Physics

Covariational reasoning -- reasoning about how changes in one quantity relate to changes in another quantity -- has been examined extensively in mathematics education research. Little research has been done, however, on covariational reasoning in introductory physics contexts. We explore one aspect of covariational reasoning: ``goes like'' reasoning. ``Goes like'' reasoning refers to ways physicists relate two quantities through a simplified function. For example, physicists often say that ``the electric field goes like one over r squared.'' While this reasoning mode is used regularly by physicists and physics instructors, how students make sense of and use it remains unclear. We present evidence from reasoning inventory items which indicate that many students are sense making with tools from prior math instruction, that could be developed into expert ``goes like'' thinking with direct instruction. Recommendations for further work in characterizing student sense making as a foundation for future development of instruction are made.

Module Analysis for Multiple-Choice Responses (MAMCR) was applied to a large sample of Force Concept Inventory (FCI) pretest and post-test responses ( N pre =4509 and N post =4716 ) to replicate the results of the original MAMCR study and to understand the origins of the gender differences reported in a previous study of this data set. When the results of MAMCR could not be replicated, a modification of the method was introduced, Modified Module Analysis (MMA). MMA was productive in understanding the structure of the incorrect answers in the FCI, identifying 9 groups of incorrect answers on the pretest and 11 groups on the post-test. These groups, in most cases, could be mapped on to common misconceptions used by the authors of the FCI to create distactors for the instrument. Of these incorrect answer groups, 6 of the pretest groups and 8 of the post-test groups were the same for men and women. Two of the male-only pretest groups disappeared with instruction while the third male-only pretest group was identified for both men and women post-instruction. Three of the groups identified for both men and women on the post-test were not present for either on the pretest. The rest of the identified incorrect answer groups did not represent misconceptions, but were rather related to the the blocked structure of some FCI items where multiple items are related to a common stem. The groups identified had little relation to the gender unfair items previously identified for this data set, and therefore, differences in the structure of student misconceptions between men and women cannot explain the gender differences reported for the FCI.

Investigating student learning and understanding of conceptual physics is a primary research area within Physics Education Research (PER). Multiple quantitative methods have been employed to analyze commonly used mechanics conceptual inventories: the Force Concept Inventory (FCI) and the Force and Motion Conceptual Evaluation (FMCE). Recently, researchers have applied network analytic techniques to explore the structure of the incorrect responses to the FCI identifying communities of incorrect responses which could be mapped on to common misconceptions. In this study, the method used to analyze the FCI, Modified Module Analysis (MMA), was applied to a large sample of FMCE pretest and post-test responses ( N pre =3956 , N post =3719 ). The communities of incorrect responses identified were consistent with the item groups described in previous works. As in the work with the FCI, the network was simplified by only retaining nodes selected by a substantial number of students. Retaining nodes selected by 20\% of the students produced communities associated with only four misconceptions. The incorrect response communities identified for men and women were substantially different, as was the change in these communities from pretest to post-test. The 20% threshold was far more restrictive than the 4% threshold applied to the FCI in the prior work which generated similar structures. Retaining nodes selected by 5% or 10% of students generated a large number of complex communities. The communities identified at the 10\% threshold were generally associated with common misconceptions producing a far richer set of incorrect communities than the FCI; this may indicate that the FMCE is a superior instrument for characterizing the breadth of student misconceptions about Newtonian mechanics.

The observed performance difference between women and men on assessments in physics---the "gender gap"---is a significant and persistent inequity which has broad implications for the participation of women in physics. Research also shows that gender-based inequities extend to affective measures, such as self-efficacy. In this exploratory study, we report on gender disparities in self-efficacy and test anxiety and their relationship to assessment scores in our active-learning introductory physics course. Overall, gender-based differences in favour of men are observed in all our measures, with women having lower scores on measures associated with success (self-efficacy and assessment scores) and a higher score on a possibly detrimental affective factor (test anxiety). Using a multiple regression model-selection process to explore which measures may explain end-of-course Force Concept Inventory (FCI) and final exam scores, we find that the best fitting models include FCI pretest and self-efficacy as predictors, but do not include test anxiety.

This study examines whether including more contextual information in data analysis could improve our ability to identify the relation between students' online learning behavior and overall performance in an introductory physics course. We created four linear regression models correlating students' pass-fail events in a sequence of online learning modules with their normalized total course score. Each model takes into account an additional level of contextual information than the previous one, such as student learning strategy and duration of assessment attempts. Each of the latter three models is also accompanied by a visual representation of students' interaction states on each learning module. We found that the best performing model is the one that includes the most contextual information, including instruction condition, internal condition, and learning strategy. The model shows that while most students failed on the most challenging learning module, those with normal learning behavior are more likely to obtain higher total course scores, whereas students who resorted to guessing on the assessments of subsequent modules tended to receive lower total scores. Our results suggest that considering more contextual information related to each event can be an effective method to improve the quality of learning analytics, leading to more accurate and actionable recommendations for instructors.

