Development and validation of an achievement test in introductory quantum mechanics: The Quantum Mechanics Visualization Instrument (QMVI)

Open Access
Cataloglu, Erdat
Graduate Program:
Curriculum and Instruction
Doctor of Philosophy
Document Type:
Date of Defense:
January 14, 2001
Committee Members:
  • Vincent Norman Lunetta, Committee Chair
  • Peter A Rubba Jr., Committee Member
  • Richard Wallace Robinett, Committee Chair
  • Hoi Kin Suen, Committee Member
  • College students
  • Validation
  • Psychometrics
  • Science Education
  • Quantum Mechanics
  • Test Development
  • Physics Education
The purpose of this study was to construct a valid and reliable multiple-choice achievement test to assess students’ understanding of core concepts of introductory quantum mechanics. Development of the Quantum Mechanics Visualization Instrument (QMVI) occurred across four successive semesters in 1999-2001. During this time 213 undergraduate and graduate students attending the Pennsylvania State University (PSU) at University Park and Arizona State University (ASU) participated in this development and validation study. Participating students were enrolled in four distinct groups of courses: Modern Physics, Undergraduate Quantum Mechanics, Graduate Quantum Mechanics, and Chemistry Quantum Mechanics. Expert panels of professors of physics experienced in teaching quantum mechanics courses and graduate students in physics and science education established the core content and assisted in the validating of successive versions of the 24-question QMVI. Instrument development was guided by procedures outlined in the Standards for Educational and Psychological Testing (AERA-APA-NCME, 1999). Data gathered in this study provided information used in the development of successive versions of the QMVI. Data gathered in the final phase of administration of the QMVI also provided evidence that the intended score interpretation of the QMVI achievement test is valid and reliable. A moderate positive correlation coefficient of 0.49 was observed between the students’ QMVI scores and their confidence levels. Analyses of variance indicated that students’ scores in Graduate Quantum Mechanics and Undergraduate Quantum Mechanics courses were significantly higher than the mean scores of students in Modern Physics and Chemistry Quantum Mechanics courses (p < 0.05). That finding is consistent with the additional understanding and experience that should be anticipated in graduate students and junior-senior level students over sophomore physics majors and majors in another field. The moderate positive correlation coefficient of 0.42 observed between students’ QMVI scores and their final course grades was also consistent with expectations in a valid instrument. In addition, the Cronbach-alpha reliability coefficient of the QMVI was found to be 0.82, a relatively high reliability coefficient for an achievement test. This study also provided data from which preliminary findings were drawn on students’ understanding of introductory quantum mechanics concepts. The data included limited information about students’ visual understanding of quantum mechanics concepts. Data suggested that the construct of quantum mechanics understanding is most likely multidimensional and the Main Topic defined as “Quantum Mechanics Postulates” may be an especially important factor for students in acquiring a successful understanding of quantum mechanics. Students’ difficulties with concepts including momentum-space and time-dependence were observed. Limited data on visualization indicated that students were able to relate their mathematical and verbal knowledge with visual representations of quantum mechanics concepts. However, data also suggested that students did not perform as well, in general, when they had to connect conceptual ideas with quantitative interpretation. The results of this study suggest recommendations for further development of the QMVI, for development of understanding of introductory quantum mechanics, and for possible applications of the QMVI. The recommendations have potentially important implications for the teaching of introductory quantum mechanics and for the development of text and technology resources.