Our longitudinal, mixed methods study explores the experiences of over five hundred youth in long-term mentored research experiences outside of school, paired with data on their reports of plans to pursue STEM. Our participants, youth from historically marginalized communities, represent the most promise for diversifying STEM: 81% are students of color, and almost half are multilingual. This paper shares an analysis of a crosssection of quantitative data collected from this large-scale study as well as qualitative data in the form of participant interviews. Drawing from our quantitative data, we find that in stark contrast to the opportunity gaps that youth like our participants encounter, participating in out of school research generates a 'yield' of opportunities to engage in science practices-significantly more than in school- and to contribute meaningfully to a science community of practice. Our qualitative data suggests that this 'opportunity yield' may also contribute to their continued pursuit of STEM. Taken together, these findings underscore the critical role that learning in outof-school mentored research settings can play for students revealing its important, complementary role in a STEM ecosystem.

The current study explored individual and gendered differences in Black students' motivation for learning mathematics using three key Situated Expectancy-Value Theory (SEVT) constructs (expectancies of success, in-terest, and importance). It also evaluated whether math motivational profiles in 6th grade or 10th grade pre-dicted math achievement and STEM career aspirations in 10th grade among Black students while controlling for prior math achievement. Black students (n = 408, 55% female) attending schools in a metropolitan area of Tennessee, USA and mostly from families surviving economic marginalization completed surveys and math achievement assessments across middle and high school. Latent Profile Analysis identified three profiles of math motivation in 6th grade, including a profile of high motivation across constructs, and Black girls were less likely to be in the high motivational profile than Black boys. Profile membership in 6th grade predicted 10th grade math achievement. In contrast, math motivation profiles in 6th grade did not predict STEM career aspirations in 10th grade. Parallel analyses for concurrent relations in 10th grade were similar, except that there were no gender differences in profile prevalence. Overall, findings suggest that SEVT is useful for understanding moti-vation and academic performance among Black students when a person-centered analytic approach is used, but more work is needed to expand the theory to understand the development of Black students' STEM career aspirations.

This study tested how prompting learners to compare their drawings to instructional visuals affects their perceived and actual performance. Undergraduates ( n = 116) created two drawings while studying a text on the human circulatory system. Then they made a series of retrospective and prospective judgments of their drawing performance and prospective judgments of their comprehension. In a subsequent restudy phase, students were randomly assigned to either compare their drawings to instructional visuals (compare group; n = 56) or to restudy the text and review their drawings without receiving instructional visuals (control group; n = 60), followed by a series of new judgments of drawing and comprehension. All students then completed drawing and comprehension post-tests. Results indicated that comparing one's drawings to instructional visuals caused students to become underconfident in the quality of their drawings (lower retrospective accuracy) and overconfident in their future drawing performance (lower prospective accuracy). Exploratory analyses indicated that the compare group tended to make surface -level (rather than conceptual) comparisons when processing the provided visuals, such as attending to the aesthetic style or conventions used in the instructional visuals. Furthermore, despite a strong link between drawing and comprehension performance, comparing drawings to instructional visuals did not significantly affect students' judgments of comprehension. These findings highlight potential drawbacks of comparing generative drawings to instructional visuals in learning by drawing.

The factors to which teachers attribute students’ successes and failures have important consequences for teachers’ instructional decisions as well as their expectations of students. Yet few, if any, experimental studies have been conducted to investigate the role that students’ race and gender play in how teachers make sense of students’ academic performance. In this exploratory experimental study, conducted with 413 mathematics teachers across the United States, we investigated the extent to which teachers attributed students’ performance disparities in mathematics to internal and external factors based on the students’ race and gender and explored the extent to which teachers’ beliefs and dispositions moderated their attributions. To do so, teachers were first given a collection of the student solutions with no gender or racial performance disparities. They were then randomly assigned to one of four conditions in which they were told that on this particular assessment: boys outperformed girls, girls outperformed boys, Black and Hispanic students outperformed White and Asian students, or that White and Asian students outperformed Black and Hispanic students. They were asked to report the reasons behind the disparities in math performance of these groups. We found that teachers attributed gender disparities in student performance to innate math ability, effort, and external social factors, whereas they attributed racial disparities in student performance to biological influences on intelligence, effort, external social factors or the assessment context. Teachers’ self-reported personal experience with racial discrimination moderated race differences in teacher attributions. © 2024 The Authors

Block construction is ubiquitous in early development, yet is surprisingly complex, involving stepby-step sequenced actions to create specific structures. Here, we use novel analytic methods to characterize these action sequences in detail, including which individual parts of the structure ('states') are built and how these structures are combined, creating a fully specified build path towards the final structure. We find that, like adults tested in a previous study, 4- to 8-year-olds build by creating a small subset of possible individual states and full build paths, and that they prioritize building layer-by-layer. The individual states and build paths that children produce are strikingly similar to those of adults, resulting in structures that are more stable than other possible (but not attested) states and paths. Our approach serves as a lens into the cognitive processes underlying block building and suggests that children's building is guided by significant cognitive constraints consistent with computational thinking.

