Development and validation of the ray optics in converging lenses concept inventory

Optics is a core field in the curricula of secondary physics education. In this study, we present the development and validation of a test instrument in the field of optics, the ray optics in converging lenses concept inventory (ROC-CI). It was developed for and validated with middle school students, but can also be adapted for the use in higher levels of physics education. The ROC-CI can be used as a formative or a summative assessment of students’ conceptual understanding of image formation by converging lenses, assessing the following: (i) the overall understanding of fundamental concepts related to converging lenses, (ii) the understanding of specific concepts, and (iii) students’ propensity for difficulties within this topic. The initial ROC-CI consists of 16 multiple-choice items; however, one item was removed based on various quality checks. We validated the ROC-CI thoroughly with distractor analyses, classical test theory, item response theory, structural analyses, and analyses of students’ total scores at different measurement points as quantitative approaches, as well as student interviews and an expert survey as qualitative approaches. The quantitative analyses are mostly based on a dataset of $N=318$ middle school students who took the ROC-CI as a post-test. The student interviews were conducted with seven middle school students after they were taught the concepts of converging lenses. The expert survey included five experts who evaluated both individual items and the test as a whole. The analyses showed good to excellent results for the test instrument, corroborating the 15-item ROC-CI’s validity and its compliance with the three foci outlined above.

Figure 1

An illuminated object being refracted by a lens and projected on a screen.

Figure 2

Conceptual idea of the refraction and imaging process drawn in a ray diagram according to the three rules of refraction. The three construction rays predict where a point of the object is projected (parallel ray in green, central ray in red, and focal-point ray in blue). The yellow shaded area represents the bundle of light rays originating from the top point of the object that is refracted by the lens.

Figure 3

Exemplary item of the ROC-CI (item Q7) with the default format: text and picture in both item stem and all answer options.

Figure 4

Percentage of the students who selected each answer option for all 16 items in the pre-, post-, and follow-up test (split up in Q1–Q8 and Q9–Q16). Correct answer options are indicated by an asterisk.

Figure 5

Item statistics for all original 16 items of the ROC-CI. Item Q2 shows negative discrimination.

Figure 6

Probability function of item Q2. P1 (blue) indicates 0 points, P2 (pink) 1 point, and P3 (green) 2 points scored. The axes represent the learner’s ability ($x$ axis, theta) and the probability of solving this item correctly ($y$ axis).

Figure 7

Probability function of item Q14. P1 (blue) indicates 0 points, P2 (pink) 1 point, and P3 (green) 2 points scored. The axes represent the learner’s ability ($x$ axis, theta) and the probability of solving this item correctly ($y$ axis).

Figure 8

Distribution of the 15 ROC-CI items to the 8 factors MR1-MR8 determined in an exploratory factor analysis. The connecting arches on the right indicate correlations between the single factors, which were allowed in this model due to the oblique rotation used in the analysis.

Figure 9

Histogram of students’ total test score (without item Q2) for the pre- (light blue) and post-test (dark blue).