At this time of the year, my smugness at being an alumnus of one of India’s respected colleges is severely punctured by tense conversations at cocktail parties that remind me my admission was merely a lucky result of not having been born a generation later.
But, I ask (and not from any defensiveness, I assure you)—are today’s children really scholastically smarter than we were? A game theoretic model developed by microeconomist Robertas Zubrickas enables us to examine this question.
In this model, a teacher looks for a grading rule that would incentivise students to work. Students incur an effort cost of working, with this cost increasing as the inherent ability of the student worsens. The effort put in and the ability of students result in a raw score. The teacher must decide if the raw scores should be converted into grades using a grading scale which clumps students into coarser partitions than those indicated by the raw scores.
Two kinds of motivations of students are considered—one in which they value the grade for its own sake (the absolute value model), and another in which they value the grade for its value relative to their peers in the eyes of an external party like a college or a recruiter. In both models, students are assumed to only care about the score or grade they receive, and not the knowledge they gain.
In the absolute value model, a coarse partition at the top end, for instance a clumping of scores eligible for an A, implies a greater effort elicited from lower-ability students. Of course, this is also accompanied by lower efforts from high-ability students who can more easily get the top grade. But their number is lower than the number of low-quality students, making the coarsening of the grade structure at the top end a great idea for the earnest teacher seeking to increase the total effort put in by students.
The coarsening of the grade structure with a fixed system of awarding raw scores is equivalent to inflating the raw scores while keeping the grading scale fixed. In other words, one can incentivise more effort from the student population either by increasing the range of scores eligible for As or by inflating the raw scores at the top end.
As the number of low-ability students increases, the optimal coarsening of the grade structure at the top end increases. Close to 1.1 million students have appeared in the Class XII exam administered by the Central Board of Secondary Education (CBSE) this year as opposed to 140,000 students in 1991. While one appreciates the increasing reach of education in the country, it must be accepted that there would be a change in the distribution of student abilities towards the lower-ability end with the massification of the board.
In this situation, I am pleased to report, high raw scores may reflect grade inflation meant to elicit more effort, rather than any quantum jump in the ability of the examinees. The negative correlation of standardized test scores and school grades in the US provides further proof of the same phenomenon.
However, there are two important caveats. First, the inflation of raw scores should happen at the top ends of the spectrum, not at lower ends. The increase in the number of students passing the CBSE examination (68% in 1991 versus 82% in 2015) indicates that the inflation of scores is happening at lower ends of the spectrum as well, with possible damage to the objective of maximizing effort.
Secondly, the recommendation to inflate raw scores, or coarsen grading structures at the top, changes if we assume that grades are valued not in absolute terms but with respect to the status they confer vis-à-vis colleges or recruiters.
Now, provided the grading rule is known to the end user, the more lenient the scale that the teacher sets up, the lower the utility the student gets from a given grade. The dampening impact on the effort put in by good students may now overwhelm the increased effort expended by those of lower ability, thus making a less coarse grading structure, i.e., a less inflated raw score pattern, optimal.
The recent decision of premier institutes like the Indian Institute of Technology to disregard the board exam scores in favour of a minimum qualifying percentage can partly be interpreted as a failure of the boards to internalize the impact of raw score inflation on end users like universities. Including the board exam scores to determine ranks will make sense only if it is accompanied by a rationalization of the pattern of raw scoring.
Finally, for a complete view, the conclusions of game theory must be synthesized with the insights of “goal theory” as applied to classroom settings. A widely cited paper by Carol Midgley, Avi Kaplan and Michael Middleton in the Journal Of Educational Psychology argues that student effort driven by performance goals can be counterproductive as the aim of achieving high scores can quickly be supplanted by the driving need to avoid failure.
This leads to various defensive mechanisms like devaluing the domain ( “I don’t care about math, anyway”), keeping one’s expectations low, and even self-handicapping. Hence it is recommended that the teacher inculcates learning or mastery goals rather than performance goals. In other words, the aim is not just to elicit more effort but the right kind of effort.
I suspect a reworking of the schooling system at a fundamental level is required to address that concern. Till that happens, I will continue to seek asylum in the world of game theory to assuage my ego in the face of the rampant geniuses of the day.
Rohit Prasad is a professor at MDI, Gurgaon and author of Blood Red River. Game Sutra is a fortnightly column based on game theory.