In the first decade of this millennium, we were all impacted and shocked by some serious acts of cheating. However, had we stopped to reason about the situations in question, we might have foreseen the cheating. We might have predicted the cheating from the very motivating factors that brought the cheating about. In this page we will discuss a few famous examples of cheating from this last decade and show how their common elements relate to mathematical reasoning.

Let's reason about cheating. Two main factors contribute to the likeliness of cheating. First, how easy is it to cheat? When it becomes easy to cheat, then cheating is more likely. Second, what are the rewards for cheating? The higher the incentive, the more motivation to cheat. Cheating becomes most probable when the incentives are very high and simple, arbitrary, one dimensional definitions of success make cheating very easy. We will look at examples below.

Ease increases the likeliness of cheating. But strong incentives increases the motivation to cheat much more.


Last Update: April 2012


Cheating in Educational Settings

Case Study Washington DC Schools under Michelle Rhee and NCLB

Motivation & Ease: Attempting to improve schools, Rhee implemented a system of strong consequences. Teachers and principals who failed to produce got fired. Teachers and principals who oversaw large increases in performance got large bonuses. Under Rhee's management the incentive for results was extremely high. This alone would have led to cheating. Rhee used an excessively simple definition of success: test scores. Simple definitions of success lead to simple formulas for cheating: alter the answers. When the testing service found evidence of cheating, Rhee failed to investigate. Lack of regulatory oversight, also makes cheating very easy. The excessively strong emphasis on overly simplistic results combined with a lack of regulatory oversight is a formula for cheating. Cheating will occur when systems are managed this way. It turns out that teachers and parents suspected the cheating and reported it. Nothing was done to address their concerns. In the Washington DC schools, as well as many other school districts regulated under NCLB, programs that incentivise cheating were created. Everybody should have anticipated the cheating. Nobody should have been shocked when the cheating was finally exposed.

Rhee and her supporters wanted to prove that schools can produce results the same way that businesses produce results. Unfortunately, as we shall briefly review below, they were correct. In the same decade much of the economic success occurring in America was not real success; it was cheating. But first, we will review a few less obvious examples of academic cheating.

General Cheating in Education

The cheating under Rhee and in Chicago was blatant, intentional, and committed by a small group who had something to gain. But there are forms of cheating that are subtle and committed by many.

Teaching to the Test: Overemphasis on standardized testing creates a situation where the one dimensional definition of success makes cheating easier. When teachers are given strong incentives to increase test scores, this simplistic definition of success combined with the incentives make cheating very probable. Instead of providing students a good general education that meets their needs and reaches their natural curiosity, teachers can reduce education to nothing more than test-prep. Many school administrators even reward this method of raising test scores. They are gaming the system. The consequence is that the test scores no longer represent real gains in general education. Instead, the tests scores represent learning having been limited to the tested material. The higher scores can actually represent less effective learning!

Learning to the Test: Students can and will commit the same error. When the measure of results are limited to test grades and material to be tested is clearly defined, when grades are overemphasized by either the teacher or the parent, then cheating becomes easy. A student can limit their learning to what will be tested. It is not obvious that this is a form of cheating, but it is. The students are gaming the system. The students limit their learning to get the highest grade for the least work. The desired outcome was learning. But the real outcome was limiting learning to get the grade. Too much incentive being placed on simplistic arbitrary outcomes actually serves to limit performance rather than expand it.

Grade Inflation: The problem of grade inflation is well known. Again, this form of cheating has the same basis as the others. Too much incentive placed on simplistic arbitrary outcomes. Parents and administrators can be very abusive with educators when their children get low grades. Thus, the incentive to inflate grades is very high. Since all grading systems are arbitrary, it is easy to cheat: simply by changing the grading system to make grades higher for low performance.

Adjusting Test Scores to the Level: Much effort and money must be invested into ensuring that the tests actually address the correct material without introducing accidental biases. To ensure that the tests provide accurate results, testing organizations compare test scores to grades and survey teachers about student performance. However, if the state organization has high incentive to prove increased scores, or if they have high incentive to demonstrate that the tests are successful, then they have high motivation to adjust the scoring system and question difficulty downward. Again, the method of cheating is easy. All that is needed to guarantee that that downward adjustments will happen is strong incentives to produce higher scores.

Author's notes: When I first read about Michelle Rhee's management style in the Washington DC schools I recognized that her approach would more likely lower standards and increase failure than raise standards. I was surprised to see the reports of significant improvements. A year later I saw the investigation that demonstrated that the increases in test scores were the result of cheating. I realized that had I reasoned mathematically about the methods Rhee used in the DC schools, I would have inferred cheating from the initial reports. This page was motivated by our common failure to recognize how we motivate and fail to audit cheating.

