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1. Schneider, R.M., & Barner, D. (2020). Children use one-to-one correspondence to establish equality after learning to count. 42nd Annual Meeting of the Cognitive Science Society.

   Schneider, R.M. ( January 2020 , 42nd Annual Meeting of the Cognitive Science Society.)

   null (Ed.)

   Humans make frequent and powerful use of external symbols to express number exactly, leading some to question whether exact number concepts are only available through the acquisition of symbolic number systems. Although prior work has addressed this longstanding debate on the relationship between language and thought in innumerate populations and seminumerate children, it has frequently produced conflicting results, leaving the origin of exact number concepts unclear. Here, we return to this question by replicating methods previously used to assess exact number knowledge in innumerate groups, such as the Piraha, with a large sample of semi- numerate US toddlers. We replicate previous findings from both innumerate cultures and developmental studies showing that numeracy is linked to the concept of exact number. However, we also find evidence that this knowledge is surprisingly fragile even amongst numerate children, suggesting that numeracy alone does not guarantee a full understanding of exactness. 

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2. Counting and the ontogenetic origins of exact equality

   https://doi.org/10.1016/j.cognition.2021.104952  

   Schneider, R. M. ( January 2022 , Cognition)

   Humans are unique in their capacity to both represent number exactly and to express these representations symbolically. This correlation has prompted debate regarding whether symbolic number systems are necessary to represent large exact number. Previous work addressing this question in innumerate adults and semi-numerate children has been limited by conflicting results and differing methodologies, and has not yielded a clear answer. We address this debate by adapting methods used with innumerate populations (a “set-matching” task) for 3- to 5-year-old US children at varying stages of symbolic number acquisition. In five studies we find that children’s ability to match sets exactly is related not simply to knowing the meanings of a few number words, but also to understanding how counting is used to generate sets (i.e., the cardinal principle). However, while children were more likely to match sets after acquiring the cardinal principle, they nevertheless demonstrated failures, compatible with the hypothesis that the ability to reason about exact equality emerges sometime later. These findings provide important data on the origin of exact number concepts, and point to knowledge of a counting system, rather than number language in general, as a key ingredient in the ability to reason about large exact number. 

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3. Predictors of Jurors’ Understanding of Evidence Strength

   McCowan, K. ( March 2020 , Annual Conference of the American Psychology-Law Society.)

