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.

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/).

The acquisition of domain-specific number knowledge and domain-general cognitive processes, including working memory, have shown to contribute to math learning and achievement. Correlational work has emphasized a reciprocal relationship between these processes; however, little is known about their relative and causal contributions to math learning. Here, we test the individual and additive benefits of playing tablet-based games targeting domain-specific and domain-general skills to improve mathematical knowledge and working memory in a diverse population of kindergarten children (N = 235, 50 % female, 45 % Hispanic/Latino, 35 % African American/Black, 21 % White, 6 % biracial/mixed race, 51 % annual household income less than $30,000). Our results provide causal evidence for the reciprocal relations between numerical knowledge and working memory. Specifically, we found that playing a working memory game led to improvements in mathematical knowledge as compared to an active control and after taking into account baseline performance. Importantly, we also found that children who played both a working memory game and a numerical knowledge game showed the most pronounced and sustained benefits in mathematical knowledge, with benefits remaining present several weeks after intervention completion. Our findings illustrate the importance of targeting both domain-general and domain-specific skills in order to maximize the benefits of interventions to improve mathematical knowledge. Yet, given the inconsistent results across various studies, we argue that it is critical to further investigate underlying mechanisms and training features, as even subtle variations seem to dramatically affect training outcomes.

The distributive property plays a pivotal role in advancing students' understanding of multiplication, enabling the decomposition of problems and the acquisition of new facts. However, this property of multiplication is difficult for students to understand. We used two unique data sets to explore middle school students' use of the distributive property. Study 1 involved data from 1:1 structured interviews of students (N = 24) discussing worked examples and solving associated practice problems. We examined whether or not students used the distributive property to solve the problems and whether or not interviewers followed the recommended distributive property prompts or defaulted to more conventional methods. Despite exposure to worked examples using the distributive property and a protocol calling for attention to it, students and interviewers favored methods like PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction) or long multiplication. Study 2 used a data set with middle school students' (N = 131) item -level responses on Kirkland's (2022; doctoral dissertation, University of Notre Dame) Brief Assessment of Mature Number Sense along with several related measures of domain -general and domain -specific skills. We extracted problems involving the distributive property for analysis. Surprisingly, there was no evidence that students' use of the distributive property improved from sixth grade to eighth grade. However, both gradelevel mathematics achievement and cognitive reflection uniquely predicted the correct use of the distributive property. Results suggest that middle school students who exhibit stronger reflective thinking tend to perform better on distributive property problems. Findings highlight cognitive reflection as a potentially important construct involved in the understanding and use of the distributive property. (c) 2024 Elsevier Inc. All rights reserved.

The changes in adolescents' math motivational beliefs (i.e., expectancies for success, interest, and utility value) across Grades 9-11 and the associations between these changes and adolescents' experiences with socializers (i.e., perceived teacher unfairness and parent-adolescent discussions) were examined within each of the four largest racial/ethnic groups in the United States using the High School Longitudinal Study, a nationally representative data set (n = 19,010; 50% female; 9% Asian; 11% Black; 18% Latine; 62% White; M-age = 14.53 in Grade 9). Cross-tabulation analyses suggested that similar developmental trends emerged within each racial/ethnic group (which were tested separately). Many adolescents maintained their high or low expectancies, interest, and utility values across Grades 9-11. Some patterns varied by belief; for example, several adolescents switched from high to low interest by Grade 11, whereas several adolescents switched from low to high utility value. Parent-adolescent discussions predicted positive changes among Asian and Latine adolescents, whereas perceived teacher unfairness predicted negative changes among Black adolescents. The findings from the present study highlight the diverse developmental trends in adolescents' motivational beliefs and the potential role of socializers as sources of strength or challenge in their motivational belief development.

High-quality science assessments are multi-dimensional. They promote disciplinary practices, core ideas, cross-cutting concepts, and science sense-making. In this paper, we investigate the feasibility of using generative artificial intelligence (GenAI), specifically multimodal large language models (MLLMs), to annotate and provide improvement ideas for K-12 science assessments. The AI-generated annotations critique how the assessments align with the three dimensions of the Next Generation Science Standards (NGSS) and suggest ideas to elicit students' science sense-making. We outline our process with various prompting strategies: few-shot and zero-shot learning (prompting with and without examples), chain of thought (eliciting the MLLM's reasoning), and sampling strategies (outputting high or low level of randomness). Overall, the AI annotations can reason about the alignment between the assessments and NGSS dimensions and overlap with annotations from K-12 educators. Annotations generated with few-shot learning generally score higher overall and provide more details than zero-shot prompts. Further, interviews with science teachers reveal that the MLLM annotations can support teachers' reflection on instructional practices and assessment revision. We discuss the application of MLLMs to develop three-dimensional science assessments.

Integrating microintervention strategies and the bystander intervention model, we examined social cognitive predictors (i.e., moral disengagement, empathy, and self-efficacy) of the five steps of the bystander intervention model (i.e., Notice, Interpret, Accept, Know, and Act) to address racial microaggressions in a sample of 452 racially diverse college students. Data were collected using an online survey. Path analyses showed that moral disengagement was significantly and negatively related to each step of the model for White students, but for students of color, it was only significantly negatively associated with Act. Empathy was significantly and positively associated with Interpret, Accept, and Act for White students. For student of color, however, there was a significant and positive association solely between Empathy and Act. For both White students and students of color, self-efficacy was positively associated with Notice, Interpret, Accept, Know, and Act. Finally, race did not significantly moderate any relationships. Strengths, limitations, future directions for research, and implications of the study findings are discussed.

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.

Given math -related fields are still highly racialized and gendered (NCSES, 2021), this study assessed: 1) whether there were racial differences in adolescents' perceived math cost alongside expectancies and values and 2) the extent to which perceived math cost alongside expectancies and values explained yearly changes in achievement differences by race and gender. This study assessed 2,338 Black (39.4 %) and White (60.6 %) adolescents, roughly half girls (47.8 %), in the 6th to 12th grades (M = 14.71 years old, SD = 1.93, 61.7 % qualifying for free or reduced priced lunch). The results indicated that Black adolescents perceived higher costs to learning math than their White peers but value math in similar ways. Perceived math cost was the only motivational belief to explain achievement differences between Black and White girls but not boys after adjusting for socioeconomic status and grade level. In contrast, perceptions of ability beliefs explained achievement differences between Black boys and girls. These findings point to the importance of employing intersectional approaches to understand the relationship between math motivation and achievement.