Tales from three countries: reflections during COVID-19 for mathematical education in the future

How can school mathematics prepare citizens for a democratic society? Answers to this question are not static; they change as society and its problems change. The SARS-CoV-2 pandemic with its corresponding disease COVID-19 presents such a problem: what is needed to navigate this complex situation that involves, among other things, mathematics? Using the essay genre, we use three narratives from three countries—Italy, the USA (California), and Germany—to reflect on the goals of teaching mathematics during this crisis and examine aspects of each country’s standards for mathematics education. These three stories are framed by the authors’ backgrounds, experiences, interests, their country’s situation, and response to the pandemic. We first present the three narratives and then examine common issues across them that might provide insights beyond this current crisis, for preparing students to become active citizens. In particular, we focus on three issues: (1) developing a positive mindset toward mathematics to engage with and reflect on real-world problems, (2) improving interdisciplinary connections to the sciences to better understand how science professional practices and insights are similar or different from everyday practices, and (3) considering interpersonal and collective matters beyond the individual.

     

Parameter Estimation Accuracy of the Effort-Moderated Item Response Theory Model Under Multiple Assumption Violations

As low-stakes testing contexts increase, low test-taking effort may serve as a serious validity threat. One common solution to this problem is to identify noneffortful responses and treat them as missing during parameter estimation via the effort-moderated item response theory (EM-IRT) model. Although this model has been shown to outperform traditional IRT models (e.g., two-parameter logistic [2PL]) in parameter estimation under simulated conditions, prior research has failed to examine its performance under violations to the model’s assumptions. Therefore, the objective of this simulation study was to examine item and mean ability parameter recovery when violating the assumptions that noneffortful responding occurs randomly (Assumption 1) and is unrelated to the underlying ability of examinees (Assumption 2). Results demonstrated that, across conditions, the EM-IRT model provided robust item parameter estimates to violations of Assumption 1. However, bias values greater than 0.20 SDs were observed for the EM-IRT model when violating Assumption 2; nonetheless, these values were still lower than the 2PL model. In terms of mean ability estimates, model results indicated equal performance between the EM-IRT and 2PL models across conditions. Across both models, mean ability estimates were found to be biased by more than 0.25 SDs when violating Assumption 2. However, our accompanying empirical study suggested that this biasing occurred under extreme conditions that may not be present in some operational settings. Overall, these results suggest that the EM-IRT model provides superior item and equal mean ability parameter estimates in the presence of model violations under realistic conditions when compared with the 2PL model.     

The Long Decay Model of One-Dimensional Projectile Motion

This article introduces a research study on student model formation and development in introductory mechanics. As a point of entry, I present a detailed analysis of the Long Decay Model of one-dimensional projectile motion. This model has been articulated by Galileo (in De Motu) and by contemporary students. Implications for instruction are discussed.

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Adolescent caregiving success as a predictor of social functioning from ages 13 to 33

Adolescent success providing satisfying support in response to a close friend's call in a caregiving task was examined as a potentially fundamental developmental competence likely to predict future social functioning, adult caregiving security, and physical health. Adolescents (86 males, 98 females; 58% White, 29% African American, 8% mixed race/ethnicity, 5% other) were followed from ages 13 to 33 (1998–2021) using multiple methods and reporters. Early caregiving success was found to predict greater self- and partner-reported caregiving security, lower negativity in adult relationships, and higher adult vagal tone. Results are interpreted as advancing our understanding beyond simply recognizing that adolescent friendships have long-term import, to now identifying specific capacities within friendships that are linked to longer-term outcomes.     

Schedule-induced polydipsia contrast in the rat

Schedule-induced polydipsia was studied using a behavioral contrast paradigm. Food pellets were delivered to food-deprived rats on a response-independent FT 1-min schedule. Licking on a tube produced water on a MULT FR 10 FR 10, MULT FR 10 EXT, or MIXED FR 10 EXT for three rats (Experiment 1) and on a MULT VI VI, MULT VI EXT, or MIXED VI EXT schedule for three other rats (Experiment 2). On the FR schedules, rats could drink more water by increasing lick rates, but on the VI schedules the amount of drinking was fixed by the schedule parameters and was relatively unaffected by lick rates. Relative to MULT FR FR, positive polydipsia contrast was clearly demonstrated on MULT and MIXED FR EXT; but relative to MULT VI VI, contrast was not demonstrated on MULT and MIXED VI EXT. These data suggest that polydipsia contrast occurs only if increased licking permits increased drinking.     

Using Drawing Technology to Assess Students’ Visualizations of Chemical Reaction Processes

In this study, we investigated how students used a drawing tool to visualize their ideas of chemical reaction processes. We interviewed 30 students using thinking-aloud and retrospective methods and provided them with a drawing tool. We identified four types of connections the students made as they used the tool: drawing on existing knowledge, incorporating dynamic aspects of chemical processes, linking a visualization to the associated chemical phenomenon, and connecting between the visualization and chemistry concepts. We also compared students who were able to create dynamic visualizations with those who only created static visualizations. The results indicated a relationship between students constructing a dynamic view of chemical reaction processes and their understanding of chemical reactions. This study provides insights into the use of visualizations to support instruction and assessment to facilitate students’ integrated understanding of chemical reactions.     

The determinants of progress to the doctoral degree

The time doctoral students expect to take to complete their degree is investigated in a model which stresses the effects of economic factors. The model also accounts for the interdependency among such variables as employment hours, study hours, household income, and part-time study. We find that field of study, amount of borrowing, household income, and study hours have direct effects on expected time to degree. Indirect effects also occur from employment hours and the amount of fellowship, scholarship, or grant aid. When the sample is separated into foreign and U.S. students, we find that U.S. students underestimate their time to degree. Also, household incomes are higher for U.S. students and increase the time to degree, while the opposite is true for foreign students. Teaching assistantships increase the time to degree for foreign students while research assistantships reduce it.