For Whom the Bell (Curve) Tolls: A to F, Trade Your Grade Based on the Net Present Value of Friendships with Financial Incentives

TL;DR

This paper proposes a financial-inspired marketplace for trading grades to address issues with traditional grading systems, advocating for viewing certifications as personal equity and suggesting alternative assessment methods.

Contribution

It introduces a novel marketplace model for grades based on net present value and advocates for rethinking grading as personal equity, with implications for policy and assessment.

Findings

Grades can be traded like financial assets.

Traditional grades may have unintended negative consequences.

Alternative assessment methods are proposed.

Abstract

We discuss a possible solution to an unintended consequence of having grades, certificates, rankings and other diversions in the act of transferring knowledge; and zoom in specifically to the topic of having grades, on a curve. We conduct a thought experiment, taking a chapter (and some more?) from the financial markets, (where we trade pollution and what not?), to create a marketplace, where we can trade our grade, similar in structure to the interest rate swap. We connect this to broader problems that are creeping up, unintentionally, due to artificial labels we are attaching, to ourselves. The policy and philosophical implications of our arguments are to suggest that all trophies that we collect (including certificates, grades, medals etc.) should be viewed as personal equity or private equity (borrowing another widely used term in finance) and we should not use them to determine the outcomes in any selection criteria except have a cutoff point: either for jobs, higher studies, or, financial scholarships, other than for entertainment or spectator sports. We suggest alternate methods for grading and performance assessment and put forth tests for teaching and learning similar to the Turing Test for intelligence.

Equations

$$\min \left(15,\max \left(0,\frac{10^{\left\{\sqrt{\ln \left(e^4\right)}\right\}}}{\left\{\sqrt{\ln \left(e^{25}\right)}\right\}}-X\right)\right)$$

$$40-\min \left(15,\max \left(0,\frac{10^{\left\{\sqrt{\ln \left(e^4\right)}\right\}}}{\left\{\sqrt{\ln \left(e^{25}\right)}\right\}}-X\right)\right)$$

$$\%\text{ Change from Zero to One}=\frac{1-0}{0}=\infty$$

$$\%\text{ Change from Zero to One}=\underset{a\to 0^{+}}{\lim }\frac{1-a}{a}=+\infty$$

$$f(x\mid \mu ,{\sigma }^2)=\frac{1}{\sqrt{2\pi {\sigma }^2}}{e}^{-\frac{(x-\mu {)}^2}{2{\sigma }^2}}$$

$$\underset{x\to 0}{\lim }\frac{\sin x}{x}=1$$

$$\underset{x\to 0^{+}}{\lim }\frac{1}{x}=\infty$$

Full text

1. 1 Abstract

2. 2 Good Intentions, Bad Consequences … Ugly Repercussions

3. 3 The Grade Trade in a Light Pool

4. 3.1 Some More Simple Lessons from a Seemingly Complex Marketplace

5. 3.2 Luminaries in the Light Pool

6. 3.3 Risk Management of Structured Products & Grade Payoffs

7. 4 Infinite Progress Benchmark

8. 5 Turing Tests for Learning and Teaching

9. 6 The Crux of the Curve

10. 7 Conclusion

11. 8 Acknowledgments and End-notes

12. 9 References

1 Abstract

We discuss a possible solution to an unintended consequence of having grades, certificates, rankings and other diversions in the act of transferring knowledge; and zoom in specifically to the topic of having grades, on a curve. We conduct a thought experiment, taking a chapter (and some more?) from the financial markets, (where we trade pollution and what not?), to create a marketplace, where we can trade our grade, similar in structure to the interest rate swap. We connect this to broader problems that are creeping up, unintentionally, due to artificial labels we are attaching, to ourselves. The policy and philosophical implications of our arguments are to suggest that all trophies that we collect (including certificates, grades, medals etc.) should be viewed as personal equity or private equity (borrowing another widely used term in finance) and we should not use them to determine the outcomes in any selection criteria except have a cutoff point: either for jobs, higher studies, or, financial scholarships, other than for entertainment or spectator sports. We suggest alternate methods for grading and performance assessment and put forth tests for teaching and learning similar to the Turing Test for intelligence.

2 Good Intentions, Bad Consequences

… Ugly Repercussions

Stating that we have all been students at some point in our lives would be an assumption not far from reality. Here, we are referring to students in the currently understood sense of the word, as of the 21st century, who wish to get good grades since we seem to think that there is a high correlation between grades and employment opportunities, scholarships, further academic pursuits, financial assistance and many other benefits (Jones & Jackson 1990; Loury & Garman 1995; Rumberger & Thomas 1993; French, Homer, Popovici & Robins 2015; Daley & Green 2014; End-note 2).

We discuss a possible solution to an unintended consequence of having grades (and related artifacts such as college diplomas or course completion certificates), which is that students are more focused on grades rather than on learning, which is the true purpose of being students. Another unintended consequence which has immediate repercussions, to both students and educational institutions is that certain students who are receiving financial scholarships might end up losing their funding if they fail to obtain a certain minimum level of grades: (Johnstone 2004) is a discussion of the shift in at least part of the higher educational cost burden from governments, or taxpayers, to parents and students, which has necessitated that students look out for different financial assitance schemes to provide for their higher education costs; (Monks 2009) finds that merit aid has a statistically significant but inelastic effect on enrollment of extremely high ability students; (Henry, Rubenstein & Bugler 2004) study students just above the eligibility threshold for assistance and find that losing scholarships may substantially reduce any potential positive effects of receiving it in the first place, suggesting that efforts to increase the number of students who retain the scholarships should be a major focus of future policy initiatives.