Just a few years earlier I was working at a school with very high standards. Test scores were mediocre, but students completed projects that made adults say, "Wow!" A new administrator was hired who insisted that we spend less time on projects and more time on low level skills. Test scores rose slightly. Administrators celebrated their successes. But staff who had been at the school a few years were disappointed by the drop in complex project-based accomplishments, and the drop in student group and self-management skills. Testing had replaced high level projects.

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Standardized testing is extremely costly. In the first decade of the millennium, for example, North Carolina averaged more than $30 million each year in direct spending on testing, about the same amount as they spent on text books. Many schools also spent additional resources on test-prep materials and other costs directly related to testing. Even much of the spending on textbooks was driven by the need to teach to the test. The time costs of testing were also very high. The typical classroom lost a few days potentially useful days each school year to standardized testing. With the tight budget, school districts had to forgo much needed resources, and teachers had to omit potential learning opportunities, to make resources available for the mandated testing.



Economic - Fiscal Cheating

The bubble economy of the first decade

Although it is natural to discuss academic cheating, it follows that economic situations have the same factors that lead to cheating. Fiscal situations are their own strong incentive. All that is needed to guarantee that cheating will occur in fiscal situations is simple one dimensional arbitrary definitions of success combined with a lack of auditing. When the bottom line is the sum total of incentivized outcomes, altering the paperwork, cooking the books, doctoring the numbers becomes the most straightforward means to create the rewarded outcome. In the same decade that highly rewarded test scores brought about cheating in Washington DC schools, we saw the exact same thing happen in our businesses: Enron, Countrywide, Madoff, Bear Sterns, etc. They all were given strong incentives. They were all given arbitrary one dimensional measures of success that made cheating easy. They all lacked regulatory auditing that could have caught the cheating. For many of these cases, the cheating was reported but not investigated. These businesses were achieving the same way that Rhee's schools were achieving. They were gaming the system, changing the numbers, cheating.

Mergers - takeovers - down sizing

Mergers, takeovers, and downsizing are much like teaching to the test and learning to the test. An oversimplistic one dimensional measure get rewarded, even while that measure becomes inversely related to the intended outcome. Corporate executives are highly rewarded for creating profitable companies, not new products, and new jobs. Historically, the bottom line has been an indirect measure of the creation new products, new jobs, and the growth of the company. However, executives have found that through mergers and downsizing they can temporarily increase the bottom line by eliminating jobs, products, and the long term viability of the company. The executives game the system, they cheat, by artificially increasing the bottom line using methods that destroy the very successes that the bottom line is meant to measure. Like test based grading systems, the one dimensional target made cheating easy by failing to measure the complex outcomes intended. The huge incentives given for raising the measure guaranteed that cheating would occur.

The "jobless recovery"

All of these negative outcomes were overlooked, because they occurred during the infamous "jobless recovery." Just like all the examples above, willingness to accept a simple one dimensional measure of success, the GDP, led to claims of success that were not real. Politicians celebrated the jobless recovery as proof that their programs had succeeded. But actually, their willingness to acknowledge only one simple arbitrary measure did not prove that they had succeeded. It proved that they had cheated. They intentionally ignored evidence to the contrary, failed to audit suspicious evidence, while bragging about the GDP. One dimensional thinking, with strong incentives, and no auditing guaranteed that cheating would occur.

References and related discussions:


Fiscal - economic

Other cheating



We have discussed a simple formula to guarantee that cheating will occur. First, create a simple one dimensional definition of success. Second, create strong incentives to achieve that outcome. Third, fail to audit the methods by which involved parties achieve that outcome. When you do this you guarantee that cheating will occur.

What then are the antidotes to cheating? Address the three main factors. Resist the temptation to reduce any situation to a simple one dimensional scoring system. Real success is never a one dimensional concept. Keep incentives sufficiently small and the measures sufficiently complex. Never base a large reward on an arbitrary one dimensional outcome. Audit. Audit in multiple dimensions. Audit especially unusually high performers. In sports constant auditing is required. Multiple auditors (referees, line judges) watch every play. Odd that so many believe that every sports competition requires multiple auditors to watch every play, but that our economic institutions will be automatically self-regulating.

When test scores rose rapidly in a few Washington DC Schools, auditors should have interviewed the students. Real gains in student performance are evidence in student behavior and attitudes. If you can't see the improvements in the behavior and attitudes then the gains in the test scores are not real. When housing prices rose rapidly, federal and bank auditors should have checked for evidence that the properties and neighborhoods in question experienced real improvements. When the numbers are too good to be true in any situation, people should audit and analyze. We should watch for evidence of motivation to cheat, and evidence that the measure being used is too simple and easy to doctor. We should expect cheating any time we see high incentives or one-dimensional goals.


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