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The quantum double well is familiar to most of us as a model of molecular orbitals and of wiggling ammonia molecules. It&#39;s also a step toward understanding band structure in periodic potentials, an elementary system that exhibits tunneling, and, when only the lowest pair of states is accessible, a beautiful example of a qubit. As a qubit with wavefunctions, it&#39;s the perfect system for making the connection between continuous wave mechanics and discrete matrix methods. On top of all this, a double well in two dimensions provides a good first example of an entangled two-particle state. But how can students actually solve the double well energy eigenvalue equation without getting bogged down in transcendental equations or the WKB approximation? The solution is fast and easy if they have learned any of several numerical methods.

AAPT SM 20

The Amazing Quantum Double Well

numerical

qubit

quantum

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The quantum double well is familiar to most of us as a model of molecular orbitals and of wiggling ammonia molecules. It's also a step toward understanding band structure in periodic potentials, an elementary system that exhibits tunneling, and, when only the lowest pair of states is accessible, a beautiful example of a qubit. As a qubit with wavefunctions, it's the perfect system for making the connection between continuous wave mechanics and discrete matrix methods. On top of all this, a double well in two dimensions provides a good first example of an entangled two-particle state. But how can students actually solve the double well energy eigenvalue equation without getting bogged down in transcendental equations or the WKB approximation? The solution is fast and easy if they have learned any of several numerical methods.

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The 2020 AAPT Virtual Summer Meeting brought together physics educators from around the globe to learn about the latest in physics theory, research methodology and education from leaders in their field. 

College faculty commonly participate in professional development to learn how to improve their teaching. Typically after the program finishes there is little support for faculty to bring new teaching practices into their classrooms. By employing the Situative Perspective and Pedagogical Reasoning and Action, we investigate how faculty take up ideas from a professional development program and the factors that influence their instructional design choices. In this study we investigate a program that aims to bring Three-Dimensional Learning (3DL) into undergraduate STEM classrooms. During this program participants are tasked with creating a teachable unit that aligns with 3DL. Using interviews, fellowship recordings, and online forum responses we look at two different faculty members, Ron and Charlie, and investigate influences that impact their design of classroom materials. Moving forward, we plan to expand the case study to more participants in order to explore how these influences effect the design of professional development programs.

How Faculty Take Up Ideas from a Professional Development Program

The AAPT Speakers Bureau can be a powerful tool to share the expertise of AAPT members and disseminate the diverse work we do to support physics education at all levels throughout the world. The work of my group, at Chicago State University, focuses on supporting students underrepresented in physics by creating opportunities for faculty to collaborate with students on education reform efforts. Much of this work leverages the Learning Assistant Model, input from students, and input from undergraduate education researchers. This student expertise can create effective, inclusive learning environments as well as shifts in who has power in the classroom and who has power in how our learning environments are structured. These are exciting spaces to work in for both faculty and students who all play a role in how we think about physics teaching and learning.

Contributing to the AAPT Speakers Bureau: Students as collaborators in creating effective, inclusive learning spaces

Research has shown that traditional instruction often falls short of helping students develop deep understanding in learning physics. To support the assessment and instruction that promote knowledge integration and deep learning, a new modeling approach, the Conceptual Framework, has been developed, which establishes models of plausible student knowledge structures that focus on the core idea(s) and sub-dimensions for a given concept. Assessments based on conceptual frameworks focus on determining what connections students exist for students in both familiar and novel problem formats, while instruction based on conceptual frameworks suggests which material to teaching in order to best facilitate building expert-like connections within the students’ knowledge structures. This presentation will introduce the conceptual framework approach and review the recent studies that have shown promising outcomes from applying this method.

The Conceptual Framework Approach for Modeling Deep Learning in Physics

In a flipped classroom model, students are expected to master a base level of information before coming to class. Such a structure can result in not only more class time to explore more complex topics, but also a more equitable classroom. To achieve these goals, the level of knowledge students are expected to master must be appropriate. Moreover, quality materials and support, which focus solely on what is needed for preparation, must be available so that all students, regardless of prior experience, can come prepared for class. In order to ensure accessibility, these materials should be free or very low cost and conform to Universal Design for Learning principles. In this talk we present a free-and-open multi-modal textbook developed in Pressbooks for a second semester IPLS course at University of Massachusetts Amherst. Student mastery of the preparation is further developed through formative online assignments in the low-cost Edfinity homework system.

