Section 1 Introduction
A common refrain in education is the adage that in order to grow, one must learn from one’s mistakes. However, as faculty in higher education, we seem to frequently forget this maxim in the design of our own courses. Anecdotal evidence suggests that the most common grading scheme in STEM courses is weighted average grading (WAG), in which the total number of available points are divided amongst categories (e.g. homework, quizzes, and exams), points in each category are allocated using the average of assignment grades, and letter grades are assigned based on the percentage of available points the student has accumulated throughout the course. Counter-intuitively, WAG offers a punishment for mistakes made – loss of points – and no reward for remedying those mistakes. Indeed, while we may attempt to incentivize students to fix gaps in their knowledge under threat of losing even more points on, say, a cumulative final exam, the points lost on previous assignments may never be regained.
Structuring our courses this way creates a perverse incentive structure wherein students erroneously conflate accumulation of points and understanding. This often gives rise to undesirable behaviors in our students, such as superficial learning and disengagement [1], as well as undesirable outcomes.
“The chair of the department of a Big Ten university once observed, probably after a bad day, that it was possible for a student to graduate with a mathematics major without ever having solved a single problem correctly. Partial credit can go a long way.” — Dudley Underwood [2]
Recently, in an effort to combat these problems, segments of the mathematics community have begun to employ grading techniques[3] other than WAG in their courses, known collectively as alternative grading. While these approaches to grading may look dramatically different in practice, they all share a common goal of prioritizing accurately measuring student learning over accumulation of points.
As a framework, Standards-Based Grading (SBG) aims to provide a more accurate measure of knowledge through a grading process that is both iterative and forgetful. The course material is discretized into bite-sized chunks called standards – such as a concept or a mechanical task – each student is expected to master by the end of the course. These standards are assessed at regular intervals, similar to WAG, and are graded based on whether the student has or has not demonstrated mastery of the standard – meaning there is no partial credit and no points to accumulate. Throughout the course, students have opportunities to reassess standards not already mastered and, by demonstrating mastery on the reassessment, previous mistakes are forgotten. This provides a mechanism by which students are incentivized to learn from their mistakes without penalty.
While this approach has been shown to reduce students’ anxiety around mathematics [4] [5] and reduce avoidance goals in students [6], claims that SBG increases engagement [7] and perseverance [8] [5], generates grades that better reflect student knowledge [9] [4], and promote deeper understanding of the material [5] [10] [11] [12] remain largely anecdotal. This lack of rigorous evidence is particularly notable for the latter two claims, which are frequently cited as compelling arguments for implementing SBG. We address this critical gap in the literature by examining student outcomes in College Algebra courses and subsequent courses at a National Science Foundation (NSF) Established Program to Stimulate Competitive Research (EPSCoR) eligible institution.
By definition, “a jurisdiction is eligible to participate in EPSCoR programs if its level of NSF funding is equal to or less than 0.75 percent of the total NSF budget over the most recent five-year period, excluding NSF funding to other federal agencies and EPSCoR RII and workshop/conference funding.” [13] These jurisdictions tend to be more rural with lower median household incomes and limited access to advanced educational resources. As a result, many students at institutions of higher education (IHE) in these jurisdictions are first-generation college students and exhibit wide variation in academic preparation.
By rigorously analyzing the impact of SBG on student performance and learning, we aim to contribute to the body of evidence supporting SBG as a more effective alternative to WAG for promoting deeper conceptual understanding in university-level mathematics courses.
