Test on the effectiveness of the sum over paths approach in favoring the construction of an integrated knowledge of quantum physics in high school

Abstract

In this paper we present the results of a research-based teaching-learning sequence on introductory quantum physics based on Feynman's sum over paths approach in the Italian high school. Our study focuses on students' understanding of two founding ideas of quantum physics, wave particle duality and the uncertainty principle. In view of recent research reporting the fragmentation of students' mental models of quantum concepts after initial instruction, we collected and analyzed data using the assessment tools provided by knowledge integration theory. Our results on the group of n ¼ 14 students who performed the final test indicate that the functional explanation of wave particle duality provided by the sum over paths approach may be effective in leading students to build consistent mental models of quantum objects, and in providing them with a unified perspective on both the photon and the electron. Results on the uncertainty principle are less clear cut, as the improvements over traditional instruction appear less significant. Given the low number of students in the sample, this work should be interpreted as a case study, and we do not attempt to draw definitive conclusions. However, our study suggests that (i) the sum over paths approach may deserve more attention from researchers and educators as a possible route to introduce basic concepts of quantum physics in high school, and (ii) more research should be focused not only on the correctness of students' mental models on individual concepts, but also on the ability of students to connect different ideas and experiments related to quantum theory in an organized whole.

Towards a better understanding of conceptual difficulties in introductory quantum physics courses

“…Students learning QP construct knowledge for themselves where their prior ideas serve as both a foundation and building material for constructing new (i.e. QP) knowledge (e.g., Malgieri et al, 2017;Modir et al, 2019;Taber, 2005;Wan et al, 2019). Conceptual difficulties occur when students try to interpret new knowledge in their existing conceptual framework (e.g., Duit & Treagust, 2003;Vosniadou, 1994;Vosniadou et al, 2008).…”

“…Conceptual difficulties persist over an extensive period, since developing conceptual understanding of QP requires a comprehensive reconstruction of students' mostly classical conceptual frameworks that they have become comfortable using when they first started learning physics (e.g., Kalkanis et al, 2003;Malgieri et al, 2017). The development of conceptual understanding is not instantaneous and during the process the understanding is fragmented; consistent in one QP context, but inconsistent in another .…”

“…Students' meaning-making is hindered when they fail to recognise first that this deterministic view on reality is contrary to the probabilistic interpretation of QP and second that basic assumptions in classical physics, such as locality and determinism, are invalid in QP (Bungum et al, 2018;Chhabra & Das, 2017;Henriksen et al, 2014). Accepting this change in worldview is a gradual process for students where they incorporate new QP elements in their conceptual framework while essential features of a classical world view are retained over an extended period (e.g., Dangur et al, 2014;Malgieri et al, 2017). Research into students' understanding of atomic models shows similar development in students' thinking, as students first develop hybrid models that merge previously learned semi-classical models and QP models when learning QP (Dangur et al, 2014;Krijtenburg-Lewerissa et al, 2017).…”

“…Scholars tend to use different theoretical frameworks and have different interests and objectives in their research on students' conceptual difficulties in QP. Students' conceptual difficulties have been studied from different learning theories such as conceptual change (Dai et al, 2019;Malgieri et al, 2017), mental models (Didiş et al, 2014), and socialconstructivism (Asikainen & Hirvonen, 2009). These learning theories allow for a broad perspective to be taken on students' conceptual difficulties but they might fail to allow for recognising particular difficulties students might have to develop their conceptual understanding.…”

“…Students' conceptual difficulties often persist over an extensive period of time, as students are unaware that their underlying assumptions derived from a mainly classical conceptual framework are invalid (e.g., Oh, 2011). Students have to come to a new conceptual framework that requires an extensive restructuring of their 'old' one (e.g., Ayene et al, 2019;Kalkanis et al, 2003;Malgieri et al, 2017;Oh, 2011). Exploring the reasons for the experienced abstract nature of QP will allow for a better understanding of the origin of students' conceptual difficulties, the struggles students have to overcome these conceptual difficulties, and the problems teachers face supporting students' conceptual development of QP.…”