Ensuring student preparation using Pressbooks and the Edfinity homework system

At San Francisco State, the Alma Project was created to support connections to students’ life experiences and affirm their identities in STEM classrooms. In Spring 2017, the Alma Project was piloted in select sections of the Supplemental Instruction (SI) program, which offers 1-unit courses that support “large lecture” STEM classes. In Fall 2018, the project was expanded to all SI classes and to all introductory physics and astronomy labs, allowing over 1000 students to share their experiences in STEM spaces each semester. Through instructor interviews we identify implementation challenges and success as well as the perceived effect of reflective journaling on the classroom environment. Interview questions also allowed instructors to reflect on their teaching practices and ways in which they support and encourage a sense of belonging in their classrooms.

Promoting Inclusion Through Reflective Journaling in Introductory Physics

Many students experience their first practical application of statistics and error analysis in their introductory physics laboratory courses. The activities they conduct in their lab courses teach definitions, concepts, and skills in statistics and error analysis that they will use for the rest of their academic and postgraduate career. We analyze the use of statistical methods in college-level introductory physics laboratory courses by reviewing a sample of student lab manuals collected from two-year community colleges and four-year universities. Approaches to introducing statistical concepts and procedures are examined for consistency, with particular reference to national and international statistical guidelines such as the National Institute of Standards and Technology (NIST) and the International Organization for Standardisation (ISO). Our analysis reveals a severe inconsistency in the treatment of statistics and error among the sampled lab manuals for courses aimed at science and engineering students.

Treatment of statistics and error in introductory physics lab manuals

Integrating computation into the classroom has been an uncharted journey; from learning to code at a week long seminar to encouraging students in the classroom to interpret code and solve problems. Gathering information gained through practice and discussion, I introduced my students to vpython using trinket. Programming activities ranged from moving and creating shapes to using the program to confirm physics homework challenges. The results have been varied as I learn to understand how quickly (or not) students pick up the logic flow of programming. Exposing students to the world of coding is valuable in that no matter where and what they end up doing in their lives, they will be exposed to some need for programming. As an experienced teacher, but not an experienced programmer, I am a great model for “anyone can do this”.

The Experience of Integrating Computation into the Physics Classroom

Physics laboratory classes offer great potential for learning, often in ways that are distinct and complementary to theory-focused courses. However, there are relatively few research-based assessments that are suitable for use in an upper-division physics laboratory course. Our group has created a new set of research-based assessments for measuring a central aspect of laboratory learning: modeling. The assessments, known as the Modeling Assessment for Physics Laboratory Experiments (MAPLE), are computer-based surveys with two parts. The first part is a "choose your own adventure," while the second part consists of standard coupled multiple response items. There are three surveys in MAPLE, each contextualizing modeling within different experimental apparatus: a pendulum, an op-amp circuit, and a laser incident on two polarizers. I present the development process and theoretical foundations of MAPLE, describe the assessments themselves, and discuss how they can be used to measure and improve laboratory learning.

MAPLE, the Modeling Assessment for Physics Laboratory Experiments

The first two semesters of introductory calculus-based physics at George Mason University are taught in two parallel formats: a flipped section (taught in a SCALE-UP-style active learning classroom, replacing lecture and recitation) and a traditional lecture section. To assess the influence on these formats on student performance and retention, we analyzed a data set of over 1000 students who took the traditional and/or flipped introductory courses in 2013-15, and tracked them longitudinally through their subsequent physics and engineering courses. Initial results suggest that taking flipped Physics I is associated with higher grades in later courses, and taking flipped Physics II is associated with lower grades. However, the full picture is more complicated. A greater fraction of the students who take flipped Physics II go on to take advanced courses, which suggests that flipped Physics II is associated with higher overall retention in physics and related fields.

Longitudinal impact of flipped and traditional introductory physics

Recent work by Kanim and Cid [2] suggests that the data used in PER is not representative of students enrolled in physics courses at the national level. Using university-level demographics, Kanim and Cid showed that PER studies oversample from white, wealthy, mathematically-prepared populations of students. What we do not yet know is whether these university-level demographics are representative of introductory physics courses, which are a primary site of research in PER. In this talk, we present data from nine US institutions, comparing the composition of introductory physics classes to aggregate university demographics across a number of social markers, including gender, race/ethnicity, and socio-economic status. Our aim is to make progress in characterizing the demographics of introductory physics courses, which is imperative to deepening our understanding of how social disparity is manifested in physics classrooms and the institutions that host them. We discuss limitations of our approach, including problematizing our use of statistics to make sense of who is enrolling in introductory physics.

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