(Carruthers & Özek 2016) find that losing one’s scholarship results in a small degree of detachment from college, though thankfully, no effect on timely completion in majority of the cases; (Gross, Hossler, Ziskin & Berry 2015) find no relationship between institutional merit aid and student departure, instead need-based aid was consistently related to decreased odds of departure; (Zhang & Ness 2010) find that state merit scholarship programs do indeed stanch the migration of “best and brightest” students to other states; (Sjoquist & Winters 2015) find that exposure to state merit aid programs have no meaningfully positive effect on college completion; also see: (Cohen-Vogel, Ingle, Levine & Spence 2008; Henry & Rubenstein 2002; Cornwell, Mustard & Sridhar 2006 for the pros, cons and other aspects of merit based financial aid; End-note 3).

Giving scholarships based on grades on a curve can be one way to provide an incentive for students to maintain high scores (significant debate exists on the use of grades, with or without a curve, as incentives to learn: Stan 2012; Betts & Grogger 2003; Kulick & Wright 2008; Grant & Green 2013; Figlio & Lucas 2004). As long as students are not too caught up on their grades, (easier said than done, but we discuss ways that could accomplish this in later sections) scholarships built upon a grade curve can be a decent decision making criteria of handing out limited resources, which in this case are monetary funds available, to the large body of students that seek assistance. Also, grading on a curve could be one way mitigate the effects of grade inflation (Chan, Hao & Suen2007; Johnson 2006; Eiszler 2002; Kohn 2002; Sabot & Wakeman-Linn 1991; Zangenehzadeh 1988; End-note 4).

There has been significant debate regarding the usage of the Bell Curve in societal contexts: Murray, C., & Herrnstein 1994 is a highly controversial book titled the Bell Curve. The book’s title comes from the bell-shaped normal distribution of intelligence quotient (IQ) scores in a population; the authors argue that human intelligence is substantially influenced by both inherited and environmental factors and that it is a better predictor of many personal dynamics, including financial income, job performance, birth out of wedlock, and involvement in crime than are an individual’s parental socioeconomic status. Kincheloe, Steinberg & Gresson 1997 is a collection of essays criticizing this book. Sternberg 1995; Ma & Schapira 2017 are other reviews on this topic that highlight the fact that the factors affecting IQ are still poorly understood. Beardsley 1995; Jacoby & Glauberman 1995; Fendler & Muzaffar 2008 consider the historical aspects of the bell curve, both the concept and the above mentioned book, and highlight the possibility that history is usually intertwined with politics. End-note 5.

The issue of students losing assistance is exacerbated (or, perhaps, even caused) due to guidelines (more of a law, since they need to be followed), which prescribe that students must be graded on a curve (Fendler & Muzaffar 2008; Taylor 1971; Reeves 2001; End-note 7; Figure 1), which limits the number of students that can obtain top grades. (Durm 1993) is a summary of the history of how grading policies developed and the assumptions that might have led to academe creating its own nightmare; this is covered in greater detail in (Finkelstein 1913; Smallwood 1969; Cureton 1971; Schneider & Hutt 2014). There is a good amount of research on grading policies, whether it is a good practice, potential obstacles to reform, and other aspects of classroom performance and related consequences: (Zeidner 1992; Polloway, Epstein, Bursuck, Roderique, McConeghy & Jayanthi 1994; Stiggins, Frisbie & Griswold 1989; Pintrich & De Groot, 1990; Harackiewicz, Barron, Carter, Lehto & Elliot 1997; Barron & Harackiewicz 2003; Tomlinson 2005; Guskey 1994; 2011).

We want to emphasize, that these are unintended consequences, since the establishment of universities, educational foundations, introduction of grades, or, having grades on a curve are wonderful innovations, done with honorable intentions, that might have been fabricated to solve certain other problems. One reason, why such unwanted outcomes creep up, is because, we live in a world that requires around 2000 IQ points, to consistently make correct decisions; but the smartest of us has only a fraction of that (Ismail 2014; End-note 10). Hence, we need to rise, above the urge to ridicule, the seemingly obvious blunders of others, since without those marvelous mistakes, the path ahead will not become clearer for us.

Another more unwelcome unintended consequence of having grades on a curve, is perhaps that students end up competing, with one another (Bell, Grekul, Lamba, Minas & Harrell 1995 found that students were most likely to help when the other students were friends, when there was frequent contact, and when the test was not graded on a curve, that is absence of competition; Schneider & Hutt 2014 is a historical interpretation, origins, uses and evolution, of grades; also see: Schinske & Tanner 2014; Brookhart etal 2016; Bresee 1976; Natriello 1987; Aviles 2001). While a competitive spirit, is to be encouraged; an overtly competitive environment destroys the spirit of co-operation among the members of the classroom, who are all travelers on the same journey of learning since they learn not only from the instructors, but perhaps, more from one another.

We conduct a thought experiment, taking a chapter (and some more?) from the financial markets, (where we trade pollution and what not?), to create a marketplace, where we can trade our grade, similar in structure to the interest rate swap (section 3). We want to emphasize that this experiment is meant to be merely hypothetical at this stage. Most importantly we highlight the practical obstacles and many legal and moral implications of even considering such an approach. The benefit of this thought excercise is that it possibly provides solutions to the unintended consequences of having grades, certificates, rankings and other diversions in the act of transferring knowledge; and zoom in specifically to the topic of having grades, on a curve. We connect our discussion to broader problems that are creeping up, unintentionally, due to artificial labels we are attaching, to ourselves.

The policy and philosophical implications of our arguments are to suggest that all trophies that we collect (including certificates, grades, medals etc.) should be viewed as personal equity or private equity (borrowing another widely used term in finance) and we should not use them to determine the outcomes in any selection criteria except have a cutoff point: either for jobs, higher studies, or, financial scholarships, other than for entertainment or spectator sports. Given our fascination with testing and measurement, we suggest alternate methods for grading (sections 4, 3.3) and put forth tests for teaching and learning similar to the Turing Test for intelligence (section 5).