The ability to communicate about exact number is critical to many modern human practices spanning science, industry, and politics. Although some early numeral systems used 1-to-1 correspondence (e.g., 'IIII' to represent 4), most systems provide compact representations via more arbitrary conventions (e.g., '7' and 'VII'). When people are unable to rely on conventional numerals, however, what strategies do they initially use to communicate number? Across three experiments, participants used pictures to communicate about visual arrays of objects containing 1-16 items, either by producing freehand drawings or combining sets of visual tokens. We analyzed how the pictures they produced varied as a function of communicative need (Experiment 1), spatial regularities in the arrays (Experiment 2), and visual properties of tokens (Experiment 3). In Experiment 1, we found that participants often expressed number in the form of 1-to-1 representations, but sometimes also exploited the configuration of sets. In Experiment 2, this strategy of using configural cues was exaggerated when sets were especially large, and when the cues were predictably correlated with number. Finally, in Experiment 3, participants readily adopted salient numerical features of objects (e.g., four-leaf clover) and generally combined them in a cumulative-additive manner. Taken together, these findings corroborate historical evidence that humans exploit correlates of number in the external environment - such as shape, configural cues, or 1-to-1 correspondence - as the basis for innovating more abstract number representations.

Time management is crucial for college students' academic success and learning of computer programming. Yet the changes of time management behaviors and their associations with learning outcomes are underexplored in online learning of programming. To address the gap, this study employed an intensive longitudinal approach to examine undergraduates' time management behaviors in an online programming problem system. Specifically, we analyzed weekly indicators of academic procrastination and spaced practice derived from programming traces. We applied dynamic structural equation modeling to examine the changes in these behaviors over time and their correlations with weekly quiz performance. Academic procrastination and selfselected spaced practice showed a significant upward trend over time, while incentivized spaced practice exhibited a significant downward trend. Moreover, students with prior programming experience showed a greater growth rate in spacing behaviors. At both within- and between -person levels, procrastination predicted quiz performance significantly and negatively, while self-selected spaced practice predicted quiz performance significantly and positively. In contrast, incentivized spaced practice predicted quiz performance positively at the within -person level but negatively at the between -person level. Additionally, quiz performance in the current week predicted subsequent time management behaviors significantly. These findings contribute to the understanding of procrastination and spaced practice in online programming learning and have implications for the design of scaffolding on time management. Furthermore, this study demonstrates the significance of combining intensive longitudinal approaches and action logs in examining the temporality of learning in online environments.

The approximate number system (ANS) is a hypothesized mechanism responsible for the representation and processing of numerical information in an imprecise fashion. According to the predominant theory, the ANS is essential in solving simple numerical tasks such as comparing which of two quantities is numerically larger, and some research has indicated that individual differences in its acuity influence higher-level mathematical performance. Because of this farreaching role of the ANS, it is essential to assess its acuity with measures that are reliable, and valid. The present work reviews and synthesizes many of the methodological problems that are relevant for measuring ANS acuity in young children. We discuss issues related to task comprehension, the role of non-numerical perceptual properties of the stimuli, the role of inhibition, and the appropriateness and reliability of the ANS acuity indices. Recommendations and open questions are summarized.

Children's performance on the number line estimation task, often measured by the percentage of absolute error, predicts their later mathematics achievement. This task may also reveal (a) children's ordinal understanding of the target numbers in relation to each other and the benchmarks (e.g., endpoints, midpoint) and (b) the ordinal skills that are a necessary precursor to children's ability to understand the interval nature of a number line as measured by percentage of absolute error. Using data from 104 U.S. kindergartners, we measured whether children's estimates were correctly sequenced across trials and correctly positioned relative to given benchmarks within trials at two time points. For both time points, we found that each ordinal error measure revealed a distinct pattern of data distribution, providing opportunities to tap into different aspects of children's ordinal understanding. Furthermore, children who made fewer ordinal errors scored higher on the Test of Early Mathematics Ability and showed greater improvement on their interval understanding of numbers as reflected by a larger reduction of percentage of absolute error from Time 1 to Time 2. The findings suggest that our number line measures reveal individual differences in children's ordinal understanding of numbers, and that such understanding may be a precursor to their interval understanding and later mathematics performance. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY -NC -ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).