Design and validation of a two-tier questionnaire on basic aspects in quantum mechanics

We present the design, statistical analysis, and validation of a questionnaire to assess students’ knowledge about basic aspects of quantum mechanics (QM). The QM evaluation (QME) is a true-false and multiple-choice mixed questionnaire that features 10 two-tier items spanning three relevant themes in quantum mechanics: wave behavior of matter, measurement, and atoms and electrons behavior. Its validity was assessed through a pilot administration to students and interviews with course instructors. We checked its internal consistency using both classic test theory and Rasch analysis to account for the different difficulty of each tier and for different scoring methods of the items. The questionnaire was administered to about 450 undergraduate physics students and high school physics teachers. Data show that it is a reliable instrument and all items have a good discriminatory power. Since the test does not require an advanced mathematical knowledge, it ideally lends itself to probe students’ knowledge about quantum mechanics in a variety of university courses, from the introductory ones to those more formal and mathematically oriented.

Figure 1

(a) Dispersion plot of the QME items’ difficulty in the T1–T2 plane when tiers are analyzed separately. See text for the definition of regions A and B. See Table 5 for further details. (b) Dispersion plot of QME items discrimination in the T1–T2 plane when tiers are analyzed separately. Straight dotted lines indicate the 0.1 threshold under which items have poor discrimination power. See Table 5 for further details.

Figure 2

Wright map of the QME. Items are grouped according to the three themes described in Sec. 3. One extreme person ($\text{ability}=-4.63$) is not represented.

Figure 3

Ability distributions of the four groups involved in the study. One extreme person ($\text{ability}=-4.63$ logit) is not represented.