Lastly, it would not be entirely incorrect to state that the majority of the attempts at evaluating students, and perhaps even most (all?) of knowledge creation, starts with answering questions. In present day society, we seem to be focused on answering questions that originate in different disciplines. Hence, as a first step, we recognize that one possible categorization of different fields can be done by the set of questions a particular field attempts to answer. Since we are the creators of different disciplines, but not the creators of the world in which these fields need to operate (based on our present understanding of our role in the cosmos, which might very well change), the answers to the questions posed by any domain can come from anywhere or from phenomenon studied under a combination of many other disciplines.

Hence, the answers to the questions posed under the realm of education or knowledge transference can come from seemingly diverse subjects, such as, physics, biology, mathematics, chemistry, marketing, economics, finance and so on. This suggests that we might be better off identifying ourselves with problems and solutions, which tacitly confers upon us the title Problem Solvers, instead of calling ourselves teachers, professors, physicists, biologists, psychologists, marketing experts, economists and so on. This quest for answers is bounded only by our imagination (Calaprice 2000). Our paper then becomes an example of how concepts from finance and trading, can be used to solve problems in education with many connections to deeper dilemmas in society.

3 The Grade Trade in a Light Pool

Our innovation is to use the financial markets to facilitate trades on grades (End-note 11). Students that have good scores or higher grades, can trade their grade with someone that might end up losing their scholarships, or other opportunities, because of missing out the grades they need. We call this marketplace for grades, “A Light Pool”, in contrast to dark pools used for financial instruments since we would aim for complete transparency and also because knowledge represents light (Mittal 2008; Domowitz, Finkelshteyn & Yegerman 2008; Ganchev, Nevmyvaka, Kearns & Vaughan 2010; Zhu 2014 explain dark pools in finance and their potential benefits and possible harmful aspects; End-note 12; Kvanvig 2003; Pritchard 2009; Kashyap 2017c are discussions about the value of knowledge and the long held beliefs regarding higher powers in the knowledge realm; also see: Turner & Coulter 2001; Hallam 1996; Ludvik 2007; End-notes 13, 14; Dancy, Sosa & Steup 2009; DeRose 2005; Figueroa 2016; Pritchard 2018; Hetherington 2018; End-note 15 are an excellent collection of articles on leading theories, thinkers, ideas, distinctions, central questions and concepts in epistemology).

The person who is giving up the higher grades, in return, benefits from the following items: 1) They earn the good will and friendship of the person who would have lost out a much needed source of money (Berndt 2002 discuss the relationship between the quality of friendships and social development; End-note 16). 2) They can get a certain percentage of the funds that might have been lost without the trade. 3) The grade swap will be reversed when there is no benefit to the person receiving the higher grade in the original trade; perhaps even with another financial component as agreed upon initially when the first trade is made. The structure, which is discussed in detail below, is given in Figure 2.

To ensure fairness, we set a guideline, based on a recent example (as of October 25, 2017) set by Facebook founder Mark Zuckerberg, who has pledged, on Dec 1, 2015, to give away 99% of his wealth to advancing human potential (Schervish, Davis, Cosnotti & Rosplock 2016; Chua, Aricat & Goh 2017; End-note 17, 18); technically, 99% of his Facebook shares will be put into a legal entity, a limited liability company and not a charity, which would be owned and controlled by Zuckerberg. As a private company, this initiative can spend its money on whatever it wants, including private, profit-generating investment (Aron 2016; Clark & McGoey 2016; End-note 19). His net-worth at that time was around, $45 Billion USD. Hence, we suggest that the trade for a grade, should involve a financial component, that is less than 1with$45 Billion USD can give away 99% of it. Then anyone, with much less than $45 Billion, (we do not recollect any financial scholarship to any institution, let alone to any individual student, being more than or equal to this amount) can afford to give away something much less than that one percentage amount.

We would again like to highlight that, this less than 1% suggestion is not to poke fun at Mark Zuckerberg for keeping a few hundred million before giving out everything else. He has every right to keep everything he has earned. His earnings are surely much lesser in value compared to the wonderful legacy he has established, which connects most of humanity, as we know it, with one other. We merely use this example to come up with a number that can act as a upper bound for the financial component to this grade trade.

We further provide theoretical and mathematical justifications based on three axioms (End-note 20):

The value of grades generally decline, as time passes (Figure 3). 2. 2.

The value of friendships usually rallies, as time passes (Figure 4). 3. 3.

The value of money, can increase, as time passes, even after considering inflation, provided, judicious investments are made (Figure 4).

If we have trouble accepting the first two axioms, we must question our moral compass. If we are judging a person, based on grades received long back; is that a good criteria we are using for evaluating someone? If friendships don’t grow over time (or, somehow, become less), should we not examine, whether we as a society, are becoming too caught up with ourselves, (our lives perhaps) to ignore (or wrong or begrudge or resent) the ones that have been a part of our lives, for long periods of time? Hence the NPV (Net Present Value: Ross, Westerfield & Jaffe 2002; End-note 21) of any grade trade is significantly higher for the person who is giving up the higher grade to make a friend, who is likely to wish him well for the rest of his life and also get some monetary benefit, which is going to grow, unless the federal reserve, or other central banks, intervene to set zero interest rates. The third axiom has countless papers discussing it, hence we do not consider that in detail here (Petters & Dong 2016 has a comprehensive discussion of the time value of money and all the related paraphernalia; also see: Cochrane 2009; Bierman Jr & Smidt 2012).

