Instructor-Examiners, External-Examiners, and Student Learning Under the Shadow of Examination: A Game-Theoretic Analysis of Two Educational Institutions

Abstract

The present study takes examinations as a mechanism by which to elicit student learning and compares student learning effort provision under alternative methods of examination content generation. A two-stage game is constructed in which the examiner sets the predictability of exam content in the first stage (via content clue provision) and students exert learning efforts under the shadow of examination in the second stage. In equilibrium, an instructor-examiner is found to set content to be more predictable than that of an examination written independently of specific lecture material, review material, and past years’ examinations. This result is consistent with surveyed instructor reports of “teaching to the (instructor-generated) test,” “spoon-feeding” information to students, reviewing to the test, and re-testing students. Moreover, an instructor-examiner is found to provision more content clues as the marginal cost of student learning effort in a given class rises. In turn, student learning effort provision strictly decreases in examination content predictability. As such, instructor-generated examinations are found to cause student learning detriments and compound “naturally-occurring” inequalities in learning effort provision (learning outcome) as compared to an examination that is independently-generated. Parameterizations of the model suggest that these effects lead to potentially large proportional decreases in learning (increases in learning effort variability) across class. We discuss a solution to these unintended consequences of instructor-generated examinations. External-examiners, as used in the British educational system since the 19th century, can create independence between instruction and examination to improve learning effort provision (decrease inequality of learning effort provision).