Components of the preparation gap for physics learning vary in two learner groups

The preparation gap [Salehi et al., Phys. Rev. Phys. Educ. Res. 15, 020114 (2019)] refers to gaps in students’ prior knowledge that can negatively affect their learning as they engage in introductory physics courses. To better characterize the gap, the current study distinguished the impact of various prior knowledge components on learning gains. Measured components came from within the course domain (e.g., energy and force, angular kinematics) and outside it (e.g., algebra, vectors, calculus, and scientific reasoning). We conducted the study in two different institutional contexts: An algebra-based course offered at a Northeastern State University (NESU) and a calculus-based course offered at a Midwestern Private University (MWPU). Furthermore, we defined three levels of physics learning outcome measures with increasing difficulty. Multiple regression analysis was used to predict learning gains with the various prior knowledge components as predictor variables. The results indicate that greater prior knowledge from both within and outside the domain predicted higher learning gains and explained 30%–50% of the variance in outcome measures. Predictive, in-domain prior knowledge was the same for both groups—i.e., prior knowledge of energy and force, as measured by the Mechanics Baseline Test [Hestenes and Wells, Phys. Teach. 30, 159 (1992)]. Predictive, outside-domain prior knowledge differed between the groups. Better scientific reasoning was highly predictive of learning in the NESU (algebra-based) group but did not predict learning in the MWPU (calculus-based) group. Math prior knowledge predicted learning in both groups, although different topics within the math domain. These results suggest that measuring distinguishable components of prior knowledge will better characterize the preparation gap in ways that can be informative to educators. Specifically, measuring multiple, distinct types of prior knowledge can indicate which types are leading to a preparation gap for some students, putting them at a disadvantage for learning, whereas measuring a single type of prior knowledge or measuring prior knowledge too coarsely (without distinguishing among types) cannot provide sufficient diagnostic power.

Figure 1

Four categories of variables that could impact learning in the physics domain: domain prior knowledge (DPK), ancillary prior knowledge (APK), prior achievement or aptitude (PA), and metacognition and motivation (M&M). The specific variables included are noted with an asterisk (*). The horizontal blocks for APK, PA, and M&M signify they have the potential to apply across domains, i.e., in more than one domain, but, importantly, are not general in the sense that each would apply indiscriminately for every domain.

Figure 2

(a) Interaction (not significant) of NESU students’ college major and their APK-A on the N-change EF L1 outcome (i.e., the L1 physics knowledge gained during the term). STEM majors’ N-change EF L1 scores positively correlated with better APK-A, whereas HSS (humanities and social sciences) majors’ scores negatively correlated with it. (b) This same interaction (not significant) is present for STEM vs HSS majors when considering the relationship between greater N-change A (i.e., the amount of algebra learned during the term) and N-change EF L1. $R^2$ is the percentage of the variance in the outcome measure that is explained by the predictor variable.

Figure 3

(a) Significant interaction of institution and DPK-EF L2 on the N-change EF L2 outcome. Both NESU and MWPU students’ DPK-EF L2 scores negatively correlated with N-change EF L2, such that students who started with higher scores tended to gain less new knowledge. However, NESU had more students who were below the mean in starting DPK and whose gains were above the mean compared with MWPU students who clustered above the mean in DPK and therefore had less room for growth. (b) A significant interaction of institution and APK-SR on the N-change EF L2 outcome. NESU students’ scores were generally better as a function of more APK-SR, whereas MWPU students’ scores were not clearly related to APK-SR. A few outlier scores for MWPU students who scored low on APK scientific reasoning but high on N-change energy and force L2 account for the negative relationship in that group and suggest APK-SR was not a factor in MWPU students’ domain learning. $R^2$ is the percentage of the variance in the outcome measure that is explained by the predictor variable. All measures were mean centered.