3.1 Some More Simple Lessons from a Seemingly Complex Marketplace

We collect a few more lessons from the financial markets for our system (which, could be a computer software solution as well), that is meant for both trading and grading. If we can trade a stock or financial security hundreds of times in a day (or, perhaps in a millisecond, since it is becoming harder to keep track of the high frequency with which, trades happen these days, in certain venues), we don’t have to restrict our grade trade to happen just once. The grades can (or will?) be traded back; in fact, once the necessity of the grade for the person who would miss an opportunity, financial or otherwise, has disappeared, the grades can, (should?) be reversed back. When the reverse swap happens, we need to make sure, that the financial component obeys any net present value constraints, or, the time value of money rules; this would be in comparison to the financial component in the first trade.

Also, as with any trading, it would only be proper, to ensure that some licensing requirements are met. There are many regulatory bodies in the financial industry, which provide licenses allowing the practice of different types of regulated activities. Some examples of these licenses in financial services are: Series 7, SFC Type 4, and so on (Warschauer 2002; Goetz, Tombs & Hampton 2005 are discussions about how colleges can prepare students to get licenses as financial advisers or practitioners, aiding with an early transition into such careers; clearly in our case there will need to be involvement from universities or educational institutions; End-note 22; Egan, Matvos & Seru 2016 find that misconduct is very prevalent among financial advisers). The license to trade will be granted only to students, that can provide proper documentation, establishing their requirement for maintaining, a certain level of grades, who will be the buyers in the first round of trades on grades; and to all students with higher grades, since they would be the sellers in the first round. When the grades are reversed of course the roles would be exchanged. To be more precise in the use of financial terminology, we could term this a grade swap and the mechanics of how it would work, would have lots of similarities, with an interest rate swap (Hull & Basu 2016; Tuckman& Serrat 2011; Darbyshire 2016; End-note 23).

3.2 Luminaries in the Light Pool

It would seem on the surface, before actually engaging in establishing this market and seeing how this experiment would play out, that there would many buyers for high grades, but perhaps less students willing to lower their grades. Hence, in addition to the two benefits they would receive, the school could provide a certificate stating that this person was willing to give up something, very precious in the perception of most, to aid another fellow student, and in the process, displayed exemplary humanitarian ideals (perhaps, no less than blood or organ donors, who save the lives of others in need: Becker & Elias 2007; Erin & Harris 2003; Barnett, Blair & Kaserman 1992 are discussions about markets for human organs).

It is very likely that this market for trading grades might raise some ethical questions regarding whether it is right, or, wrong, to allow trades on grades. But surely, in a world where we allow emissions, or, pollution to be traded (Drury, Belliveau, Kuhn & Bansal 1998; Burtraw, Evans, Krupnick, Palmer & Toth 2005; Demailly & Quirion 2008; Fisher-Vanden & Olmstead 2013), allowing trades on grades, only when someone badly needs a higher grade to survive and complete their education, must be an acceptable option. If not, have we completely lost our sense of justice (and our minds too?) or have we no idea or clue about what we should or should not be trading?

Another dilemma is whether, corporations would view this as a sort of deception being used by universities to send them inferior candidates. For this we have two refutations: as mentioned, the grades can be reversed back before graduation; also, employers should not be overtly concerned about grades. All corporations have extensive training programs to coach their employees for the duties they would need to perform. If this becomes such a sticking point, which seems unlikely, but just for completeness we mention that perhaps, corporations, also other institutions, need to relax their requirements about using grades as selection criteria. This is especially important for internships, since the grades might not yet have been reversed. We consider the topic of education as a signal of better skills later in section 6.

A much more effortless solution than trading grades would, of course, be to eliminate grading based on curves, eliminate grades entirely or not have such a strong link between grades and financial assistance. We could also cultivate an environment where grades are not taken too seriously, but are viewed simply as the outcome in any competitive spectator sport, wherein, we expect to have winners and losers; we simply need to await the next round of games, while reminding ourselves that winners can take all in some scenarios (Frank & Cook 2010; Garcia-del-Barrio & Pujol 2007; Leeds & Kowalewski 2001; Whannel 2005; Frank 1999 discuss the winner take all effect in sports and other areas of society including higher education applications, which unfortunately are quite sensitive to rankings. Though this effect might be okay in some situations, it does cause deep rifts in segments of society; our core message of ignoring artificial categorizations is likely to produce a tempering effect). Alternately, we could remind Mark Zuckerberg, that his honorable ambition of advancing human potential includes ensuring that humans who have a need are to be taken care of. Because, if we take care of people they will advance their own potential and take care of the world (highly likely, that he might have overlooked this facet of human capability, or, we might have missed the connection between his dreams and our conundrums).

3.3 Risk Management of Structured Products

& Grade Payoffs

A picture is worth a thousand words; and a picture with a few words, must be worth much more? (Figures 5, 6). If we really need to have grades, we suggest one approach to combine, the exam scores, towards a final grade (better termed, the overall grade, since we might allow students to retake the exams, so they can improve their scores. They can retake the exams, when the course is offered next [semester or year], so that the overhead, or, the cost of administering the exam, is minimal). Here, we suggest the use of Structured Products (common in Finance, Kat 2001) to determine the weight of various component exams towards the final grade. Introducing a random component to the weights, and some complex notation, means that perhaps, we will realize that no matter what the weight, if we study the material well, it will be reflected in our grades. Also, the one place, many of us, are likely to notice notation (which is easily overlooked in books, papers and presentations), is with regards, to how exam weights are calculated.

If we cannot completely do away with grades, then perhaps an alternate approach for a grade construction scheme can be,

Attendance, assignments and participation, should guarantee a C+ in tough courses. 2. 2.

The mid-term and the finals (plus other components) can determine whether someone will get A+ or B+. 3. 3.

The percentage weight of the mid-term examination, M%, to the overall grade can be given by expression 1 below. 4. 4.