   Abstract Expert testimony varies in scientific quality and jurors have a difficult time evaluating evidence quality (McAuliff et al., 2009). In the current study, we apply Fuzzy Trace Theory principles, examining whether visual and gist aids help jurors calibrate to the strength of scientific evidence. Additionally we were interested in the role of jurors’ individual differences in scientific reasoning skills in their understanding of case evidence. Contrary to our preregistered hypotheses, there was no effect of evidence condition or gist aid on evidence understanding. However, individual differences between jurors’ numeracy skills predicted evidence understanding. Summary Poor-quality expert evidence is sometimes admitted into court (Smithburn, 2004). Jurors’ calibration to evidence strength varies widely and is not robustly understood. For instance, previous research has established jurors lack understanding of the role of control groups, confounds, and sample sizes in scientific research (McAuliff, Kovera, & Nunez, 2009; Mill, Gray, & Mandel, 1994). Still others have found that jurors can distinguish weak from strong evidence when the evidence is presented alone, yet not when simultaneously presented with case details (Smith, Bull, & Holliday, 2011). This research highlights the need to present evidence to jurors in a way they can understand. Fuzzy Trace Theory purports that people encode information in exact, verbatim representations and through “gist” representations, which represent summary of meaning (Reyna & Brainerd, 1995). It is possible that the presenting complex scientific evidence to people with verbatim content or appealing to the gist, or bottom-line meaning of the information may influence juror understanding of that evidence. Application of Fuzzy Trace Theory in the medical field has shown that gist representations are beneficial for helping laypeople better understand risk and benefits of medical treatment (Brust-Renck, Reyna, Wilhelms, & Lazar, 2016). Yet, little research has applied Fuzzy Trace Theory to information comprehension and application within the context of a jury (c.f. Reyna et. al., 2015). Additionally, it is likely that jurors’ individual characteristics, such as scientific reasoning abilities and cognitive tendencies, influence their ability to understand and apply complex scientific information (Coutinho, 2006). Methods The purpose of this study was to examine how jurors calibrate to the strength of scientific information, and whether individual difference variables and gist aids inspired by Fuzzy Trace Theory help jurors better understand complicated science of differing quality. We used a 2 (quality of scientific evidence: high vs. low) x 2 (decision aid to improve calibration - gist information vs. no gist information), between-subjects design. All hypotheses were preregistered on the Open Science Framework. Jury-eligible community participants (430 jurors across 90 juries; Mage = 37.58, SD = 16.17, 58% female, 56.93% White). Each jury was randomly assigned to one of the four possible conditions. Participants were asked to individually fill out measures related to their scientific reasoning skills prior to watching a mock jury trial. The trial was about an armed bank robbery and consisted of various pieces of testimony and evidence (e.g. an eyewitness testimony, police lineup identification, and a sweatshirt found with the stolen bank money). The key piece of evidence was mitochondrial DNA (mtDNA) evidence collected from hair on a sweatshirt (materials from Hans et al., 2011). Two experts presented opposing opinions about the scientific evidence related to the mtDNA match estimate for the defendant’s identification. The quality and content of this mtDNA evidence differed based on the two conditions. The high quality evidence condition used a larger database than the low quality evidence to compare to the mtDNA sample and could exclude a larger percentage of people. In the decision aid condition, experts in the gist information group presented gist aid inspired visuals and examples to help explain the proportion of people that could not be excluded as a match. Those in the no gist information group were not given any aid to help them understand the mtDNA evidence presented. After viewing the trial, participants filled out a questionnaire on how well they understood the mtDNA evidence and their overall judgments of the case (e.g. verdict, witness credibility, scientific evidence strength). They filled this questionnaire out again after a 45-minute deliberation. Measures We measured Attitudes Toward Science (ATS) with indices of scientific promise and scientific reservations (Hans et al., 2011; originally developed by National Science Board, 2004; 2006). We used Drummond and Fischhoff’s (2015) Scientific Reasoning Scale (SRS) to measure scientific reasoning skills. Weller et al.’s (2012) Numeracy Scale (WNS) measured proficiency in reasoning with quantitative information. The NFC-Short Form (Cacioppo et al., 1984) measured need for cognition. We developed a 20-item multiple-choice comprehension test for the mtDNA scientific information in the cases (modeled on Hans et al., 2011, and McAuliff et al., 2009). Participants were shown 20 statements related to DNA evidence and asked whether these statements were True or False. The test was then scored out of 20 points. Results For this project, we measured calibration to the scientific evidence in a few different ways. We are building a full model with these various operationalizations to be presented at APLS, but focus only on one of the calibration DVs (i.e., objective understanding of the mtDNA evidence) in the current proposal. We conducted a general linear model with total score on the mtDNA understanding measure as the DV and quality of scientific evidence condition, decision aid condition, and the four individual difference measures (i.e., NFC, ATS, WNS, and SRS) as predictors. Contrary to our main hypotheses, neither evidence quality nor decision aid condition affected juror understanding. However, the individual difference variables did: we found significant main effects for Scientific Reasoning Skills, F(1, 427) = 16.03, p <.001, np2 = .04, Weller Numeracy Scale, F(1, 427) = 15.19, p <.001, np2 = .03, and Need for Cognition, F(1, 427) = 16.80, p <.001, np2 = .04, such that those who scored higher on these measures displayed better understanding of the scientific evidence. In addition there was a significant interaction of evidence quality condition and scores on the Weller’s Numeracy Scale, F(1, 427) = 4.10, p = .04, np2 = .01. Further results will be discussed. Discussion These data suggest jurors are not sensitive to differences in the quality of scientific mtDNA evidence, and also that our attempt at helping sensitize them with Fuzzy Trace Theory-inspired aids did not improve calibration. Individual scientific reasoning abilities and general cognition styles were better predictors of understanding this scientific information. These results suggest a need for further exploration of approaches to help jurors differentiate between high and low quality evidence. Note: The 3rd author was supported by an AP-LS AP Award for her role in this research. Learning Objective: Participants will be able to describe how individual differences in scientific reasoning skills help jurors understand complex scientific evidence. 

