How to prevent students from using modified calculators to cheat on exams?

Question

Recently my faculty (mathematics and statistics) and I have been dealing with widespread cheating due to calculators that have been modified so as to have more functionality than is permitted.

At my university we have a standardized calculator that is to be used for tests. This brand of calculator has limited functionality however recently these calculators have been modified and sold so that students can cheat on tests. We have managed to get a hold of one of them and it appears that the electronics inside have been modified. We have managed to identify the group of individuals responsible for modifying and selling these calculators however we are not sure what to do about it.

Here are the options we have considered so far:

1. Check each calculator individually before tests to see if it has been modified. This is impractical as they don't look any different on the exterior and are no different in weight. We would need to open them all up and look inside.

2. Provide our own calculators to the students. This approach, although better than the last, has its drawbacks. It would be expensive for the department to purchase enough calculators initially and then they would over time break and be lost, resulting in more cost so we would prefer not to go this route for that reason. Additionally, students could still quite easily take a modified calculator of their own into exams and swap it out for the provided one.

3. Change the official calculator model. We could move to a new model of calculator however I suspect this would only be a temporary fix as the group responsible for modifying and selling the calculators could easily switch to modifying the new model.

4. Stop having calculators all together. We would prefer not to resort to this as we don't think forcing students to do lengthy arithmetic calculations is the best way to test them. We could try to avoid such things however sometimes it is simply necessary to ask such questions, for example, in an introductory stats class we would like to ask students to find the standard deviation of a set of data points. Asking them to do this without a calculator seems unfair however we can't simply avoid asking such questions if we want to test the students properly.

5. Taking action against the group responsible for making the calculators. Fortunately this group has been identified, however they are not students at my university so we cannot take direct action against them for academic disintegrity. We would like to take legal action against them if possible however my faculty and I are unsure if there is precedent for such a thing. As far as I can tell they are not committing any crimes. If there is something we could do in this regard please let me know.

6. Simply ignore the problem. This is obviously not ideal as using these calculators gives students a clear advantage over those without them. Additionally, students using them often don't need to learn how to perform various calculations and can instead just plug in the various values and have the answer come out.

Has anyone has this happen at their institution before? If you have any suggestions as to what we can do in this situation it would be greatly appreciated.

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Here is some clarification on the exact nature of the modifications:
To enter into the modified "mode" you type in a sequence of numbers (eg: 1234567) then it enters into the new mode in which you can do many advanced calculations.
pressing the reset button on the back causes it to appear to reset without actually resetting. If you type the password in you will still get back to the modified mode. In this mode formulas can be saved for example.

Answer 1

I received my bachelor's degree in mathematics in 1970. I didn't own a calculator.

There were some adjustments that helped with no-calculator tests:

• Many of my exams had ten points per question. 9 of the points were for clearly showing correct working. One point was for getting the right answer. A student who understood the material but was bad at arithmetic could get 90% without a single correct answer. A student who depended on a fancy calculator could miss more points for not showing all their work.
• The exam booklet included, at the back, any trig and similar tables we were going to need. Answers only had to be to the rather low precision supported by those tables.
• Questions were designed with easy numbers. For example, fractions would often simplify by just crossing out common factors.
• Questions were structured to minimize difficult arithmetic. For example, ask for the variance rather than the standard deviation, but also ask what they would have done differently to get the standard deviation.

Given the problem of the modified calculators, you can go in one of two directions. The first is real world. Full Internet access, statistical calculators etc. The other is to go back to the 1960's, and design tests for no calculators.

Answer 2

Don't use the calculators. The final number you get in a math/stat exam is not that important, is it? Have them write down the standard deviation formula, instead of having them calculate it by pressing two buttons. Find ways around not using the calculator. @Geoffrey suggestion is a good one. Are you interested in the correct number or in them understanding the meaning of variance and how it is calculated?

I am against using a calculator in any exam unless you get to very high levels of math or physics, at that point you can have all the hacked calculators you want but you will need to use your brain 100 times more than your intro stats class.

In addition, I might tell the students that the calculators have been banned because of the cheating, or tell them they should focus on the process.

Answer 3

I question the assumption that the department buying calculators is infeasible.