The percentage weight of the final examination to the overall grade can be given by expression 2 below. 5. 5.

Here, $X$ is the volatility of the mid-term scores, of the exam taking members. The expressions 1 and 2 are aimed at ensuring that students pay attention to the principles and usage of logarithms and min / max functions. This can also be helpful to understand how payoffs of many financial products can be made to depend on variables that are not seemingly related to the financial markets and how creativity is important for the creation of structured products. It is important to keep in mind that many alternate expressions can be used to obtain different types of payoffs. 6. 6.

It should be clear that the below is a very specific example, wherein the weight of the mid-term score changes between 0 to 15%; and the final score weight changes as the difference between 40% and the mid-term weight. The extent to which the score weights will change depends on the performance of the entire class, more specifically, it is based on the volatility of the scores (Broadie & Jain 2008; Javaheri, Wilmott & Haug 2004 discuss derivative products that depend on the volatility or the variance, of certain assets. In this case, the scores are given to human assets).

[TABLE]

[TABLE] 7. 7.

Another example of using random variables as exam or assignment score weights could be more directly related to finance. If the students are managing an investment portfolio for an investment analysis course, then the weights of midterms, assignments or finals could depend on the volatility of the portfolio value or the P&L (profit and loss). Such an approach could mean that the weights might be unique for each individual or group in the course, leading to the scores being directly tied to their own destiny or the matter is much more in their own hands than otherwise. This is equivalent to each individual or group picking random numbers (surely an alternative for courses where there is no portfolio being managed), which would then become inputs into the structured product created to give the weights for their scores.

4 Infinite Progress Benchmark

Another more rigorous mathematical justification to eliminate grading and other methods of labeling learning is outlined using an axiom and a theorem that follows from it below.

Axiom 1**.**

The benchmark to be successful in a course is to have made infinite progress.

Surely, anyone who has made such a tremendous amount of progress should not just be deemed to have completed the course, but to have completed the course with the highest possible distinctions or with an A grade say.

Theorem 1**.**

To make a significant amount of progress, in anything we do, we just need to recognize that anyone who has taken one step forward has made an infinite percentage change from their starting position, which we label as zero. It is safe to assume that infinite progress is significant progress.

Proof.

Since the starting point is zero and the first step denotes a unit increment, the percentage change becomes,

[TABLE]

To be precise, we need to express this as,

[TABLE]

Here, $a$ approaches zero from the positive real number axis, denoted as $a\rightarrow 0^{+}$. This completes the proof (End-note 24).

∎

If we think of any course as a mountain and the enrolled students as hikers seeking to climb to the summit, then as the course progresses and a certain amount of time has elapsed, someone would have climbed higher than others due to innate ability, or due to better practice either as the course goes on or some familiarity with the concepts from before the course started. Here the analogy is that someone who has climbed higher is to be awarded a better grade. We need to recognize that our real competition is not with anyone else, but with ourselves. Our real goal from any learning objective (or any endeavor) is that we are better than our own past selves.

If we have moved forward compared to where we were when we started, we have made infinite progress and it deserves its due recognition. If a student has learned one new concept or idea in a course, they have fulfilled the criteria for infinite progress. If this seems like a rather easy condition, we need to remind ourselves that over the course of an entire formal educational cycle many of us might not even remember the names of the courses we have taken, let alone mastering all the material we have studied. If we learn one concept thoroughly in a course, that can be a noteworthy accomplishment. Hence, if everyone is making infinite progress, their performance is equivalent in one particular way and needs to be acknowledged accordingly.

5 Turing Tests for Learning and Teaching

The Turing Test (TT) developed by Alan Turing (Turing 1950; French 2000 chronicles the comments and controversy surrounding the first fifty years of the TT; End-note 25), is a test of a machine’s ability to exhibit intelligent behavior equivalent to, or indistinguishable from that of a human. Turing proposed that a human evaluator would judge natural language conversations between a human and a machine designed to generate human-like responses. The evaluator would be aware that one of the two partners in conversation is a machine, and all participants would be separated from one another. The conversation would be limited to a text-only channel such as a computer keyboard and screen so the result would not depend on the machine’s ability to render words as speech (Turing originally suggested a teleprinter, one of the few text-only communication systems available in 1950). If the evaluator cannot reliably tell the machine from the human, the machine is said to have passed the test. The test does not check the ability to give correct answers to questions, only how closely answers resemble those a human would give.

In an educational setting, we can devise a Turing Test for Learning (TTL) similar to the TT, that would be useful for conducting examinations and evaluating performance. The first phase of assessment would involve answering a written test based on standard questions (as the discussion progresses, it should become clear that the questions should be designed to be more than straightforward application of concepts, they should gauge the level of comprehension of the topics). The student can use any resource possible including the internet, talking to classmates, professors (including the instructor of the concerned course), books, notes, etc. The students can even leave the examination room and take the test at any location they deem conducive for them to answer the written part. They can also be provided ample time as they deem necessary (in the versions of this test we have conduced, we gave more than one week for some courses).

The first phase will contribute only partially towards the total score. The second phase of the test, which makes up the rest of the total score, involves the student trying to convince the teacher how well they have understood the answers they have submitted in writing. The weighting scheme that combines the first phase and second phase towards an overall score can even be done based on the discussion in section 3.3.

An often omitted criteria that needs to be considered when administering the TTL is the ability, or, the level of skill of the person conducting the test. This gives us another tool for examining the ability of teachers, which becomes the Turing Test for Teaching (TTT). Surely, different individuals are satisfied with different levels of impersonation. When we see any drama, play or movie that depicts the life of any real person, (while reminding ourselves that movies might not be real, but real life can become movies); different people are satisfied with different levels of acting ability. We all know that the person playing the role in the theatrical version is not the same, as the person, that is being enacted. But in many cases, (perhaps, in most cases, when it is well produced), we leave feeling satisfied with the result of the replication. The lesson for us here is this: how far does the test administrator need to go, to believe that the student perfectly understands the subjects being discussed.

