Using simulation approaches when conducting randomization tests for comparing two groups in the context of experimental studies has been promoted as a beneficial approach for supporting student learning of statistical inference. Many researchers have suggested that the data production process in simulations for the randomization test intuitively connects to the random assignment used in the original study design, thus supporting students' understanding of the logic of inference. Yet, there is little empirical research on how students initially think about the concepts and processes underlying the randomization test as they engage in constructing and using probability models to solve a problem. This work makes a contribution by deepening our understanding of students' reasoning about randomization tests by focusing on a group of three students as they create and use a TinkerPlots model to simulate data and use this data to make a statistical inference. This work adopts a narrative lens through which to view these students' reasoning and modeling activity. We compare and contrast the narratives we constructed for these students along with a narrative we constructed for a statistician. We discuss possible implications for teaching randomization tests for comparing two groups using a modeling and simulation approach.

To sustain the higher education industry and address U.S. economic downturns, researchers must prioritize research on undergraduates aged 24 or above - contemporary students. This empirical study finds contemporary students have lower chances of attaining degrees-any degrees-than their younger peers. Using nationally representative U.S. data from the Beginning Postsecondary Longitudinal Study, our interaction models reveal that the penalty experienced by contemporary-age students is more significant at four-year colleges where older students are less than half as likely to attain degrees as their younger peers. Transferring also distinctly and positively enhances the predicted probability of degree attainment for contemporary-age students (p < .000), reducing the age penalty. Our findings underscore the significance of prioritizing contemporary students in research and practice to increase degree attainment. We close with implications for practice, policy, and research.

Integrating situated expectancy-value and family systems theories, the current study tested the extent to which Latinx adolescents' 9th-grade school-related science conversations with parents and older siblings/cousins positively predicted their 10th-grade science ability self-concepts and task values. We also tested whether these links were moderated by who primarily initiated the conversations (i.e., adolescents, family members, or both). We used two-wave, multi-reporter survey data from 104 Latinx families, consisting of triads of parents, older siblings/cousins, and adolescents (89% Mexican-descent, 40% female; M-age = 14.53 years). Partially supporting our hypotheses, parent-adolescent school-related science conversations predicted adolescents' 10th-grade science ability self-concepts. Moreover, the links between parent-adolescent conversations and science ability self-concepts and task values were positive and significant when parents more frequently initiated conversations than adolescents. Similar but weaker associations were found for sibling/cousin-adolescent school-related science conversations. These findings underscore the motivational benefits of family members initiating school-related science conversations with Latinx adolescents.

There is a need for a more robust conceptualization of engagement in mathematics education research. Investigating how teachers describe engagement can provide insight into relationships between purposes of engagement and dimensions of engagement. In this exploratory study, we examined how 28 secondary mathematics teachers in two states in the USA talked about their students' engagement. During interviews, we asked teachers to provide their definitions for engagement, describe their teaching strategies for engaging students, and describe their observations of engagement during a video clip from their own classroom. We interpreted teachers' talk to identify how they described the nature of mathematics engagement (dimensions such as behavioral, cognitive, affective, and/or social engagement) and purposes of engagement (engagement in learning or in schooling [Harris, 2011]). When teachers described the purpose of engagement as engagement in learning, they also tended to describe the nature of engagement with cognitive and social dimensions and with multiple dimensions of engagement.

Objective: To determine whether rates of online racial discrimination changed over the course of 2020 and their longitudinal effects on Black youths' mental health. Method: This longitudinal study collected 18,454 daily assessments from a nationally representative sample of 602 Black and White adolescents in the United States (58% Black, 42% White; mean age = 15.09 years, SD = 1.56 years) across 58 days during the heightened racial tensions between March and November 2020. Results: Black youths experienced increases in online racial discrimination, and these increases were not fully explained by time spent online or by general cybervictimization experiences. Online racial discrimination predicted poorer same-day and next-day mental health among Black youths but not among White youths. Black youths' mental health did not predict their online racial discrimination experiences. Conclusion: Online racial discrimination has implications for shaping mental health disparities that disadvantage Black youths relative to their White peers. Programs can be implemented to decrease online hate crimes, and health providers (eg, pediatricians, psychiatrists) should develop procedures that mitigate the negative mental health effects following online racial discrimination experiences.

