On this page
When pocket calculators first reached classrooms, many teachers feared students would never learn arithmetic. Today the same worry is aimed at AI. The calculator debate has one advantage: it has decades of research behind it. This post summarises what that research found and what it suggests for using AI tools in maths and science.
Did calculators damage students' maths skills?
Mostly not. The first large review was a meta-analysis by Hembree and Dessart (1986) in the Journal for Research in Mathematics Education. It combined 79 research reports. At every grade except Grade 4, using calculators alongside traditional teaching appeared to improve average students' paper-and-pencil skills, both in routine exercises and in problem solving. Students who used calculators also had better attitudes towards maths and a better view of themselves as maths learners.
The exception is the part worth remembering. In Grade 4, sustained calculator use appeared to hinder the development of basic skills in average students. That is a stage when basic number skills are still forming.
What did later studies add?
Ellington (2003) updated the picture with a meta-analysis of 54 studies. Students' operational skills and problem-solving skills improved when calculators were part of both teaching and testing. When calculators were not allowed in the test, results were mixed, but in no case did calculator use hinder the development of maths skills.
A second meta-analysis by Ellington (2006) looked at 42 studies of graphing calculators, from middle school to first-semester calculus. With calculators in teaching and testing, students' procedural, conceptual and overall achievement improved.
Three lessons for AI
1. Timing matters. The Grade 4 finding shows that a tool can get in the way while a skill is still forming. For AI, the parallel is the stage where you are learning a method for the first time, such as setting up a free-body diagram or balancing a redox equation. Let the AI help you after you can do it, not instead of learning it.
2. What you are tested on shapes what you learn. Ellington's results depended on whether calculators were allowed in the test. Your practice should match the conditions of your exam, including whether calculators are allowed at all. Check the rules in your exam's official information bulletin each year.
3. AI can do more than a calculator. A calculator does arithmetic; you still choose the method. An AI chatbot can choose the method for you, which is the part you most need to practise. A recent trial with nearly 1,000 high school students found that students with unrestricted ChatGPT access did better during practice and worse once it was taken away. We cover that study in Does leaning on AI weaken learning?
How to keep your number sense
A simple test of whether a tool is helping or replacing you: can you tell when its answer is wrong? Estimation is the check.
Example. Your calculator or an AI says 48 × 52 = 2,596. Is that right?
Both numbers are close to 50, so the answer should be close to 2,500.
Use the identity (a − b)(a + b) = a² − b² with a = 50 and b = 2: 48 × 52 = 2,500 − 4 = 2,496.
So 2,596 is wrong. A slip like this is easy to miss if you only copy the answer.
In physics, the same habit is checking units and orders of magnitude. If a calculation gives a car's speed as 3,000 m/s, something has gone wrong before you even reach the options. Our guide to dimensional analysis as a fast check shows how.
A weekly routine for using tools well
One no-tool session a week. Do a timed set of problems with no calculator and no AI, matching your exam's rules.
Estimate before you compute. Write a rough answer first, then use the tool, then compare.
Use AI after an attempt, for the step you are stuck on. Ask for the next step or a hint, not the full solution.
Redo it bare. After any problem where a tool helped, solve a similar one without it the next day.
Getting help without skipping the reasoning
When you are stuck, what you need is the reasoning behind the step, not just the number. The Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer, so you can see why each step follows and then try the next problem yourself.
This week, do one problem set with no tools at all and compare your score with your usual one.