To obtain a lower bound for passing the test, we reason as follows: our benchmark for success (section 4) implies that the benchmark for learning has been surpassed if at-least one concept has been mastered and the corresponding questions are answered to the satisfaction of the person administering the TTL. In this context, answering a question and the relevant decision making involved are the lessons learnt, at display to satisfy the success threshold. In an analogous manner, someone can be deemed to have succeed in the TTT if they have ensured that any student has comprehended one additional concept compared to when the student started learning under this instructor.

6 The Crux of the Curve

While it is tempting to feel contented, with any new innovation, or, solution that comes up for any problem; the real responsibility lies in distilling down to the heart of the matter, which in this case, are the bells and whistles we have attached to the the act of transferring knowledge. We need to see beyond the artificial ornaments that we confer upon the torch bearers of knowledge in our later generations. These are nothing but certificates, diplomas, awards and rankings of the institutions from which these artifacts have been gathered that adorn all of us covering the true beauty within each of us.

There is a huge literature on the signalling effect of grades (Grant 2007; Liu & Neilson 2011; Arkes 1999; Bills 2003). A point to be noted is that the industry is less critical of lower grades while higher education institutions are more stringent in checking the grades of incoming student applications. If we need to rely on the signals given by others and are unable to apply our independent thinking to make decisions, we need to question why everyone needs an education. It is worth highlighting that any recognition we give to anyone, or, any form of respect for anyone is well placed. But we should not let these adornments distract us from the luminous brilliance that can burn brightly from each of us, if we are given the right spark that can ignite it and a conducive environment that can nurture it. If we feel that it is tedious to understand each person that we meet and use our interactions to gauge how to give flight to everyone’s full potential, then perhaps, we all need more training on how to be better social beings (not just human beings?), than the time we spend reading textbooks and gathering decorations that merely serve to act as diversions.

This is the appreciation we need to give all our fellow beings and is our primary duty not just to others, but to ourselves, since we are all creations of the same mother, evolution (Darwin 1859; Dawkins 1976), that has nourished us for millions of years through countless trials and errors, making us perfect in every way possible, tirelessly, cycle upon cycle. Everything we do is because of this evolutionary training we have received for millions of years (this hints at an answer to the question: what we should do in terms of life goals and career choices; perhaps, we should pursue what interests us rather than what we seem to be good at; simply because with such extensive preparation we can be good at everything and accomplish whatever we aspire to do). The information from these historical lessons are coded and passed on through our genes so that there is improvement with every generation (International Human Genome Sequencing Consortium 2001; Venter, Adams, Myers, … & Gocayne 2001). Again we need to be reminded that perfection is a moving target. We have perfection only till the next shortcoming is spotted and then the tireless cycles that mother nature spins will continue with improvements to adapt to the new challenges.

Needless to say, the introduction of any solution, is fraught to bring new problems of their own, or unintended consequences, if you will. Periodic revisions of any policy and ensuring that organizations are not too complex, (maybe smaller would suffice, to keep it less complex, in many cases?) might be some ways to minimize the unintended consequences, within the uncertain world, we live, trade and grade in.

7 Conclusion

We have developed a framework and a solution to use the financial markets to facilitate trades on grades. Students that have good scores or higher grades, can trade their grade with someone that might end up losing their scholarships, or other opportunities, because of missing out the grades they need. In return, the person who is giving up the higher grades, will get two things: 1) They earn the good will and friendship of the person who would have lost out a much needed source of money. 2) They can get a certain percentage of the funds that might have been lost without the trade.

We have considered the moral, ethical, legal, humanitarian constraints and considerations involved in managing such a grading / trading system. The other unintentional outcomes, (due to having man-made furnishings labeling us), that have arisen and distracted us from properly evaluating, the true splendor of all of nature’s creations, were pointed out. We have barely stopped discriminating based on race, religion, color, other dividers; we have found new ways to differentiate, such as the ranking of the schools we have attended, the grades we obtain, the advanced degrees we have, the titles we confer upon ourselves both within the corporate culture or outside, the neighborhoods we live in, and so on.

The current set up of rankings and the best ranked institutions attracting the best minds and resources, become self-fulfilling prophecies that segment society, which is one of the primary outcomes that education seeks to eradicate (if it does not, then perhaps, it should; Kashyap 2017c has a discussion of one unintended yet welcome consequence of trying to understand the world, also known as knowledge creation or research, which is that, we might end up understanding one another better, becoming more tolerant in the process). Excessive competition in the process of transferring knowledge dilutes the essence of collaboration, the inculcation of which, among all us, is the end game, or, the overall goal of education. Surely, if we need to produce better citizens, who are willing to lend a helping hand, to their fellow human beings who are in need, we need to learn to co-operate more than we compete, since we have plenty of sports, for those of us, who have minds (and bodies?), made for competitions. On this note, if we start of think of grades as games, then that might solve the problem too, and we could use a reminder that, it does not matter who wins, or, loses, as long as the games go on.

Our thought experiment becomes another example of ideas from diverse fields being applied to solve problems in a particular field illustrating that the many disciplines we have created are artificial. In this case, finance concepts and the principles of trading were utilized to solve a problem in education and deeper issues for why problems such as these arise were discussed. It should be clear that this experiment applies only to higher education institutions, though we have not been specific about what higher education means. That being said, if someone is old enough to elect the head of their nation, they can be deemed old enough to trade their grade. Though, if we want allow toddlers in kinder-garden or kids in primary school to trade grades, we should be more worried about whether the labelling business has started at such an early age. We will leave those cans of worms unopened for now.