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4. Money matters (especially if you are good at math): Numeracy, verbal intelligence, education, and income in satisfaction judgments

   https://doi.org/10.1371/journal.pone.0259331  

   Bjälkebring, Pär ; Peters, Ellen ( November 2021 , PLOS ONE)

   Luciano, Michelle (Ed.)

   Objective numeracy, the ability to understand and use mathematical concepts, has been related to superior decisions and life outcomes. Unknown is whether it relates to greater satisfaction in life. We investigated numeracy’s relations with income satisfaction and overall life satisfaction in a diverse sample of 5,525 American adults. First, more numerate individuals had higher incomes; for every one point higher on the eight-item numeracy test, individuals reported $4,062 more in annual income, controlling for education and verbal intelligence. Combined, numeracy, education, and verbal intelligence explained 25% of the variance in income while Big-5 personality traits explained less than 4%. Further, the higher incomes associated with greater numeracy were related to more positive life evaluations (income and life satisfaction). Second, extant research also has indicated that the highly numerate compare numbers more than the less numerate. Consistent with numeracy-related income comparisons, numeracy moderated the relation between income and life evaluations, meaning that the same income was valued differently by those better and worse at math. Specifically, among those with lower incomes, the highly numerate were less satisfied than the less numerate; this effect reversed among those with higher incomes as if the highly numerate were aware of and made comparisons to others’ incomes. Further, no clear income satiation point was seen among those highest in numeracy, and satiation among the least numerate appeared to occur at a point below $50,000. Third, both education and verbal intelligence related to income evaluations in similar ways, and numeracy’s relations held when controlling for these other relations. Although causal claims cannot be made from cross-sectional data, these novel results indicate that numeracy may be an important factor underlying life evaluations and especially for evaluations concerning numbers such as incomes. Finally, this study adds to our understanding of education and intelligence effects in life satisfaction and happiness. 

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5. The Effects of Gist Information and Scientific Quality on Damages in a Civil Trial

   Dellapaolera, K.S. ( March 2020 , Annual Conference of the American Psychology-Law Society.)

