Particle waves in boxes for Dutch secondary schools

Charles H. Holbrow, James N. Lloyd, Joseph C. Amato

Dick J. Hoekzema, Ed van den Berg, Gert Schooten +1 more

The combination of mathematical and conceptual difficulties makes teaching quantum physics at secondary schools a precarious undertaking. With many of the conceptual difficulties being unavoidable, simplifying the mathematics becomes top priority. The particle/wave-in-a-box provides a teaching model which includes many aspects of serious quantum physics, while avoiding most of the mathematics. In a Dutch quantum physics project for secondary schools, this model was adopted to play a key role. Much to our surprise, we ran into many more applications than we originally expected. In many instances the model yields order of magnitude estimates, for instance of atomic and nuclear size, or qualitative insights, for instance about energy levels, molecular bonding and electron pressure. Moreover, either directly or with minor modifications, the particle-in-a-box model provides reasonable approximations of a range of phenomena, including the absorption spectra of organic pigments, the mass of the proton and the spectra of quantum dots.

Rutger Ockhorst, Freek Pols

Abstract Wave-particle duality is included in many secondary school and university physics curricula as a concept central to quantum physics. The very term wave-particle duality suggests that a firm grasp of the individual classical concepts of wave and particle is crucial to studying quantum mechanics successfully. This raises the question whether students’ mental models of these concepts are sufficiently addressed and developed prior to the teaching of wave-particle duality. We explored Dutch upper secondary school students’ mental models of waves and particles using a short questionnaire. It was administered to a total of 147 students from two different groups. One group consisted of secondary school students prior to receiving formal education in introductory quantum mechanics while students from the other group had recently completed the Dutch national curriculum for pre-university education, which includes wave-particle duality. Our findings support the notion that students model classical particles and waves as mutually exclusive phenomena. Mental models of wave-particle duality, which require mixing the two classical models, appear to be only superficially developed. Our findings open avenues for future research on students’ mental models of waves and particles as basis for wave-particle duality.

Charles H. Holbrow, James N. Lloyd, Joseph C. Amato +2 more

Ed van den Berg, Aernout van Rossum, Jeroen Grijsen +2 more

A lesson series on quantum physics was taught to grade 12 students in 5 different secondary schools. Among others, the series contained a special demonstration experiment for particle-wave duality (double-slit single-photon interference) which was supplemented by the PhET applet quantum wave interference. Preconceptions on particles and waves were assessed in a pretest. Interviews were conducted with 24 students in 4 schools after the demonstration. A posttest was administered to 112 students in 3 schools. Some lessons were observed by an outside observer and/or videotaped, followed by interviews. Results indicate that learning objectives of quantum physics are well within reach of the 12th grade students. This shows especially in student discussions of the PhET applet. However, understanding of wave-particle duality is hindered by insufficient understanding of the prerequisite wave concept that waves are spread out in space. Most students associated a wave with an oscillation and somehow forgot about the spatial aspects. As a consequence, the “strangeness” of wave-particle duality was underappreciated. Also, the link with the de Broglie wavelength discussed early in the lesson series was not made. As in the 5th school quantum physics started several weeks later, we were able to try an improved lesson design for the demonstration successfully. Interviews are very helpful in catching misinterpretations of demonstrations and generating suggestions for improvement. Students do appreciate the confusing wonders of quantum physics but in the post-interviews seem unaware of the many quantum-based devices around them and the many everyday phenomena (like color) which need quantum physics for explanation. Perhaps as teachers and curriculum developers, we are too eager to overemphasize the exotic and strange aspects of quantum theory and underemphasize utility in everyday applications.