The creation of a grade swap market is purely hypothetical. The ramifications of actually embarking upon such an endeavor are many, and such an effort is bound to be met with numerous challenges. A simple suggestion that the thought process in this article brings about is not to have grades or rankings determine the outcomes in any selection criteria except have a cutoff point: either for jobs, higher studies, financial scholarships, etc unless those rankings are used only for entertainment such as in reality shows or spectator sports. Instead the one use for grades or rankings might be that they are helpful to let students or recipients know, what are their areas of weakness and what improvements might be necessary. All trophies that we collect (including certificates, grades, medals etc.) should really be viewed as personal equity or private equity (borrowing another widely used term in finance). This issue needs to be thought about by many, and tackled by everyone, before a satisfactory solution can be put in place.

8 Acknowledgments and End-notes

Dr. Yong Wang, Dr. Isabel Yan, Dr. Vikas Kakkar, Dr. Fred Kwan, Dr. William Case, Dr. Srikant Marakani, Dr. Qiang Zhang, Dr. Costel Andonie, Dr. Jeff Hong, Dr. Guangwu Liu, Dr. Humphrey Tung and Dr. Xu Han at the City University of Hong Kong provided advice and more importantly encouragement to explore and where possible apply cross disciplinary techniques. The students of SolBridge International School of Business provided the inspiration for this paper and many others. The faculty members of SolBridge International School of Business, particularly Dr. Jay-Won Lee, Dr. Kyun-Hwa Kim, Dr. Andrew Isaak and Dr. Hsing Chia Huang provided patient guidance and valuable suggestions on how to further this solution and most importantly about the practical implications of even considering such an approach. 2. 2.

A student is primarily a person enrolled in a school or other educational institution who attends classes in a course to attain the appropriate level of mastery of a subject under the guidance of an instructor. Alternately, a student is anyone who applies themselves to the intensive intellectual engagement with some matter necessary to master it as part of some practical affair in which such mastery is basic or decisive. Student, Wikipedia Link 3. 3.

Student financial aid is financial support given to individuals who are furthering their education. Student financial aid can come in a number of forms, including scholarships, grants, student loans, and work study programs. Each of these methods of providing financial support to students has its advantages and drawbacks. Student Financial Aid, Wikipedia Link 4. 4.

Grade inflation is used in two senses: (1) grading leniency: the awarding of higher grades than students deserve, which yields a higher average grade given to students (2) the tendency to award progressively higher academic grades for work that would have received lower grades in the past. The majority of the current debates on grade inflation are about the second issue: Grade Inflation, Wikipedia Link 5. 5.

An intelligence quotient (IQ) is a total score derived from several standardized tests designed to assess human intelligence. Scores from intelligence tests are estimates of intelligence. Unlike, for example, distance and mass, a concrete measure of intelligence cannot be achieved given the abstract nature of the concept of "intelligence" (End-note 6). Intelligence Quotient, Wikipedia Link (Weinberg 1989; Bartholomew 2004) describe the status of controversies regarding the definition of intelligence, whether intelligence exists and, if it does, whether it can be measured, and the relative roles of genes versus environments in the development of individual differences in intelligence. 6. 6.

Intelligence has been defined in many ways, including: the capacity for logic, understanding, self-awareness, learning, emotional knowledge, reasoning, planning, creativity, and problem solving. More generally, it can be described as the ability to perceive or infer information, and to retain it as knowledge to be applied towards adaptive behaviors within an environment or context. Intelligence, Wikipedia Link (Kashyap 2017d) provides an alternate definition of intelligence and has a deeper discussion on whether intelligence can be increased or even created in non-human entities. 7. 7.

In education, marking on a curve or grading on a curve (also referred to as curved grading, bell curving, or using grading curves) is a method of assigning grades to the students in a class in such a way as to obtain a pre-specified distribution of these grades, such as a normal distribution (also called Gaussian distribution; Rao 1973; End-note 8). The term "curve" refers to the bell curve, the graphical representation of the probability density of the normal distribution, but this method can be used to achieve any desired distribution of the grades – for example, a uniform distribution (Rao 1973; End-note 9). Grading on a Curve, Wikipedia Link

For example, if there are five grades in a particular university course, A, B, C, D, and F, where A is reserved for the top 20% of students, B for the next 30%, C for the next 30%-40%, and D or F for the remaining 10%-20%, then scores in the percentile interval from 0% to 20% will receive a grade of D or F, scores from 21% to 50% will receive a grade of C, scores from 51% to 80% receive a grade of B, and scores from 81% to 100% will achieve a grade of A. 8. 8.

In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution. The normal distribution is sometimes informally called the bell curve. However, many other distributions are bell-shaped (such as the Cauchy, Student’s t, and logistic distributions). Normal Distribution, Wikipedia Link. The probability density of the normal distribution is:

[TABLE]

where $\mu$ is the mean or expectation of the distribution (and also its median and mode),$\sigma$ is the standard deviation, and $\sigma^{2}$ is the variance. 9. 9.

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of $n$ values has equal probability $1/n$. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen". 10. 10.

(Ismail 2014) mentions the following quote from Taleb, “Knowledge gives you a little bit of an edge, but tinkering (trial and error) is the equivalent of 1,000 IQ points. It is tinkering that allowed the industrial revolution”. Nassim Taleb and Daniel Kahneman discuss Trial and Error / IQ Points, among other things, at the New York Public Library on Feb 5, 2013. 11. 11.

The creation of a grade swap market is only a thought experiment and is purely hypothetical. The views and opinions expressed in this article, along with any mistakes, are mine alone and do not necessarily reflect the official policy or position of either of my affiliations or any other agency. 12. 12.