There are consistent correlations between mathematics achievement, attitudes, and anxiety, but the longitudinal relations among these constructs are not well understood nor are sex differences in these relations. To address this gap, mathematics achievement, attitudes, and anxiety were longitudinally assessed for 342 (169 boys) adolescents from seventh to ninth grade, inclusive, and latent growth curve models (LGCM) were used to assess the relations among these traits and developmental change in them. Spatial abilities (seventh and eighth grades) and trait anxiety (eighth and ninth grades) were also assessed and used to control for sex differences in these traits. Overall, boys had stronger spatial abilities and more positive mathematics attitudes and were less anxious than girls, but there were no sex differences in mathematics achievement. Across grades, mathematics achievement improved, attitudes became less positive, and anxiety increased for both boys and girls. Higher than average cross-grade growth in mathematics achievement mitigated boys' developmental declines in mathematics attitudes and increases in anxiety. Girls with strong spatial abilities had lower mathematics anxiety, but girls overall maintained higher mathematics anxiety and less positive mathematics attitudes relative to boys, even when they showed strong cross-grade gains in mathematics achievement. The study demonstrated that longitudinal gains in mathematics are associated with cross-grade changes in attitudes and anxiety but with several different developmental patterns for boys and girls.

Number talks offer one way for beginning teachers to engage in ambitious instruction (Lampert et al., 2010) that fosters students' conceptual understanding. This paper explores: (1) features of the number talk routine and (2) how beginning teachers' enactment of number talks are aligned with ambitious instruction. The authors utilized Cazdan's (2001) sequential and selectional dimensions to systematically analyze videos of 17 number talks enacted by seven beginning teachers. Findings indicate that the number talk routine consisted of introducing, collecting, idea sharing, and closing phases. Additionally, using the M-Scan instrument (Berry et al., 2013) to measure whether lessons were ambitious, the authors found that more ambitious lessons included number talks where teachers supported multiple students to engage in another student's strategy rathter than simply shaing individual strategies. We discuss several important implications for mathematics teacher education and research on ambitious mathematics instruction.

Teachers' mathematical knowledge has important consequences for the quality of the learning environment they create for their students to learn mathematics. Yet relatively little is known about how teachers reason proportionally, despite the fact that proportional reasoning is foundational for several mathematics concepts and that ratios and proportional relationships constitute a major component of the middle school mathematics curriculum. In this study, we investigated how teachers reasoned proportionally on a nonroutine ratio task and the extent to which their proportional reasoning was able to predict their overall understanding of the relevant concepts: ratios and proportional relationships. Using data collected from 238 US mathematics teachers, we found that teachers' proportional reasoning could be grouped into four categories: incorrect, additive, relative, and proportional reasoning. Our results also indicated that teachers' overall knowledge of ratios and proportional relationships aligned with the way they reasoned proportionally, meaning that teachers who used incorrect reasoning on a separate task received the lowest scores on average on the ratios and proportional relationships measure, whereas those who reasoned proportionally had the highest mean scores on average. Implications of the study include the need to shift attention to the way teachers reason in relation to the two elements of proportional reasoning (covariance and invariance) to capture the nuances in their understanding of ratios and proportional relationships.

Teachers' knowledge of students' mathematical thinking is a growing area of research in mathematics education. The literature has reported plentiful evidence of the interplays between teachers' mathematical knowledge and their knowledge of students' mathematical thinking. The present study builds on this body of work to explain how such interplays occur. Over a semester, I worked in partnership with a secondary school mathematics teacher on cycles of task design, interactions with a student, and in-depth reflection on the student's thinking about linear programming. Adopting and extending Piagetian constructs of assimilation and accommodation, I describe several key mental processes that illuminate the teacher's learning of mathematics and of the student's mathematical thinking. I conclude with a discussion of the study's empirical and theoretical contributions to understanding teachers' mathematical learning in relation to student thinking.

Math anxiety (MA) and math performance are generally negatively correlated (Barroso et al., 2021; Namkung et al., 2019). However, the mechanisms underlying this negative association remain unclear. According to the attentional control theory (ACT; Eysenck et al., 2007), anxious individuals experience impaired attentional control during problem solving, which compromises their performance on cognitive tasks. In a sample of 168 elementary and middle school students, the current study used an eye-tracking approach to investigate whether math-anxious students exhibit deficits in their attentional control during a math problem solving task and whether such attentional control deficits account for the negative association between MA and performance on this math task. Consistent with the ACT, we found that students with higher MA were more likely to engage attention to both task-relevant and task-irrelevant distractors during problem solving, and their enhanced attention to these distractors was associated with their impaired performance on the math task. These findings suggest that the MA-related math performance deficit is partly mediated by impaired attentional control, which is indicated by the maladaptive attentional bias toward distracting information during math problem solving.