Images of an explosion can be used to study some of its physical properties. After reviewing the key aspects of the method originally developed to study the first nuclear detonation and analyzing the Trinity blast data, the method is applied to the Beirut explosion of August 2020 by using images from videos posted online. The applicability of the method is discussed and the process of selection, extraction, and analysis of the data is presented. The estimate for the energy yield of the Beirut explosion is found to be 2.3 +1.1 −1.1 TJ or 0.6 +0.3 −0.3 kt of TNT equivalent. The result is consistent with others recently appeared in the literature using different methods. Notice that this article includes content that some readers may find distressing.

Machine learning algorithms have recently been used to classify students as those likely to receive an A or B or students likely to receive a C, D, or F in a physics class. The performance metrics used in that study become unreliable when the outcome variable is substantially unbalanced. This study seeks to further explored the classification of students who will receive a C, D, and F and extend those methods to predicting whether a student will receive a D or F. The sample used for this work ( N=7184 ) is substantially unbalanced with only 12\% of the students receiving a D or F. Applying the same methods as the previous study produced a classifier that was very inaccurate, classifying only 20\% of the D or F cases correctly. This study will focus on the random forest machine learning algorithm. By adjusting the random forest decision threshold, the correct classification rate of the D or F outcome rose to 46\%. This study also investigated the previous finding that demographic variables such as gender, underrepresented minority status, and first generation status had low variable importance for predicting class outcomes. Downsampling revealed that this was not the result of the underrepresentation of these students. An optimized classification model was constructed which predicted the D and F outcome with 46\% accuracy and C, D, and F outcome with 69\% accuracy; the accuracy of prediction of these outcomes is called "sensitivity" in the machine learning literature. Substantial variation was detected when this classification model was applied to predict the C, D, or F outcome for underrepresented demographic groups with 61\% sensitivity for women, 67\% for underrepresented minority students, and 78\% for first-generation students. Similar variation was observed for the D and F outcome.

Brewe, Bruun, and Bearden first applied network analysis to understand patterns of incorrect conceptual physics reasoning in multiple-choice instruments introducing the Module Analysis for Multiple-Choice Responses (MAMCR) algorithm. Wells {\it et al.} proposed an extension to the algorithm which allowed the analysis of large datasets called Modified Module Analysis (MMA). This method analyzed the network structure of the correlation matrix of the responses to a multiple-choice instrument. Both MAMCR and MMA could only be applied to networks of incorrect responses. In this study, an extension of MMA is explored which allows the analysis of networks involving both correct and incorrect responses. The extension analyzes the network structure of the partial correlation matrix instead of the correlation matrix. The new algorithm, called MMA-P, was applied to the FCI and recovered much of the structure identified by MMA. The algorithm also identified sets of correct answers requiring similar physical reasoning reported in previous studies. Beyond groups of all correct and all incorrect responses, some groups of responses which mixed correct and incorrect responses were also identified. Some of these mixed response groups were produced when a correct response was selected for incorrect reasons; some of the groups helped to explain the gender unfairness previously reported for the FCI.

We demonstrated the fabrication of a low-cost and high-resolution papercraft smartphone spectrometer and characterized its performance by recording spectra from gas discharge lamps. The optical design and a lab-made narrow slit used in the fabrication led to fine images of the slit on the image sensor, resulting in high spectral resolution. The spectral resolution of the fabricated papercraft smartphone spectrometer was measured to be 0.5 nm, which is similar to that of the best smartphone spectrometer reported thus far. Extending the exposure time of the phone's camera revealed the fine structure of a spectrum with high sensitivity. The build cost of the papercraft smartphone spectrometer was less than $3. We demonstrated that the papercraft smartphone spectrometer is a low-cost device that can record spectra with high resolution and high sensitivity.

Most students do not enroll in introductory astronomy as part of their major; for many, it is the last science course they will ever take. Thus, it has great potential to shape students' attitudes toward STEM fields for the rest of their life. We therefore argue that it is less important, when assessing the effectiveness of introductory astronomy courses, to explore traditional curricular learning gains than to explore the effects that various course components have on this attitude. We describe the results of our analysis of end-of-semester surveys returned by a total of 749 students in 2014-2015, at 10 institutions that employed at least part of the introductory astronomy lecture and lab curriculum we first implemented at UNC-Chapel Hill in 2009. Surveys were designed to measure each student's attitude, and to probe the correlation of attitude with their utilization of, and satisfaction with, various course components, along with other measures of their academic background and their self-assessed performance in the course. We find that students' attitudes are significantly positively correlated with the grade they expect to receive, and their rating of the course's overall effectiveness. To a lesser degree, we find that students' attitudes are positively correlated with their mathematical background, whether they intend to major or pursue a career in STEM, and their rating of the effectiveness of the instructor. We find that students' attitudes are negatively correlated with the amount of work they perceived the course to involve, and, surprisingly, the size and reputation of their home institution. We also find that, for the subsets of students who were exposed to them, students' attitudes are positively correlated with their perception of the helpfulness of the lecture component of the course, and of telescope-based labs that utilized UNC-CH's Skynet Robotic Telescope Network.