In finance, a dark pool (also black pool) is a private forum for trading securities, derivatives, and other financial instruments. One of the main advantages for institutional investors in using dark pools is for buying or selling large blocks of securities without showing their hand to others and thus avoiding market impact as neither the size of the trade nor the identity are revealed until some time after the trade is filled. However, it also means that some market participants are disadvantaged as they cannot see the orders before they are executed; prices are agreed upon by participants in the dark pools, so the market is no longer transparent. Dark Pool, Wikipedia Link 13. 13.

A knowledge deity is a deity in mythology associated with knowledge, wisdom, or intelligence. The following link has a list of such deities. Knowledge Deities, Wikipedia Link 14. 14.

Knowledge is a familiarity, awareness, or understanding of someone or something, such as facts, information, descriptions, or skills, which is acquired through experience or education by perceiving, discovering, or learning. Knowledge, Wikipedia Link 15. 15.

Epistemology (from Greek, epistēmē, meaning ’knowledge’, and logos, meaning ’logical discourse’) is the branch of philosophy concerned with the theory of knowledge. It is the study of the nature of knowledge, justification, and the rationality of belief. Epistemology, Wikipedia Link 16. 16.

The idea that false friends will flake and true friends will reveal themselves as such in times of adversity is ancient. Friend Indeed, Wiktionary Link 17. 17.

A letter to our daughter, Mark Zuckerberg, Wednesday December 2, 2015: in many ways the world is getting better … your life should be dramatically better than ours today. We will do our part to make this happen, not only because we love you, but also because we have a moral responsibility to all children in the next generation. … We will give 99% of our Facebook shares – currently about $45 billion – during our lives to advance this mission. We know this is a small contribution compared to all the resources and talents of those already working on these issues. But we want to do what we can, working alongside many others. Zuckberg 99%, Human Potential Facebook Link; Zuckerberg 99%, Human Potential 18. 18.

Dec. 1, 2015, San Francisco: Mark Zuckerberg, the co-founder and chief executive of Facebook, announced on Tuesday that he and his wife would give 99 percent of their Facebook shares “during our lives” — holdings currently worth more than $45 billion — to charitable purposes. The pledge was made in an open letter to their newborn daughter, Max, who was born about a week ago. Zuckerberg 99%, NY Times Link; Zuckerberg 99%, BBC Link; Zuckerberg 99%, Fortune Link 19. 19.

Mark Zuckerberg had said that he was putting 99 per cent of his Facebook shares into the Chan Zuckerberg initiative, a legal entity dedicated to "advancing human potential" through personalised learning, curing disease, connecting people and building strong communities. The Independent and other media reported that this vehicle is not a charity, but a limited liability company owned and controlled by Zuckerberg. As a private company, the Chan Zuckerberg Initiative can spend its money on whatever it wants - including private, profit-generating investment. Zuckerberg 99% in Legal Entity 20. 20.

The reason we provide these rationalizations are simply because most academic journals seem to require complicated mathematics, [see, Kashyap 2017a, for a discussion of whether mathematics is incomprehensibly difficult, or, whether it is beautifully simple and has been made tremendously convoluted, unintentionally, of course], enormous amounts of data crunching, or, abstruse phrases explaining straightforward concepts, to evaluate, and in many cases even to acknowledge, the contributions in any paper. This is again an unintended consequence, (Kashyap 2017b, c have more details), though these extra measures, act as a certain filtering procedure for quality and are based on the very noble aspiration of ensuring that the best knowledge bubbles to the surface. That being said, it might be more efficient if the editors and reviewers watch out for the most innovative (to be more precise; a certain minimum level of innovation should suffice, given our subjective preferences and the complexity that our decisions need to overcome, we might be limited in our abilities to select the best works: Kashyap 2017c), or new content and coach the authors on the steps required to create a publication in their journal. This is illustrated with a simple example: a hundred lessons on physics will surely be helpful; but if we substitute one physics lesson for a lesson in biology, or, chemistry, or, astronomy, that might be more enlightening, and lead to greater productivity and impact at a later stage. Referring to our observation in section 2, that the various fields are artificial boundaries created by us, leads to the simple conclusion that, learning about a diverse variety of concepts, which are likely to be dispersed in multiple fields in our present approach to organizing and enhancing knowledge, and weaving them together to form solutions, would have a better chance of success in this world we live in. 21. 21.

In finance, the net present value (NPV) or net present worth (NPW) is the summation of the present (now) value of a series of present and future cash flows. Because NPV accounts for the time value of money NPV provides a method for evaluating and comparing products with cash flows spread over many years, as in loans, investments, payouts from insurance contracts plus many other applications. Net Present Value, Wikipedia Link 22. 22.

The following link has a list of securities examinations and the organizations that offer them. List of Securities Examinations, Wikipedia Link 23. 23.

In finance, an interest rate swap (IRS) is an interest rate derivative (IRD). It involves exchange of interest rates between two parties. In particular it is a linear IRD and one of the most liquid, benchmark products. An interest rate swap’s (IRS’s) effective description is a derivative contract, agreed between two counterparties, which specifies the nature of an exchange of payments benchmarked against an interest rate index. Interest Rate Swap, Wikipedia Link 24. 24.

Although division by zero is not defined for real numbers, limits involving division by a real quantity $x$ which approaches zero may in fact be well-defined. For example,

[TABLE]

Of course, such limits may also approach infinity,

[TABLE]

For a detailed discussion, see: Division by Zero, Mathworld Link; Division by Zero, Wikipedia Link. 25. 25.

The Turing test, developed by Alan Turing in 1950, is a test of a machine’s ability to exhibit intelligent behavior equivalent to, or indistinguishable from that of a human. Turing Test, Wikipedia Link

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