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Ordinary least squares (OLS), developed over two centuries ago, is still the most common curve-fitting method used in introductory physics labs. OLS offers best-fit parameter estimates, but best-fits may not be good fits. Moreover, OLS best fits may be biased (the outlier problem) where anomalous data is overweighted. Chi-squared minimization (CSM) provides both parameter estimation and model testing in one consistent methodology. CSM can be shown to be the optimal method of parameter estimation with Gaussian distributed uncertainties and solves the outlier problem by weighting data inversely with their uncertainties. However, more than being just a weighted least squares (WLS) method, CSM also provides two easy-to-apply criteria for model testing. CSM is a computation-intensive method whose gold-standard implementation in particle physics software is difficult for introductory physics students to use. A simplified form of CSM is implemented in an Excel spreadsheet, making this valuable tool accessible to introductory physics students.

AAPT WM 22

Curve-fitting with Model Testing using Chi-Square Minimization in Excel

introductory lab

model-testing

curve-fit

chi-squared

data

Join us in exploring emergent themes in PER as a scholarly endeavor and as a research community!  Since its inception, PER has served as a confluence of discipline, theory, research methodology, practice, and application.  How have these facets and the interplays among them been fruitful for physics education globally, regionally, locally, or otherwise?  And, how have our successes and interactions influenced the very nature of PER itself?
Following the lead of AAPT for the summer meeting, PERC 20/20 was virtual. Enjoy browsing the content.

PERC SM 20

Since its inception, PER has served as a confluence of discipline, theory, research methodology, practice, and application.  How have these facets and the interplays among them been fruitful for physics education globally, regionally, locally, or otherwise?  And, how have our successes and interactions influenced the very nature of PER itself?

technical paper

This meeting is a great opportunity to explore sessions and workshops designed with your professional development in mind. Present your research and exchange ideas on the latest in teaching and pedagogy. Participate in a wide range of events, activities, plenaries, and so much more, connecting you with peers and colleagues who share your commitment to excellence in physics education.

The arm and shoulder is a major part of the body, but unfortunately, not a lot of related simulations are available. Through GeoGebra, we developed an interactive simulation of forces of a human arm and shoulder—which these force vectors include the muscle of the bicep and deltoid, and the forces on the shoulder and elbow joints. This simulation helps us understand Newton’s Second Law and the concepts of torque and equilibrium as a learning tool, which can be used in physics classrooms. With further development, this simulation has the potential to be implemented in hospitals and in sports science.

Simulations of Shoulder and Arm

At-home wave mechanics are demonstrated with the inexpensive iOLab sensor system and a slinky. A suprising result is demonstrated by measuring the standing wave speed of a slinky. The wave speed does not appear to increase with Hookean tension on the slinky The reason is the slinky's linear density also changes in direct proportion with its stretched length. This counterintutive result can be easily explained conceptually and mathematically, providing students with a richer understanding of wave mechanics [Huggins]. Most importantly this experiment is easily accomplished at home, even without the iOLab, using a ruler and kitchen scale. The results of this activity from an introductory physics UNE Spring 2021 virtual online course student presentation are provided. Elisha Huggins, Speed of Wave Pulses in Hooke's Law Media, The Physics Teacher, 142 (2008) https://doi.org/10.1119/1.2840977

The Simple Slinky Wave Speed

This pandemic-motivated lab was created to explore ideas of&nbsp;buoyancy, static equilibrium, and experimental uncertainty for the introductory physics student. The unknown density of an object was determined by weighing it in and out of water. A make-shift scale was created using a ruler and nickels. Particular attention was paid uncertainties of measurements with the propagation of error carried out using Python.

Determining density with water, a ruler, floss, and some nickels

Based on a mechanical analog to a particle trapping technique, the Paul trap, a lab has been developed to train scientific thinking and experimental problem-solving. It also works to illustrate an important concept in many areas of modern physics. The mechanical trap will together with a simulation give students an introduction to the concept of particle trapping. The lab has been developed to contribute to the ever-important task of making high school physics more interesting, to get more students pursuing careers in STEM, and increasing scientific literacy in the public. Using a design-based approach to developing the lab, its effectiveness on student learning and interest is probed using qualitative and quantitative methods, and initial findings from the study will be presented.