• Calculators that can do basic arithmetic are dirt cheap, as little as $2, and probably less when buying in bulk.

• If you need a scientific calculator, they can be had for $5-$10, again, probably less in bulk.

On the other hand, reworking the material to not require calculators, as suggested by some, would be a huge expenditure of time and effort, probably far outweighing the cost of buying calculators when you consider the value of people's time. Also there is merit to your original premise of giving students an aid for arithmetic.

I already gave an answer attempting to stay within the parameters of the question, but it has some downsides, as commenters noted. Departmental calculators is a nice clean solution with no downside other than cost, so perhaps it is worth reconsidering.

If cost truly is prohibitive, could you require students to pay for a calculator that you hold for them? Many programs charge things like lab fees. Could you do something similar?

Edit: to prevent cheating by bringing in an identical calculator, you could come up with a scheme involving calculators that differ in appearance. Someone suggested assigning different colors of calculator by row (not known in advance), for example. Though I don't see that comment now, so I can't credit who had that idea. Or you could make the calculator too unwieldy to sneak in--for example, by mounting it to a large flat board in some way.

Answer 4

You don't have to check all calculators. Make sure to announce that you will be checking a random sample of calculators and that students caught with modified calculators will be expelled (if that's possible, e.g. for serious academical missbehaviour) or otherwise severely punished.

That way they will think twice before bringing a modified calculator because the risk is huge.

Talk to the legal department to see if you can require a sample of students to hand in their calculators at the end of the exam and have them tested then or exchange them with faculty calculators and have them tested during the exam.

Answer 5

Give them a computer, not a calculator.

Most universities have computer labs. Use them for your exam. With some help from the IT department, you can make sure that they cannot communicate on the network, and that they contain exactly the software that you allow them to run.

Besides the practical aspects, I think it is a good thing if calculators disappear from the world. They are basically crippled tablets/phones/computers with a poor user interface. If it weren't for exams, they would be a relic from the 90s, like floppy disks and programmable VHS recorders. Giving them a computer is testing them on the same skills that they will need in real life today, not on an artificial crippled setup.

Answer 6

Are you testing your students ability to do 1950s grunt work putting a large amount of numbers into a machine in the correct order in a time trial, or their understanding of math? You do not need to have your students do "lengthy arithmetic calculations". Your tests don't even need to use numbers at all. Or calculators for that matter.

if you're going with the first approach, however, modifying the calculator to best fit the requirements of the test should be encouraged rather than punished.

Answer 7

Just compose problems in the way that requires understanding rather than mechanical skills and make all calculators totally useless. For example, instead of asking "What is the antiderivative of $x^n$ with respect to $x$?" ask "What power function has an antiderivative equal to its square?". Now I challenge anyone to find a calculator that will help with this form of the question or a student with solid knowledge of algebra and calculus who will find the second question much harder than the first one.

Answer 8

Firstly let me welcome you to the 21st Century. :-)

"Calculators" went out with the dinosaur, people use smartphones now. So you're involved in the classic institutional mindset where you're trying to operate without reference to the real world and falling way behind it in the process.

The students do have calculators, smartphones and tablets.

Your tests should ideally not contain elements that test their ability to operate their electronic aids. But on the other hand they will have access to these aids in the real world - who actually doesn't use these things in the real world ?

So I'd suggest the correct policy is to :

• Structure exams to provide all the required information. Memorizing formulas is pointless so testing they can is pointless. All it does is bias tests in favor of people with good memories regardless of ability to apply their knowledge, so ...

• Test ability to apply knowledge, not ability to memorize things. We almost all nowadays carry about with us a tiny device capable of accessing almost any information we want. Could we please stop testing pupils on their ability to memorize stuff and rather on the ability to use what they can know.

• Exams may be the problem rather than the solution. We should really be moving away from exams (two hours of panic should really evaluate four or five years of work ??) and move to assessment based evaluation. The later gives a more consistent picture than some two hour exams that can be failed simply due to stress (which is huge). Shift your courses to assessment and away from the antiquated formal exam.

• Numeric calculations should deliver minimal points in an exam.

