Final Exam Problems
May 1, 2019 – Dallas, Texas, USA
Professor Larabee unlocked the door to her office on the campus of the University of Texas, Dallas. She walked inside but left the door wide open. She expected visits from faculty colleagues. They always showed up right after a meeting of the Geosciences Department to complain about university policy decisions or clueless administrators. Usually, Professor Larabee only half-listened to the griping while she read through her email, but today she was interested in how her fellow instructors would react to what they had just heard. According to their dean, cheating was rampant in all their classes.
The first person to lean into Professor Larabee’s doorway was new to the job. Professor Parks came from Berkeley and had loads of new ideas on how they should modernize geology instruction. “What did you think of that?” he asked Professor Larabee before taking a sip from his coffee mug.
“Pretty depressing,” she answered. “I’m not sure I completely believe it.”
“What part?”
“That everybody’s cheating. I realize on homework problems it’s easy to simply Google the answers . . .”
“And don’t forget Chegg,” interjected Professor Parks. “You can essentially pay someone to do an assignment or write a paper for you.”
“Sure. But that’s why most of us don’t factor homework very heavily into final grades. We mostly rely on test scores.”
“It’s just as easy to cheat on a test if you’re determined.”
“Maybe online tests, but I’m not so sure about proctored, in-class tests.”
“You might be surprised, especially if you’re using multiple choice tests.”
“How are they supposed to be doing that?”
“Signaling. One kid actually knows what he’s doing, and he sells answers to all the others. You know, tap the foot once for A. Tap the foot twice for B.”
“But how is that new? Students have been trying that stuff since the beginning of time.”
“Now they’re way better organized. They text each other. They talk on Reddit. It’s much easier to figure out who knows what’s going on and willing to sell answers. And this generation doesn’t see anything wrong with it. If they can get away with it, they will. It’s like a game.”
Professor Larabee gave her colleague a skeptical look. “Sounds a little paranoid. I think I would have noticed something suspicious by now.”
Professor Parks chuckled smugly. “Suit yourself. But kids are posting on Reddit about your Rocks and Minerals class.”
“Oh yeah? What are they saying?”
“Your tests are easy to work around.”
“They’ve said that about my class? This semester?”
“Yep.”
“Who? Who’s been saying that?”
“It’s all anonymous so I can’t really give you any names. But you might want to switch things up. You’re using the same old multiple-choice tests?”
Professor Larabee hated the way he said, “Same old.” It was like he was accusing her of being stagnant and stale. Sure, she was using multiple choice questions. They were easy to grade, and after several years, she had figured out which questions truly tested a student’s competence. “I watch the class pretty closely during a test,” she said defensively.
“I’m sure you do,” said Professor Parks. “But if you’d like ideas on changing things up, I’m happy to help.”
“Alright. I appreciate it,” said Professor Larabee dismissively. She turned toward her computer like she was no longer interested in the conversation.
A few more faculty colleagues stopped by Professor Larabee’s office to chat, sharing varying opinions on how widespread the cheating problem was and what should be done about it. None of those conversations affected her the way the first one did. Her mind returned to what Professor Parks said. It sounded like her class was a running joke on Reddit. Kids thought it was easy to cheat their way to a good grade. Professor Parks, loudmouth that he was, undoubtedly shared all of this with the entire department.
Professor Larabee thought back to the two midterm tests she had given to her Rocks and Minerals class. Each test had taken an hour and she had watched the students very carefully. But come to think of it, one particular student kept loudly sniffing. She remembered because the sniffing had been so noticeably annoying. What if those sniffs had been signals?
She looked up from the computer at her desk to the rows of books on her shelves. Next to them were her diplomas and award certificates for teaching and research. She was a good scientist and teacher, and she could not stand the thought that her students were making her a laughingstock. They thought her class was a joke, huh? It was easy to cheat, huh? If they wanted to play a game, she was pretty clever at games too.
The scheduled final exam was a week away. Professor Larabee was not the type to put things off until the last minute, so she had already compiled test questions and printed up an exam. But that did not matter. She was determined to show she could be smart and flexible. She dropped the stack of printed copies for the first version of the exam into a bin for shredding. She would start over.
Although Professor Larabee was worried by the idea that students might be using the internet to share multiple-choice test questions she had used in the past, she did not want to completely abandon her collection. She looked them over and chose the twenty-five best questions to keep and then set out to create twenty-five more. She looked over lecture notes and reading assignments, trying to capture what she considered the fundamentals of Rocks and Minerals. From what ores were they mined? Where were they found? What were their chemical compositions?
After three days of composing new questions, Professor Larabee was finally satisfied. When combined with her previous twenty-five questions, she now had fifty questions that were sure to measure how much her students had learned.
But how was she going to stop any signaling going on? If a single brilliant student was willing to broadcast the answers somehow, the test would not be a good measure of anything. As Professor Larabee looked at a first version of her test, she realized that the simplest way to combat any signaling was to mix up the questions. If they appeared in a different order on each test booklet, anyone tapping out A’s, B’s, or C’s as multiple-choice answers would only be sharing answers for their particular test. Anyone listening and using those answers would get a garbage score.
Professor Larabee would also be able to compare the answer pattern for any suspiciously low scores to those with high scores. If the patterns matched, she would know exactly who was signaling and who was listening. It was the perfect trap.
It took a lot of work to prepare 65 different versions of the final exam for each student in the class. Professor Larabee used Microsoft Word to randomly move the 50 questions around for each new version and save it as a different document file. On the front of each printed test, she included an identical title page and list of instructions to make all the tests appear the same from the outside. On the morning of the final exam, she hauled the stack of papers down to the lecture hall where the test was scheduled to take place.
