estimation from an occasional classroom exercise into a general STEM habit.
STEM.org Framework · Plausibility Loop
- Predict. What kind of answer should I expect before I calculate?
- Bound. What values would clearly be too small, too large, wrong in sign, or impossible?
- Compute. Use the appropriate calculator, code, spreadsheet, sensor, simulation or other tool.
- Compare. Does the exact output live inside the reasonable range I expected?
- Explain. If it does not, which assumption, input, unit, formula, procedure or tool behavior should I inspect first?
The point is not to make every problem slower. Once the habit becomes fluent, many plausibility checks take seconds.
What this looks like across STEM
Mathematics: before calculating 15% of 21, a student can reason that 10% is 2.1 and 5% is about 1.05, so the answer should be a little above 3. A result of 31.5 should trigger immediate suspicion.
Science: before accepting a plotted measurement, ask whether the scale and direction fit the phenomenon being observed. A sensor reading should not become true merely because it arrived digitally.
Engineering: before trusting a design calculation, identify the expected order of magnitude and the units. A misplaced conversion factor can produce a beautifully formatted answer that is wrong by a factor of 10, 100 or 1,000.
Data analysis: before interpreting a dashboard, ask which values are even possible. Percentages, rates and averages each have boundaries and assumptions that can expose a broken formula or misleading denominator.
Coding: before running a program, predict at least one test case. If the code returns an unexpected value, the discrepancy becomes evidence rather than a surprise with no reference point.
In each case, the learner creates a small piece of independent knowledge before the machine responds.
Why this matters in the age of AI
Generative AI makes this habit more important, not less.
An AI system can produce explanations, code, calculations and polished prose quickly. Sometimes that assistance is excellent. But fluency of presentation is not a substitute for independent verification.
The relevant educational principle is the same one behind our human-agency framework for responsible AI in STEM education: assistance should strengthen judgment rather than quietly replace it.
Estimation creates a small but meaningful barrier against passive acceptance. The learner arrives at the tool with a prior expectation. That expectation may be wrong, but even a wrong prediction can be educational because the discrepancy demands explanation.
This is also connected to productive struggle. A learner who has to form a rough model before seeing the exact answer performs cognitive work that disappears when the answer arrives first.
Five ways to teach the habit without adding another unit
Estimation does not need to become a separate chapter in the curriculum. It can become a routine embedded inside existing work.
- Ask for the neighborhood first. Before exact computation, require a rough range or order of magnitude.
- Make impossible answers visible. Occasionally include results with the wrong sign, scale or unit and ask students to reject them without recalculating everything.
- Compare two estimates. Let students see that different strategies can be reasonable and discuss which is faster, tighter or easier to explain.
- Keep units attached. A number without its unit can hide a conceptual error that would otherwise be obvious.
- Require a sentence after the answer. “This result is reasonable because…” forces the learner to connect output to meaning.
These practices are especially useful when students use calculators or AI because they preserve a layer of human judgment before and after the automated step.
The answer should have to earn your trust
There is nothing anti-technology about estimation.
Engineers estimate and then model. Scientists estimate and then measure. Programmers predict and then test. Analysts form expectations and then inspect the data. Expertise is not defined by refusing tools. It is defined partly by knowing when a tool’s answer deserves another look.
That is the habit worth protecting.
A student should not finish a STEM problem merely because the screen has stopped changing. The problem is finished when the learner can explain why the result is reasonable, what could have gone wrong, and what evidence would change the conclusion.
Exactness is useful.
Judgment is what makes exactness trustworthy.
Research referenced
- LaCour, M., Cantú, N. G. & Davis, T. (2019). When calculators lie: A demonstration of uncritical calculator usage among college students and factors that improve performance. PLOS ONE, 14(10), e0223736.
- Star, J. R. & Rittle-Johnson, B. (2009). It pays to compare: An experimental study on computational estimation. Journal of Experimental Child Psychology, 102(4), 408–426.
- Ganor-Stern, D. (2016). Solving Math Problems Approximately: A Developmental Perspective. PLOS ONE, 11(5), e0155515.