It doesn't matter one iota whether they can get the calculation right or wrong in a high-stress two hour exam. It proves almost nothing. Fine, it might be relevant if I was testing astronauts for the extremes of operating conditions they might have to deal with. Most people work at desks, don't have to do in-your-head calculations that decide life-or-death. People that do typically have to undergo specialist testing anyway. So ditch the numerics and stick to the theory and making them demonstrate they understand it.

• Statistics I can think of no less useful a thing than wasting test time on calculating statistics. This was only of practical use when people had to understand the operation of e.g. log tables (as we did when I started studying) because it was a relevant skill. But now ? It proves nothing but that they can type do numerical calculations under stress ( or can type accurately under stress ). It's devoid of practical value. Don't bother. Test the understanding of what they stats mean, not the ability to calculate them.

Stop having calculators all together. We would prefer not to resort to this as we don't think forcing students to do lengthy arithmetic calculations is the best way to test them. We could try to avoid such things however sometimes it is simply necessary to ask such questions, for example, in an introductory stats class we would like to ask students to find the standard deviation of a set of data points. Asking them to do this without a calculator seems unfair however we can't simply avoid asking such questions if we want to test the students properly.

As I've suggested, this is not testing them properly. It's testing the ability to type into a calculator (or do mental arithmetic) under stress - quite useless skills when they'll spend almost their entire lives walking around with pocket devices that do it all better and more accurately and they'll often get away with just cut and pasting data in.

Aim to test their understanding of what those statistical number mean and how useful they are in decision making. The mechanical act of do the calculation is simply the trivial application of formula in these cases - very, very few points or time should be allocated to this in an exam.

Taking action against the group responsible for making the calculators. ... As far as I can tell they are not committing any crimes.

Depends on local laws. I'd strongly suggest getting the state body that governs your exam and education system involved. You might, at a worst case, consider getting your institute to sue them for the costs of dealing with the cheating. Clearly they knew it was cheating as the mechanism to activate the functionality is not straightforward.

Simply ignore the problem. This is obviously not ideal as using these calculators gives students a clear advantage over those without them. Additionally, students using them often don't need to learn how to perform various calculations and can instead just plug in the various values and have the answer come out.

Simply admit it's not a problem.

Provide students with information they need to solve a problem or develop an answer. Focus on testing ability to apply information. Forget completely about memorization and calculation - these are certainly not useful tests. There are much better ways to test a person's memory (ask a psychologist) and much better ways to test their ability to calculate and type under stress. So test what they understand about the fundamentals of the subject, and their ability to extract meaning from results.

Answer 9

We haven't experienced cheating as sophisticated as described in the question. But there have been issues, and we have been moving towards a no-calculator policy. Over the last few years I have taught all levels of calculus and linear algebra, all with a no-calculator policy.

In linear algebra, in particular, row-reduction often requires doing arithmetic with fractions, and I remember years ago the students frantically punching their calculators (so much that I have indeed check that they were doing some related calculation); still, since the no-calculator policy, no issues have arisen.

Answer 10

One option I've sometimes seen used is to give students a small lookup sheet with the calculations they'll need for the exam. So if one of the questions in the exam is "find the mean of 3 and 8", the sheet would include the information that (3+8)/2 = 5.5 along with various red herrings.

It will take some work to set up and it's not practical for all situations, but sometimes it's an option.

Re. the idea of the department supplying calculators: you can deal with the problem of students sneaking in a second calculator and swapping it out during the exam by marking the department calculators in a visible way. "Today everybody in Row 1 gets the yellow calculators, Row 2 gets green, ..." etc. Then it's pretty obvious when somebody's not using the calculator you supplied.

Answer 11

Every calculator can be put "on steroids"

I am a reverse-engineer nerd, fiddled consistently with calculators (albeit never used for cheating) and can tell you that since someone found out the potential of calculator-modifying there is nothing you can do to stop it unless you provide calculators. Even in this scenario a student could sneakily switch the one he has on the table.... Every calculator, even the simplest of the Casios can be reverse engineered to display messages from e.g. an Xbee on its screen. Trust me.

It is not easy. Don`t be too harsh on the original perpetrators...

