Engaging students with well-designed multiple-choice questions during class and asking them to discuss their answers with their peers after each student has contemplated the response individually can be an effective evidence-based active-engagement pedagogy in physics courses. Moreover, validated sequences of multiple-choice questions are more likely to help students build a good knowledge structure of physics than individual multiple-choice questions on various topics. Here we discuss a framework to develop robust sequences of multiple-choice questions and then use the framework for the development, validation and implementation of a sequence of multiple-choice questions focusing on helping students learn quantum mechanics via the Stern-Gerlach experiment that takes advantage of the guided inquiry-based learning sequences in an interactive tutorial on the same topic. The extensive research in developing and validating the multiple-choice question sequence strives to make it effective for students with diverse prior preparation in upper-level undergraduate quantum physics courses. We discuss student performance on assessment task focusing on the Stern-Gerlach experiment after traditional lecture-based instruction vs. after engaging with the research-validated multiple-choice question sequence administered as clicker questions in which students had the opportunity to discuss their responses with their peers. I.INTRODUCTIONBackground: A major goal of many physics courses from introductory to advanced levels is to help students learn physics concepts [1-7] while also helping them develop problem solving and reasoning skills [8][9][10][11][12][13][14][15][16][17][18]. We have been investigating strategies to help students develop a solid grasp of physics concepts and develop their problem solving and reasoning skills [19][20][21][22][23][24][25][26][27][28][29][30][31]. In fact, many education researchers have been involved in developing and evaluating evidence-based activeengagement (EBAE) curricula and pedagogies [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50], but implementation of these EBAE approaches to help college students learn has been slow. Some of the major barriers to implementation of the EBAE pedagogies at the college-level include lack of faculty buy-in and their reluctance and/or resistance, partly due to a lack of institutional reward system for using these evidence-based approaches, the time commitment involved in effectively adapting and implementing them, and instructors' fear that their students may complain (since students may prefer to passively listen to lectures as opposed to actively engage in the learning process) [32]. Moreover, the amount of class time required to implement an EBAE pedagogy, the flexibility with which it can be implemented, the need to train instructors in how to effectively use it, and the architectural constraints of the classrooms may also increase the barrier and make it difficult to implement an EBAE pedagogy [32]. Use of Multiple-choice...

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.

We investigated the difficulties that physics students in upper-level undergraduate quantum mechanics and graduate students after quantum and statistical mechanics core courses have with the Fermi energy, the Fermi-Dirac distribution and total electronic energy of a free electron gas after they had learned relevant concepts in their respective courses. These difficulties were probed by administering written conceptual and quantitative questions to undergraduate students and asking some undergraduate and graduate students to answer those questions while thinking aloud in one-on-one individual interviews. We find that advanced students had many common difficulties with these concepts after traditional lecture-based instruction. Engaging with a sequence of clicker questions improved student performance, but there remains room for improvement in their understanding of these challenging concepts.

Engaging students with well-designed clicker questions is one of the commonly used research-based instructional strategy in physics courses partly because it has a relatively low barrier to implementation. 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 Larmor precession of spin, 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 traditional lecture-based instruction and after engaging with the CQS.

Instructional pragmatism is essential for successfully adapting evidence-based active engagement (EBAE) approaches and involves instructors viewing improving teaching and learning as a process. Promoting and supporting instructional pragmatism is critical for ensuring that instructors are not disheartened if EBAE approaches do not produce desired outcome. Cultivating instructional pragmatism entails supporting instructors so that they recognize the value of being patient and optimistic while adapting EBAE approaches and keep a variety of approaches in their instructional toolbox. Here we illustrate an example of instructional pragmatism in which a quantum mechanics instructor did not give up when an EBAE method involving implementation of a sequence of clicker questions on addition of angular momentum did not yield expected learning outcomes. Encouraging instructors to embrace instructional pragmatism and creating a community of educators who support each other and discuss their implementation of EBAE approaches can go a long way in helping students learn physics.