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We developed a guided-inquiry tutorial to foster connections between mathematics and physics in the context of undergraduate thermodynamics, specifically the heat equation. Based on literature and empirical reasons, we formulated design principles that guided the development, including promoting graphical reasoning, stimulating thinking about physical meaning first, and paying explicit attention to the mathematical and physical aspects of concepts and ideas, and as such promote interdisciplinary connections. We determined the effectiveness of the design principles by testing the tutorial in teaching-learning interviews with three groups of three students each. In this session, we present the design principles and how they impacted the students’ reasoning process. We aim to inform practitioners in the field who teach this subject, but furthermore anyone who wants to strengthen the connections between mathematics and physics in the topic they are teaching.

AAPT SM 20

Tutorial to connect mathematics and physics of the heat equation

mathematics

undergraduate physics

tutorial

Join AAPT and Physics Educators worldwide in developing and strengthening your professional connections by attending the 2021 AAPT Virtual Summer Meeting. AAPT meetings are a great way to reflect on your teaching, recommit to best practices and re-energize your career with new research, products, and techniques.

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AAPT SM 21

technical paper

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. The program featured plenary speakers, sessions, workshops and many special activities.

For more information please visit the 2020 AAPT Virtual Summer Meeting page at: https://www.aapt.org/Conferences/SM2020/index.cfm.


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. 

We present a study of a large-scale intervention designed to shift lab instruction away from "cookbook" lab norms. The intervention was implemented in a network of Professional Learning Communities of Israeli high-school physics teachers (N=250; ~20% of the national workforce). The intervention was tailored to respond to findings on teachers' dissatisfaction with the limited scope of experimental design employed in traditional labs, as well as the highly constrained setting in which these teachers work: a high-stakes exam setting, limited resources, and diverse groups of students. The intervention followed two design guidelines: a) restructuring traditional labs, by encouraging students to reflect on the considerations underlying the experimental design; b) an evidence-based learning process involving teachers in collaborative reflection on classroom enactments of the restructured labs. We found that most teachers chose to carry out the restructured labs, even though they expressed concerns about the demands, as compared to the standardized exams.

Re-defining Lab Norms via Professional Learning Communities: Meeting the Constraints

Secondary physics curricula predominantly focus on physics content established prior to the 20th century (e.g., Newtonian mechanics, conservation of energy). Rarely are students exposed to modern physics topics (e.g., quantum mechanics, special relativity) in their formal education. Even so, students inevitably encounter terms such as “quantum” and “quantum physics” in their everyday lives. The aim of this study is to provide insight on secondary student perspectives of the terms “quantum” and “quantum physics”. While there is a body of research available that analyzes university physics majors’ perspectives of quantum physics topics, little research has been done at the secondary level. Clinical interviews of students at a Midwestern high school are conducted to establish commonalities among perspective of quantum physics topics.

Students' Pre-Instructional Perspectives of Quantum Physics

For twelve years I have been using NYTimes articles on Global Warming to assist teaching fluids and heat concepts. NYTimes articles are pasted into word and edited to fit one page. Added are: graphics,introduction,questions,hints and answers to the standard printable word page. This presentation is at: http://CisePhysics.homestead.com/files/NYTOceanWarmingAAPTs2020.pdf 1000 NYTimes Physics concept applications are located at AAPT's ComPADRE site at: http://CisePhysics.homestead.com/files/NYTCisePhysics.pdf This physics and physical science resource site is listed at AAPT's ComPADRE and the AAPT's Physical Science Resource Center.

New York Times Warm Earth Physics Applications 2008-2020

Weyl's problem deals with the distribution of eigenvalues of the wave equation in a bounded domain. The integrated density of states counts the number of states up to a certain wavenumber and has important applications in nuclear physics, degenerate Fermi gases, blackbody radiation, and Bose-Einstein condensation. In the limit of large wavenumbers, the integrated density of states depends only on the volume of the domain and not on its shape. Corrections to this behaviour are well-known and depend on the surface area of the domain, its curvature and other features. We describe several computational projects that allow students to investigate this dependence for three different bounding domains – a rectangular box, a sphere and a circular cylinder. Quasi one- and two-dimensional systems can be analyzed by considering various limits. These projects could be incorporated into courses in quantum mechanics or statistical mechanics, or could stand alone in a computational physics course.