Students shuffled into the room, yawning, and complaining to each other about how brutal finals week was treating them.
“As you come in and find a spot, I want you to leave at least one empty desk between you and anyone around you,” called Professor Larabee. “And put your backpacks and phones under your chairs. All you’ll need is a pencil.”
When all 65 students were in an acceptable seat and holding only a pencil, Professor Larabee passed test booklets down the rows of chairs.
“They’re all the same. Take one and pass the rest down. Once everybody has a test, you can start. Circle the correct answer after each question. You’ve got three hours. Obviously, I don’t want to hear any talking.”
Professor Larabee watched with satisfaction from the front of the large room as every student dropped their head and began reading. Little did they know that they would all see the same questions in a different order. Creating the new version of the test had cost her 30 hours’ worth of work, but it was bound to produce an interesting result. If any signaling was taking place in the room, Professor Larabee was eager to let it naturally continue. She kept her ears open but tried to act disinterested by pretending to read a book.
She heard a cough. Then three more short coughs. Glancing up, Professor Larabee spotted the cougher. He was sitting on the end of a row with a knit cap pulled almost down to his eyes. Samuel Patrillo. He had answered a lot of questions during lectures, but come to think of it, he looked kind of shifty. Those coughs could mean something.
While scanning the crowd, Professor Larabee noticed a girl in the front row. Her first name was Simone. She kept trapping her ear with her pencil. Tap and then circle an answer. Always either one, two, three, or four taps. It had to mean something. Whenever she circled an answer, the students sitting around Simone also seemed to circle an answer.
Professor Larabee silently shook her head. Now that she was tuned into it, the signaling was not hard to notice. As an educator, she was disappointed. She liked to think that students were in college to learn, not simply to pursue a grade and a diploma. Now she had to face reality. At least she had the new test in place. She was ready to get tough.
Although the test was scheduled for three hours, Professor Larabee expected most of the class to finish in under two. She was surprised when everyone turned in their test booklets before 70 minutes elapsed. It seemed like yet another sign of cheating. She gathered up the stack of completed tests and headed for her office.
In the hallway, Professor Larabee ran into Gracie Palmer, her enthusiastic teaching assistant for the class.
“Are those the finals?” asked Gracie.
“Yes. Didn’t take them long. I was a little surprised.”
“Do you want me to grade them? I still have a couple of hours I’m supposed to work. If you give me an answer key, I can do it, no problem.”
“If you’re willing, sure. But an answer key won’t help. I scrambled up the questions for every copy of the test. But I used a little trick to make grading easier. You have to promise to keep it a secret once I show you.”
Gracie’s face lit up, eager to share a secret with a professor. “Sure, I promise.”
When they reached Professor Larabee’s office, she grabbed the first test from the stack and opened it up. She pointed toward the first question. “I put a little code in each one of the questions. If you look closely, you’ll see there’s an extra space between two of the words in that sentence. One extra space means the answer is A. Look at the next question, it has three total extra spaces, so the answer is C. You get it?”
Gracie stared skeptically at the test page. “Uh yeah. I get it.”
“So simply count the extra spaces and you know the answer. No key necessary. See, this person got all these questions right.”
“Okay. This shouldn’t take me long,” said Gracie. “I’ll find an empty conference room and bring them back to you when I’m done.”
As Professor Larabee waited for Gracie to return, she began an email to all her faculty colleagues. The message explained her concern about student integrity and how she had found a perfect way to use multiple choice questions to create a test with a built-in way to catch anyone trying to cheat. She also had a clever system for making it easy to grade. After sharing the embedded code, a student helper could spot correct answers without an answer key.
After Gracie returned with the test results, Professor Larabee planned to find some examples of students who had been caught cheating and share the information with her colleagues. How many students had been using the signals from Samuel and Simone and how bad would their scores be? Professor Larabee felt a lot like a detective waiting for results from a crime lab.
The results came back sooner than expected. Gracie was back in her office in less than an hour.
“You’re done already?”
“Yep. It went fast. Everyone got 100%.”
“What? I can’t believe that. There’s no way everyone got 100% on a Rocks and Minerals final. It would be the first time in history.”
“I’m pretty sure it was your secret system.”
“What? You mean the extra spaces?”
“Yeah. When you’re a student taking a test like this, the first thing you look for are patterns in the questions. Like do the answers always go in the same order – A, B, A, B. Or does the correct answer always sound a little different than the wrong ones. The extra spaces look totally suspicious. I noticed them before you said anything. Everybody else must have noticed too.”
“You think they caught on right away?” asked Professor Larabee in a devastated voice.
“Maybe not right away, but eventually.” Gracie opened one of the tests. “Like this guy, see how he went back and erased some of his first answers. Once he was sure of the pattern, he backtracked.”
Professor Larabee leaned back in her chair and dropped her head. “Now I don’t know if they learned anything about rocks and minerals. All I know is they’re good at spotting patterns.”
Gracie shrugged her shoulders.
“How could I have been so shortsighted? I thought I was being clever. I was too clever for my own good. How much time was that secret code going to save when grading compared to how much time I spent making up the test?”
“Sorry,” said Gracie. “I guess you could have asked me to take a look at it before you gave it to them.”
“Too late now. What am I supposed to do?”
Gracie shrugged again.
“Well, I definitely need to swear you to secrecy. Please don’t tell anyone about this disaster.”
Gracie nodded her head like she understood. The email message Professor Larabee planned to send to her colleagues was deleted. Average grades for the Rocks and Minerals class were unusually high for that semester.
Professor Parks stopped by a week later to ask how final exams had gone.
“Just fine,” replied Professor Larabee coolly. “I’ve got some new ideas to try out next year. And by the way, you shouldn’t believe everything you see on Reddit.”
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