The Mechanincal Rotating Saddle Trap in High School Physics Education

Providing students the opportunity to explore cultural aspects of cosmology (such as those of Indigenous, non-Western, or marginalized groups) can be a powerful way to foster safe spaces within astronomy. We are investigating the impacts of such a project, used in an upper-division course but adaptable to introductory astronomy. Students’ written reflections and oral interviews suggest that their interest in cosmology specifically and astronomy in general was strengthened by studying and presenting on the cosmology of a non-dominant culture or narrative. They reported surprise in the number of ways where the cosmological beliefs of their selected culture aligned with current science, within the limitations of available technology of the time. Students also reported that engaging with the projects made them feel like the astronomical community would be welcoming of them, even if they are not from the majority demographic, and that it supported goals of continued astronomical learning.

Investigating the Impacts of a Cultural Cosmology Project

To make physics relevant to non-traditional students and English language learners, I introduced children’s literature books and other reading materials into my class in the Fall semester. “The Boy Who Harnessed the Wind”, “Ricky the Rock that Couldn’t Roll”, “Pheasant and Kingfisher”, Never Play Music Right Next to The Zoo”, and “Hurricane Ida” were some pieces of literature my students read. The students could relate illustrations and text to physics contents, including electricity, projectiles, mechanical waves, motion and force, and observe physics in their everyday experience. Mixed with projects, students find my class exciting, show interest in the course and are motivated to learn. Moreover, this pedagogy effectively replaced pandemic screen learning, where over fifty percent of my class failed. My students use project grades to offset a failing traditional test in this face-to-face teaching since both have the same weight. Currently, most of my students are passing.

Integrating Physics with Literature and Projects: Pedagogy for Nontraditional Students

We have made the use of smartphone applications a centerpiece of our efforts to reform the introductory labs in both our calculus-based and algebra-based classes. Students use smartphone applications in experiments completed in the lab (Bluetooth paired with sensors) and at home (using the native sensors in the phone). This has allowed us to reduce crowding in the lab, to give students a greater sense of agency in the experiments that they do, and to incorporate more sophisticated “data handling” in the learning goals for the labs. This talk will give an overview of the project and highlight several examples of labs in which smartphones play a prominent role.

Smartphone applications as part of an introductory lab reform project

Electromagnetic waves, or light, penetrate many topics in physics, chemistry, engineering, and biology. They are the foundation for many applications such as cell phones, GPS, medical equipment and procedures, 3D movies, astronomy, and so much more! In this high school lesson, we use the new Netflix logo to lead high school students through an inquiry-based experiment on light and spectroscopy. Students use diffraction glasses and multiple gas emission tubes to observe the unique spectra of gases. They record the colors they see in each element and estimate the wavelength and corresponding frequency of each spectral line. Students then are guided to discover the relationship between the frequency and wavelength of light. In addition, students learn about energy of light, the scientists who discovered spectra, and applications of spectroscopy today. In this presentation, we will share the developed lesson and the learning progress of several classes from local schools.

“Shedding Some Light” Spectroscopy Investigation

Who are the high school students applying to college engineering programs? In this talk, we will share some preliminary findings from interviews with aspiring engineers. How do they view themselves? What is important to them? How do they manage their schoolwork? How do they make decisions, and who influences them? We will share some of the first data collected in a two-year longitudinal study of student transitions from high school to college engineering programs with long-term goals of identifying ways that high schools and colleges can better support engineering students. For now, we are starting to get to know the students and look forward to sharing a snapshot of their lives with you.

Case Studies: High School Seniors Applying to College Engineering Programs

I will present a course introducing quantum mechanics to college students from both STEM and humanities fields. The course is based on material in "Understanding Quantum Raffles" (Janas, Cuffaro and Janssen 2021). With the help of techniques in Bananaworld: Quantum Mechanics for Primates (Bub 2016), students analyze correlations allowed classically and quantum-mechanically in an EPR-Bell-type setup due to Mermin. Noting that the quantum correlations can be parametrized by the cosines of the angles between the detectors in this setup, the students are then led to the Born rule for probabilities in quantum mechanics. The idea is to introduce the basic formalism of quantum mechanics as an extension of ordinary probability theory. In line with modern information-theoretic interpretations of quantum mechanics, this basic formalism is presented as a new operating system on which many different applications can be written, ranging from spectroscopy to quantum computing.

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