Punishment-wise I`d make a distinction on who just bought the modified calculators and on who actually carried out the mod.

"Just buy" are the ones that deserve the biggest punishment, so determined at cheating that spent money on buying cheating hardware.

Actual minds behind the reverse-engineering and modding (provided that they are the original makers of the mod, not just script kiddies), should be punished, but keep in mind that as far as I know it takes the very brightest of the pack from your average engineering class to successfully reverse engineer and modify a calculator. Try to give this as a lab task and see... Honestly, regardless of the grades they are getting, they probably will prove to be the best engineers after school. Don`t kick them out please!

Modify your tests

It is entirely possible to design tests not to require a calculator (in my engineering college it was basically forbidden on every test), personally I believe such tests are the best one as they require more symbolical calculation.

Answer 12

As Pat Shanahan suggests, just don't give credit where you can't see the work. Liberal use of the phrase "Show all work" should solve some of your issues. If somebody is using a contraband calculator to skip steps on a problem, they get very little credit for the solution.

The issue you're not addressing, though, is cheating. Using an unauthorized calculator is cheating -- no ifs, ands, or buts. Protecting academic integrity should be an important part of what you strive to do, and if honest students feel disadvantaged because many students around them are cheating, that is a very poor outcome.

I suggest a) reminding the students beforehand that unauthorized help of any form, including improper calculators, on an exam is an academic honesty issue, and will be treated as such, b) exams will be designed so as to minimize the amount of help that such a calculator can provide (and then try to do that!!), c) calculators might be spot checked during exams, and d) getting caught with such a device during exams will be treated as per university policies on violations of academic honesty.

While less than ideal, I suggest that spot-checking calculators of students who lose credit on a previous exam for not showing work might be an effective strategy. I suggest that if one or two students get caught every now and again, the practice will eventually stop -- especially at US universities, where repeated violations will result in separation.

Answer 13

My Cal II professor got it right - he had two versions of the test:

Calculator-free (default)

This version had small numbers - typically 1-3, maybe 4 tops. The arithmetic was really simple, and he would give you points for showing your work (though you could get full marks if you got the answer correct without the work. But without the work and an incorrect answer then you'd get zero, so you may as well just show your work - you could get 70-90% of the points by showing correct work with wrong numbers).

Calculator-aided

I never took one of these tests, so I don't even know what was on there, but he warned us that if you had a calculator it was because you needed it, or you wouldn't be able to actually finish the test.

Answer 14

We have more computers than some, apparently.

https://www.respondus.com/

Our university uses a product called LockDownBrowser. Once the student begins the test the application full-screens itself, and prevents them from navigating away from the test.

A virtual calculator is could be displayed when necessary to do the math. I don't know the exact details, but many instructors use it.

The students put all permitted materials on top of the desk, and the rest stays either below the desk or somewhere else out of reach. Some have the students leave there other materials in their lockers on test day.

Answer 15

Two suggestions: (1) Unless the calculators are very sophisticated, ensure that full marks will only be given if all steps of the calculations are shown (though I would need information about the type of questions asked). (2) Make sure that only one type of calculator is allowed in the exam and have the department provide that model for the exam and then require that the student return the calculator after the exam.

Answer 16

If you don't want to change you tests or testing habits, here's a less impractical way of checking calculators, especially if you combine it with DonQuiKong's suggestion of taking a random subset: check calculators after the exam.

Just make a couple of students write their name on their calculators and hand them in with the exams. That way you have as much time as you want to test them, find the password to activate it, or even just unscrew the back to look if the electronics are standard.

That, with fair warning of an exemplary punishment such as automatically failing the class (or being expelled as suggested elsewhere), should be a good dissuasive measure.

If this is during a testing period and students need calculators immediately afterwards, arrange to lend them school-issued calculators as a temporary replacement, otherwise just arrange with them to pick the calculators up the next day or something like that.

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For other considerations such as swapping modded for normal calculators, I remember when I used to take tests we had to leave our bags with phones and all at the entrance of the class on test days. Make them bring to their tables only what's strictly necessary: pen, paper, calculator, snack, etc. but nothing in which they could hide a second calculator.

