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A primary goal of this study is to experimentally test the effects of a brief intervention designed to prime positive math self-concept in order to buffer against math anxiety and improve math performance. A second goal of this study is to compare the intervention to the expressive writing prompt from Park et al., 2014, and two control groups (one active and one passive), on math outcomes (i.e., math performance, math anxiety, math self-concept, and confidence).

People are constantly making judgments about incoming health information. This fact is particularly relevant in 2020 as new information is frequently conveyed related to the COVID-19 global pandemic. Our interdisciplinary team collected data from 1,297 adults at the onset of the COVID-19 pandemic to determine the effects of a novel, brief online educational intervention. The data related specifically to leveraging cognitive science principles to help people learn and preventing whole number bias (WNB) errors are presented in another paper (https://psyarxiv.com/hukyv/). The current project focuses on the participants’ confidence ratings that were made after having solved health-related math problems and typing in the strategies that they used to solve the problems. One confidence judgment was made at pretest, and three were made immediately after participants engaged in the educational intervention. In the current paper, we will (a) investigate whether pretest confidence judgments and experimental condition (educational intervention vs. business-as-usual control) predict post-intervention confidence judgments, (b) explore whether those who make whole number bias errors (as indicated in their open-ended strategy reports) have higher or lower confidence judgments as compared to those who do not report a whole number bias error, and (c) investigate the individual differences that predict confidence judgments on the health-related math problems. We will also explore whether metacognitive accuracy differs with respect to experimental condition. This study was supported in part by U.S. Department of Education Institute of Education Sciences Grants R305A160295 and R305U200004 to C.A. Thompson at Kent State University.

January 2021 Qualtrics Panel and Psychology Subject Pool Experiments Participants In mid- to late January 2021, our research team will partner with Qualtrics to launch a data collection with adults across the U.S. As with our March 2020 data collection, we will include quotas for gender, age, and educational attainment. The design of the study will be the same as our March 2020 study: half of participants will be randomly assigned to the experimental education condition and half to the business-as-usual control condition. Qualtrics “Quality Completes” and Exclusion Criteria We aim to collect data from 2,000 quality completes. Quality completes will be operationalized as those who successfully pass 2 out of 3 attention checks embedded in our survey. Additionally, we have included one other attention check that requires participants to type in the word “blue” and not answer a question about COVID-19. After all data is collected, we will exclude people who fail to answer this question correctly after we implement all other previously pre-registered exclusion criteria for our earlier data collection efforts on Qualtrics and with college students. Experimental Design and Stimuli Updates Updates to the experimental education condition include number lines to visualize the “orchard” example and the COVID-19 vs. flu example. We have included additional transfer problems that were selected from the correlational study that was conducted in Fall 2020 in the KSU and UK subject pool. In order to assess pretest-to-posttest change in the Disease A vs. Disease B problem, we have added the very same problem (with no visual model) as the first transfer problem after the COVID-19 vs. flu health-related math problem that participants complete post-intervention. To ensure that our baseline survey could be completed within 40 minutes, it was necessary to take out some measures (e.g., Need for Cognition), and minimize others (e.g., include only two of four subscales from the MAQ). In order to more easily assess relative confidence accuracy, we have added a question in which participants will indicate whether they believe they got the health-related math problem right or wrong. We made wording updates to the risk perception, worry, and severity questions that will be presented in the baseline as well as daily diary surveys. We added a new disgust scale to the baseline survey as well. Updates to Daily Diaries As with the March 2020 study, participants who are considered quality completes will be invited to complete 10 days of daily diaries. We have added a transfer question to Day 1 of the daily diaries in which we ask participants about the November 2020 COVID-19 case-fatality rate. Participants will receive $5 for completing the daily diaries. Anticipated Analyses We will conduct analyses consistent with those that were conducted for our under-review manuscript involving the March 2020 data collection (preprint here: https://psyarxiv.com/hukyv/). Specifically, we found that males/females were not actually randomly distributed across our conditions, thus we included gender as a covariate in Model 1 along with condition. Then, we added additional covariates (e.g., PAE, math anxiety, etc.) into Model 2. Of course, if males/females are equally distributed across the two conditions in our currently-proposed studies, gender will not be necessary to add as a covariate in Model 1. There is a distinct possibility that reviewers of our under-review manuscript will request additional analyses. Given the similarities of the January 2021 data collection with the March 2020 data collection, we will analyze the data similarly. As indicated in the Fall 2020 correlational pre-registration, we will analyze each health-related math problem separately and may aggregate accuracy across all transfer problems assuming an adequate level of reliability across the items. Participant Recruitment for Replication with Undergraduates We will conduct a replication of the January 2021 Qualtrics panel study with undergraduates from KSU, UK, and UW-Madison. Because psychology subject pools generally include fewer students in the Spring semester, we will plan to recruit as many students as possible before the end of the semester at each respective university. We estimate that there will be approximately 2,000 students in the KSU subject pool; the UK subject pool will allow us to collect data from approximately 250 students. There will be no follow-up daily diaries administered to the subject pool students. However, all other aspects of the experimental design and analysis plan will be the same as the Qualtrics panel study mentioned here Full Baseline Survey and Daily Diary Survey We have included exports of our surveys. We did not begin collecting data until we pre-registered these changes.

