Students’ ability to calculate their final course grade may not be as easy as you think: Insights from mathematical cognition.

Abstract

Is there an optimal grading scheme? Do psychology instructors prefer one grading scheme over another? These questions were recently posted on the Society for the Teaching of Psychology Facebook page. After reading the responses, we realized that research in the domain of math cognition might help to shed light on an optimal grading scheme and put some of the posters' comments into context. Posters often mentioned 100-point and 1,000-point grading schemes because of the ease with which students could convert course points to percentages. In this Pedagogical Points to Ponder article, we describe the quick development of whole number understanding in the 0-100 and 0-1,000 range relative to the slow development across the lifespan of rational number understanding. Although people struggle to understand fractions, percentages might serve as an intuitive bridge between familiar whole numbers and less familiar fractions. We encourage readers to ponder the fact that grading schemes are inherently relational and people of all ages, expertise levels, and cultural backgrounds fall prey to a common mathematical misconception in which they think about the components of rational numbers-the numerators and denominators-like independent whole numbers. This misconception, known as the whole number bias, may make any grading scheme challenging for students to comprehend. There are many open empirical questions about the optimal grading scheme that college instructors should adopt. Findings from the domain of math cognition can inform empirical research designs that may lead to improvements in students' comprehension of the course grading scheme and motivation, and may even diminish student requests for end-of-term grade bumps.

Number lines influence grade calculations, and grading scales influence perceptions and misconceptions.

“…A recent informal survey of psychology professors who were members of the STP Facebook group revealed trends about professors’ preferences for different course grading scales (Thompson, Fitzsimmons, et al, 2021). The current experiment was the first, to our knowledge, to investigate how number line displays and course grading scales impacted students’ grade comprehension and their preferences for these scales.…”

“…Participants provided percentages for five hypothetical grades each within four grading scales: 100 total points, 387 total points, 400 total points, and 1,000 total points (for a total of 20 grade-calculation problems). Participants responded to questions about 100-point and 1,000-point scales due to professors on the STP Facebook post endorsing these grading scales (Thompson, Fitzsimmons, et al, 2021) and because these two scales were designed to be familiar and easy to understand. Participants responded to questions about 387- and 400-point scales because these two grading scales had similar total points available and were likely more mathematically challenging than the 100- and 1,000-point scales.…”

“…Many professors shared their intuitions about students’ understanding and perception of various grading scales. In a recent Pedagogical Points to Ponder article in the journal, Scholarship of Teaching and Learning in Psychology , Thompson, Fitzsimmons, and Scheibe (2021) concluded that research in the domain of math cognition can provide insights to answer these questions and support students as they attempt to estimate, calculate, and comprehend their course grades. The present study is an empirical test of that claim.…”

“…One possible downstream negative side effect of students’ numerical misconceptions about their grades is whether students are likely to ask for a grade boost. Near the end of a semester, many students reach out to their professors to see if anything can be done to increase their grade (Hardy, 2002) or to request a grade boost (this activity is sometimes called grade grubbing; Cooper, 2020; Thompson, Fitzsimmons, et al, 2021). An example in which this might occur is when a professor details in a syllabus that students need 90% to get an “A-,” but a student ends the semester with an 89.4%.…”

“…Note that at least one instructor mentioned that instructors should be able to choose whatever point total they want because their students should be able to do the math, a point thatThompson Fitzsimmons, and Scheibe (2021) challenged.…”