Interpreting force concept inventory scores: Normalized gain and SAT scores

Preinstruction SAT scores and normalized gains $\left(G\right)$ on the force concept inventory (FCI) were examined for individual students in interactive engagement (IE) courses in introductory mechanics at one high school $(N=335)$ and one university $(N=292)$, and strong, positive correlations were found for both populations ($r=0.57$ and $r=0.46$, respectively). These correlations are likely due to the importance of cognitive skills and abstract reasoning in learning physics. The larger correlation coefficient for the high school population may be a result of the much shorter time interval between taking the SAT and studying mechanics, because the SAT may provide a more current measure of abilities when high school students begin the study of mechanics than it does for college students, who begin mechanics years after the test is taken. In prior research a strong correlation between FCI $G$ and scores on Lawson’s Classroom Test of Scientific Reasoning for students from the same two schools was observed. Our results suggest that, when interpreting class average normalized FCI gains and comparing different classes, it is important to take into account the variation of students’ cognitive skills, as measured either by the SAT or by Lawson’s test. While Lawson’s test is not commonly given to students in most introductory mechanics courses, SAT scores provide a readily available alternative means of taking account of students’ reasoning abilities. Knowing the students’ cognitive level before instruction also allows one to alter instruction or to use an intervention designed to improve students’ cognitive level.

Figure 1

(a) Plot of individual students’ normalized FCI gains versus SAT scores for 292 LMU students: $\text{slope}=0.00084$, $r=0.46$. (b) Plot of normalized FCI gains versus SAT scores, with individual student data averaged within 17 bins.

Figure 2

(a) Plot of individual students’ normalized FCI gains versus SAT scores for 335 ELHS students: $\text{slope}=0.00089$, $r=0.57$. (b) Plot of normalized FCI gains versus SAT scores, with individual student data averaged within 18 bins.

Figure 3

Plot of normalized gains versus SAT scores for 627 LMU and ELHS students, with individual student data averaged within 25 bins.

Figure 4

Plot of normalized gains versus Lawson Test scores for 297 LMU and ELHS students, with individual student data averaged within 17 bins.