Our previous study (Thompson et al., under review), tested a brief online intervention focused on teaching adults how to calculate the case fatality rate of COVID-19 vs. the flu. Those in the intervention condition were more likely to answer a transfer problem correctly as compared to the control condition. Further, those in the control condition reported using a strategy aligned with the whole number bias when solving this transfer problem. In the current study, we are investigating whether various visual models (number lines, risk models, or icon arrays) facilitate more accurate COVID-19 problem solving than no visual model at all. Further, we will investigate the relation between COVID-19 problem-solving accuracy, use of whole number bias strategies, perceived COVID-19 likelihood and worry for themselves and other people, and perceived COVID-19 severity. This study was supported in part by U.S. Department of Education Institute of Education Sciences Grants R305A160295 and R305U200004 to C.A. Thompson at Kent State University.

These are pre-registration of planned analyses for an existing dataset with new follow-up data to be collected. Data were collected in March-April of 2020 via Qualtrics panels. These analyses will be conducted on all participants who respond to follow-up recruitment via email (and meet certain criteria, described below), who also completed the daily diary from the original data collection. The primary goal of this investigation is to test how flexible emotional appraisals early in the pandemic are associated with long-term psychological functioning. This work builds on prior research conducted by our team and others.

This project will involve multiple classroom studies investigating possible additive effects of combining the well-known positive effects of testing on learning and retention with the less-known but still positive effects of generating test questions.

In March-April 2020, we collected baseline and daily diary data from a cohort of nearly 1,300 adults who were recruited by Qualtrics. Now, one year later, we will recontact these participants to assess their health-related math problem-solving, confidence, strategy reports and math anxiety. We will also assess the extent to which they consider themselves to be liberal vs. conservative and their cultural worldview. These latter two constructs were included at this follow-up because our funders (IES, U.S. Department of Education) requested that these variables, which may influence beliefs about COVID-19 be included as moderators of experimental condition on risk perceptions. We have uploaded the full survey, which we estimate will take participants approximately 20 minutes to complete. Research Questions and Data Analyses 1. How are responses on the follow-up survey associated with responses on the baseline and daily diary? a. To test this, we will explore correlations among all study variables and variables across time points. Specifically, we anticipate that math anxiety at follow-up will be positively associated with math anxiety from the baseline. Additionally, we will look at differences in math anxiety based on health-related math problem solving accuracy at baseline and follow-up. 2. Is there a lasting effect of the intervention on health-related math problem solving? a. To test this, we will conduct a logistic regression on the outcome of health-related math problem-solving accuracy (for the vaccine question) in which we enter baseline condition (intervention vs. control) as well as gender, math anxiety, PAE, baseline problem-solving accuracy as covariates. We do not anticipate that the intervention will have sustained effects over one year, given the brief nature of the intervention, but we believe it is important to examine whether condition does account for unique variance in follow-up health-related math problem-solving accuracy and/or strategy reports. b. It is important to note that this analysis hinges on whether there is a sufficient number of participants across the two experimental groups who decide to complete the follow-up survey and that the groups are approximately equal on baseline math skills. We will re-test whether groups are approximately equal on math skills (e.g., PAE, math anxiety, and pretest problem accuracy). Doing so will allow us to assess whether those who had higher overall math skills were the ones who decided to complete our 1-year follow-up survey. 3. What proportion of people make a whole number bias error when asked to compare the size of two fractions that included numerators and denominators which are the same as the COVID-19 and flu rates that were included in the intervention from one year ago? Are those who were accurate on the problem more confident than those who were not accurate? 4. Are follow-up item-level metacognitive judgments higher on each of the math items for those in the intervention vs. control condition (if indeed condition differences are found)? That is, do findings from Scheibe et al. (in preparation) replicate? a. To test this, we will run regressions as described above, but the outcome variables will be whether they believe they got the problem correct or not (logistic) as well as item-level metacognitive (confidence judgments linear). We will also account for baseline item-level metacognitive judgments (from pretest) and problem-solving accuracy on the follow-up health-related math problem of interest. b. We hypothesize that confidence will be higher for those who answered the math problem correctly relative to those who answered incorrectly. c. We will also explore whether participants’ confidence is calibrated with their performance by scoring the Yes/No confidence scale as 1 for yes and 0 for no and then taking the absolute difference (calibration) and raw difference (bias) between problem solving performance (0 = incorrect and 1 = correct). 5. Can adults identify the correct expanded notation of a number like 33.88 million? The our world in data website uses this notation to indicate the number of people who have been vaccinated across countries. a. We will explore which math variables as measured at baseline and follow-up data collections account for unique variance in accuracy on this problem. 6. Did math anxiety increase, decrease, or stay the same over a year’s time? We will compare anxiety in an ANCOVA with time-point (baseline vs. follow-up) and experimental condition (if indeed there is a condition difference in problem-solving accuracy at follow-up) as independent variables and gender as a covariate.

Schon bei der Planung einer Beregnungsanlage ist an spätere Folgekosten zu denken, denn durch die Beregnung verändern sich nicht nur Liquidität und Einkommen, sondern auch die Organisation des Betriebes muss angepasst werden. Deshalb ist es wichtig, deutliche Vorstellungen über Leistungen und Kosten der Beregnung zu besitzen. Dieser Beitrag stellt die Beregnungskosten in den Mittelpunkt und gibt kurze Hinweise zur Planung von Beregnungsanlagen., LANDTECHNIK, Bd. 54 Nr. 2 (1999)