Computational Physics Projects Related to Weyl’s Problem

Students with disabilities make up between 10-20% of postsecondary students, however instructors lack knowledge about how to support this population and little research has investigated how courses can be designed to support students with disabilities. Universal Design for Learning (UDL) is one framework we can use to identify barriers to learning in our courses and identify strategies that reduce these barriers. UDL supports the reduction of barriers to learning by providing guidelines and checkpoints which provide considerations and recommendations for supporting the variability of students’ interests, needs, and abilities. We will present how the UDL framework was used in observations of postsecondary, introductory physics courses to identify barriers to learning. We will then exhibit inclusive practices that the instructors for the observed courses chose to implement in response to feedback from the observations, along with how students responded to the implemented practices.

Using Universal Design for Learning to Identify and Implement Inclusive Practices

The use of active-learning instructional strategies in high schools is strongly emphasized in the new Course of Study in Japan. However, in the actual classroom, one-way didactic teaching is more common. This study focuses on a high-school physics teacher and examines how his beliefs and teaching change through action research. The change of his teaching from the teacher-driven way before the treatment to more student-centered way after the treatment was shown by the use of S-T graphs and co-occurrence network diagrams of the observation data. It was interesting to notice that the teacher does not recognize the change in spite of the obvious change in his teaching style. Further discussions on the effects of action research for promoting active learning in high-school physics will be included in the presentation.

Improving High-School Physics Lessons through Action Research

Hypothesis–Experiment Class (HEC) is the educational approach proposed by Itakura in 1963. Since that time, a number of HEC curricular materials have been developed to teach students of all ages a wide range of topics in both natural and social sciences. Although Hatano and Inagaki introduced HEC to the West in the 1980s, it was done in service of discussing findings in cognitive science, and HEC itself has received little attention outside of Japan. That is beginning to change, however, with the recent translation and publication of the book “Hypothesis-Experiment Class (Kasetsu)” in 2019. HEC has been compared with the well-known Predict-Observe-Explain (POE) approach as well as other educational approaches, but there are some salient features that make HEC unique. In this presentation, we will discuss how HEC is similar to and different from other educational approaches, looking in particular at a specific HEC lesson on background radiation.

Rediscovery of a child-centered Japanese educational approach: Hypothesis–Experiment Class

Students' self-efficacy, their confidence in their ability to complete a task, is a good predictor for success and persistence. Previous research indicates that improvements in learning methods can improve student self-efficacy and that classroom dynamics may impact students' self-efficacy by allowing for different kinds of self-efficacy opportunities. In this study, we analyzed interviews from 12 students enrolled in a flipped integral calculus course to understand their perceptions of their self-efficacy and how this related to classroom dynamics and activities. Preliminary findings reveal that experiences in previous math courses, particularly high school, impacted students’ perceptions of their self-efficacy in math both positively and negatively, active learning activities increased students’ confidence in their ability to do math from their perspective, and verbal persuasion (implicit encouragement) increased students’ confidence and was seen as a helpful way to learn.

Qualitative analysis of students' perceptions of their self-efficacy

COR-400, Science and Human Nature, is a general education science course required of all students at Oglethorpe University. In this course, students learn about scientific ways of knowing and the scientific process through the lens of scientific revolutions. Specifically, the course content focuses on the Copernican Revolution and the Quantum Revolution of the early 20th century. Students often enter this course with preconceived notions of the relationship between religion and the scientific community – in particular, they often perceive religious authority to have produced barriers to scientific progress and discovery throughout history. During this course, we investigate and challenge these notions. In this presentation I will discuss how this material is presented to students and highlight student comments that demonstrate their evolution in thinking about the relationship between science and religion.

Challenging Student Ideas About Religion in a General Education Course

We have a large introductory physics course for non-majors, comprised mainly of First Year Undergraduate students. We provide for them a number of multiple choice and formula response questions online to help them prepare for the exams. While we do have other graded components of the course online, this part is set to be ungraded and allows them to see the solutions after a single attempt. We use data collected on the online student responses to explore student study behavior. For example, we were curious to see how students used this online answer checker to help them study for exams - did they try until they got the answer themselves or did they simply put in a junk answer in order to be able to read the solution?

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Tutorial to connect mathematics and physics of the heat equation

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