Answer 17

A calculator provides approximate numeric solution only and would not be able to provide answers that cannot be represented with the help of its finite decimal display. Think tasks with the answers like sin(1/5), sqrt(3), 2777/4879 or similar. They can only be obtained analytically. This would reduce the problem to the few very high end models and also laptops are capable of running (rather expensive) symbolic math engines like Maple V.

Also, such tasks would show students why ability to solve without calculator is still valuable.

Answer 18

Some of these points have been brought up in other answers/comments, but there's still value in collecting them in one answer:

1. Evaluate your students in regular classes. Ask them questions, see how they respond. You should already have some idea of how well students are learning before the test. If students do well on tests but not when you actually talk to them, this is a red flag (Not necessarily a red flag for cheating. Even if they aren't cheating, there's likely something that you should be addressing.)
2. Have calculator-free tests At least some of your tests should be calculator-free. You should be testing your students' understanding of the material, not their ability to perform calculations. Ask yourself what you expect your students to learn, and how that can be tested.
3. Ask for calculator instructions If you really want to test students' ability to use a calculator, you can just ask them “What buttons would you press to get the answer to this question?” and not actually give them a calculator. This should be used sparingly, but is another tool available.
4. Redistribute Take all the students' calculators and randomly distribute them between the students.
5. Offer a bounty Combined with above: offer a bounty to students who find that the calculator they were given was modified.
6. Random sample You don't need to check every calculator, just a random sample. If the penalty is harsh enough (at the very least, they should be given a 0 for the course, if not expelled), this will still be a strong deterrent.
7. Look at legal options. Your causes of actions against the people making the modifications aren't too strong. Maybe tortious interference. However, if you can get the maker of the calculator involved, they have much stronger causes of action. For instance, if someone is selling a modified calculators and presenting them as normal, that's a violation of trademark.
8. Pay attention to use Walk around the room and watch how people are using their calculators. Are they being furtive? Using their calculators on questions that don't require any calculations? Pressing keys that don't make sense for the problem?
9. Look at patterns A modified calculator is going to be more useful on some questions than others. Look at whether there are students doing better on those types of questions. You can even deliberately make questions that only students with modified calculators can answer.

Also, it seems like this issue could be reduced if classrooms had cameras recording students taking tests, but that's probably not feasible in the current culture.

Answer 19

The only feasible way to have secure calculator use is to provide them. I guarantee you that students this resourceful and determined will outsmart any other method.

If calculator use is then desired, the only question that remains is how to make it affordable.

Treat them like required customized textbooks only available at your store.

Require each student to buy a school owned calculator equal to the cost of a calculator. The school maintains custody of this exam calculator.

Use this to fund purchases.

Provide a calculator at the time of the exam and collect afterwards.

At the end of the year, students may take possession of the calculator or sell them back to the school at a discounted rate, just like textbooks. If you make the discounted rate enough, students will keep them and sell them elsewhere if you so desire.

The important part is that no student ever has custody of a calculator used for an exam. The school always does.

Answer 20

There are a few more options not listed in other answers. They are a lot more devious but may be less successful.

• Start modding and selling calculators yourselves. Obviously don't let the students know it is you. Program the forbidden functions to produce incorrect results when specific inputs are present. Then use those inputs only on tests. Don't use them for homework problems and such so the answers in those cases are correct. There might even be money to be made.
• Examine some of the modded calculators. See if they were programmed well. If there are glitches with some inputs then craft the tests to trigger those glitches.
• Calculations done in software have limitations. There are problems with rounding and loss of precision for example. Design exam questions that will put any calculator into problem areas but wouldn't cause problems for a student not using a calculator.
• Start modding and selling calculators yourselves openly. Require that only your modded calculator can be used for some questions. Have the calculator produce encoded results or systematically altered results. Other calculators, modded or not, would not be able to produce those results. One example might be to produce the result and a check value.

Answer 21

I think you should just ignore it. If you try checking for them, or stopping them, there will always be a workaround eventually. If all they're getting is the right answer then that's not a problem. You should look at the way the tests are graded, because on all of the tests that I've taken, if you don't show work then the problem is wrong regardless of the answer, and this is the way it should be to make sure students actually know what they are doing, not just typing in numbers.