Development and validation of a sequence of clicker questions for helping students learn addition of angular momentum in quantum mechanics

Abstract

Engaging students with well-designed clicker questions is one of the commonly used researchbased instructional strategy in physics courses partly because it has a relatively low barrier to implementation [1]. Moreover, validated robust sequences of clicker questions are likely to provide better scaffolding support and guidance to help students build a good knowledge structure of physics than an individual clicker question on a particular topic. Here we discuss the development, validation and in-class implementation of a clicker question sequence (CQS) for helping advanced undergraduate students learn about addition of angular momentum, which takes advantage of the learning goals and inquiry-based guided learning sequences in a previously validated Quantum Interactive Learning Tutorial (QuILT). The in-class evaluation of the CQS using peer instruction is discussed by comparing upper-level undergraduate students' performance after engaging with the CQS with previous published data from the QuILT pertaining to these concepts.

Instructional Pragmatism: Using a variety of evidence-based approaches flexibly to improve learning

“…The learning goals of the CQS included helping students identify the dimensionality of Hilbert space of the spin of two particles, to be able to choose a suitable representation such as "coupled" or "uncoupled" representation and construct a complete set of basis vectors for the product space in the chosen representation and to be able to calculate matrix elements for operators corresponding to observables in these representations [37]. In standard notation, the basis states in the uncoupled representation are eigenstates of Ŝ 1 2 , Ŝ z1 , Ŝ Consistent with the learning goals of the CQS [37], pre/posttests were developed and validated [47] to measure comprehension of the concepts related to the addition of angular momentum. On the pretest (after traditional instruction), students were given a system of two spin-1/2 particles with a spin-spin interaction Hamiltonian…”

“…They can be interspersed within lectures to evaluate learning in each class segment, placed at the end of a class or at the beginning of a class to review materials from previous classes. While many clicker questions for introductory [28][29][30][31][32][33][34] and upper-level physics such as QM [35] have been developed, some documented efforts [36] have also focused on development and validation of clicker question sequences (CQSs) [37][38][39][40], e.g., question sequences on a concept that can be used in a few class periods when students learn the concepts and that build on each other to help students organize and extend their knowledge structure.…”

Development, validation and online and in-person implementation of clicker question sequence on quantum measurement uncertainty

“…When presented in validated Clicker Question Sequences (CQS) on a topic, they can systematically help students who are struggling with particular concepts. Previously, such CQSs related to several key QM concepts have been developed, validated and implemented [35][36][37][38][39]. Furthermore, previous work has been conducted to investigate student difficulties with the uncertainty principle as it applies to wavefunctions [40] as well as two-state systems [41], but there has not yet been a documented effort to develop, validate and implement a CQS to address those difficulties.…”

Using a clicker question sequence to teach time-development in quantum mechanics

“…When presented in sequences of validated questions that build on one another, they can systematically help students with a particular theme that they may be struggling with. Previously, such Clicker Question Sequences (CQS) have been developed, validated and implemented on several key topics in quantum mechanics [42][43][44][45][46]. Here we discuss the development, validation and implementation of a CQS focused on helping students learn time-evolution of two-state quantum systems.…”