   Abstract: 100 words Jurors are increasingly exposed to scientific information in the courtroom. To determine whether providing jurors with gist information would assist in their ability to make well-informed decisions, the present experiment utilized a Fuzzy Trace Theory-inspired intervention and tested it against traditional legal safeguards (i.e., judge instructions) by varying the scientific quality of the evidence. The results indicate that jurors who viewed high quality evidence rated the scientific evidence significantly higher than those who viewed low quality evidence, but were unable to moderate the credibility of the expert witness and apply damages appropriately resulting in poor calibration. Summary: <1000 words Jurors and juries are increasingly exposed to scientific information in the courtroom and it remains unclear when they will base their decisions on a reasonable understanding of the relevant scientific information. Without such knowledge, the ability of jurors and juries to make well-informed decisions may be at risk, increasing chances of unjust outcomes (e.g., false convictions in criminal cases). Therefore, there is a critical need to understand conditions that affect jurors’ and juries’ sensitivity to the qualities of scientific information and to identify safeguards that can assist with scientific calibration in the courtroom. The current project addresses these issues with an ecologically valid experimental paradigm, making it possible to assess causal effects of evidence quality and safeguards as well as the role of a host of individual difference variables that may affect perceptions of testimony by scientific experts as well as liability in a civil case. Our main goal was to develop a simple, theoretically grounded tool to enable triers of fact (individual jurors) with a range of scientific reasoning abilities to appropriately weigh scientific evidence in court. We did so by testing a Fuzzy Trace Theory-inspired intervention in court, and testing it against traditional legal safeguards. Appropriate use of scientific evidence reflects good calibration – which we define as being influenced more by strong scientific information than by weak scientific information. Inappropriate use reflects poor calibration – defined as relative insensitivity to the strength of scientific information. Fuzzy Trace Theory (Reyna & Brainerd, 1995) predicts that techniques for improving calibration can come from presentation of easy-to-interpret, bottom-line “gist” of the information. Our central hypothesis was that laypeople’s appropriate use of scientific information would be moderated both by external situational conditions (e.g., quality of the scientific information itself, a decision aid designed to convey clearly the “gist” of the information) and individual differences among people (e.g., scientific reasoning skills, cognitive reflection tendencies, numeracy, need for cognition, attitudes toward and trust in science). Identifying factors that promote jurors’ appropriate understanding of and reliance on scientific information will contribute to general theories of reasoning based on scientific evidence, while also providing an evidence-based framework for improving the courts’ use of scientific information. All hypotheses were preregistered on the Open Science Framework. Method Participants completed six questionnaires (counterbalanced): Need for Cognition Scale (NCS; 18 items), Cognitive Reflection Test (CRT; 7 items), Abbreviated Numeracy Scale (ABS; 6 items), Scientific Reasoning Scale (SRS; 11 items), Trust in Science (TIS; 29 items), and Attitudes towards Science (ATS; 7 items). Participants then viewed a video depicting a civil trial in which the defendant sought damages from the plaintiff for injuries caused by a fall. The defendant (bar patron) alleged that the plaintiff (bartender) pushed him, causing him to fall and hit his head on the hard floor. Participants were informed at the outset that the defendant was liable; therefore, their task was to determine if the plaintiff should be compensated. Participants were randomly assigned to 1 of 6 experimental conditions: 2 (quality of scientific evidence: high vs. low) x 3 (safeguard to improve calibration: gist information, no-gist information [control], jury instructions). An expert witness (neuroscientist) hired by the court testified regarding the scientific strength of fMRI data (high [90 to 10 signal-to-noise ratio] vs. low [50 to 50 signal-to-noise ratio]) and gist or no-gist information both verbally (i.e., fairly high/about average) and visually (i.e., a graph). After viewing the video, participants were asked if they would like to award damages. If they indicated yes, they were asked to enter a dollar amount. Participants then completed the Positive and Negative Affect Schedule-Modified Short Form (PANAS-MSF; 16 items), expert Witness Credibility Scale (WCS; 20 items), Witness Credibility and Influence on damages for each witness, manipulation check questions, Understanding Scientific Testimony (UST; 10 items), and 3 additional measures were collected, but are beyond the scope of the current investigation. Finally, participants completed demographic questions, including questions about their scientific background and experience. The study was completed via Qualtrics, with participation from students (online vs. in-lab), MTurkers, and non-student community members. After removing those who failed attention check questions, 469 participants remained (243 men, 224 women, 2 did not specify gender) from a variety of racial and ethnic backgrounds (70.2% White, non-Hispanic). Results and Discussion There were three primary outcomes: quality of the scientific evidence, expert credibility (WCS), and damages. During initial analyses, each dependent variable was submitted to a separate 3 Gist Safeguard (safeguard, no safeguard, judge instructions) x 2 Scientific Quality (high, low) Analysis of Variance (ANOVA). Consistent with hypotheses, there was a significant main effect of scientific quality on strength of evidence, F(1, 463)=5.099, p=.024; participants who viewed the high quality evidence rated the scientific evidence significantly higher (M= 7.44) than those who viewed the low quality evidence (M=7.06). There were no significant main effects or interactions for witness credibility, indicating that the expert that provided scientific testimony was seen as equally credible regardless of scientific quality or gist safeguard. Finally, for damages, consistent with hypotheses, there was a marginally significant interaction between Gist Safeguard and Scientific Quality, F(2, 273)=2.916, p=.056. However, post hoc t-tests revealed significantly higher damages were awarded for low (M=11.50) versus high (M=10.51) scientific quality evidence F(1, 273)=3.955, p=.048 in the no gist with judge instructions safeguard condition, which was contrary to hypotheses. The data suggest that the judge instructions alone are reversing the pattern, though nonsignificant, those who received the no gist without judge instructions safeguard awarded higher damages in the high (M=11.34) versus low (M=10.84) scientific quality evidence conditions F(1, 273)=1.059, p=.30. Together, these provide promising initial results indicating that participants were able to effectively differentiate between high and low scientific quality of evidence, though inappropriately utilized the scientific evidence through their inability to discern expert credibility and apply damages, resulting in poor calibration. These results will provide the basis for more sophisticated analyses including higher order interactions with individual differences (e.g., need for cognition) as well as tests of mediation using path analyses. [References omitted but available by request] Learning Objective: Participants will be able to determine whether providing jurors with gist information would assist in their ability to award damages in a civil trial. 

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