Theories of quantitative reasoning have taken precedence as an analytical tool to interpret and describe students' mathematical reasonings, especially as students engage in mathematical modeling tasks. These theories are particularly useful to describe how students construct new quantities as they model. However, while using this lens to analyze Differential Equations students' construction of mathematical models of dynamic situations, we found cases of quantity construction that were not fully characterized by extant concepts. In this theory-building paper, we present five examples of such cases. Additionally, we introduce a new construct-quantitative operators-as an extended analytical tool to characterize those cases. Our findings suggest that quantitative operators may be viewed as an extension for theories of quantity construction and complementary to symbolic forms, when localizing theories of quantity construction for mathematical modeling, especially at the undergraduate differential equation level.

The Conscientiousness x Interest Compensation (CONIC) model (Trautwein et al., 2019) assumes that the two constructs conscientiousness and interest can (partly) compensate for each other in predicting academic effort and achievement. We extend previous work by testing the CONIC model in two independent U.S. samples from different age groups (high school sample: N = 1,246, Mage = 14.86 years; college sample: N = 581, Mage = 19.83 years). We also assessed whether the compensatory relations occur when grit is substituted for conscientiousness and students' overall task value or utility value for interest. We preregistered the study and tested the various models for both science and math effort as well as achievement, using latent variable regression analyses. Overall, we found some support for the CONIC model in the U.S. samples. There was also some support for the extensions of the model to the other constructs; however, the predictive links were not as strong.

Racial stereotypes are salient to Black adolescents and to the academic domain of mathematics; however, few studies have examined the socio-cognitive mechanisms through which racial stereotypes impact math achievement. This 2-year longitudinal study (N = 790 Grade 6, 8, and 10 students during Year 1; 50.7% girls and 49.3% boys) investigated (a) the extent to which the endorsement of positively and negatively biased racial stereotypes predicted Black adolescents' math performance through their cognitive engagement and ability mindset and (b) whether gender and ethnic-racial identity moderated these links. Results suggested that endorsement of negatively biased stereotypes was associated with diminished cognitive engagement and lower math scores across 2 years (p < .05). Additionally, adolescents' ethnic-racial identity commitment moderated the negative links between stereotype endorsement and math cognitive engagement in Year 2 (p < .05). When considering the mediating role of math ability mindsets, the endorsement of both positively and negatively biased racial stereotypes operated on math performance via its links to stronger fixed ability mindset beliefs in both years (p < .05). Gender also moderated the effects of racial stereotype endorsement on math mindset beliefs in Year 1 (p < .01). This study's findings advance the field's understanding of the psychosocial mechanisms through which racial stereotypes operate, thus enabling educators to develop tailored practices that facilitate equitable access to math learning opportunities.

Crystallized intelligence (Gc)-knowledge acquired through education and experience-supports creativity. Yet whether Gc contributes to creativity beyond providing access to more knowledge, remains unclear. We explore the role of a flexible semantic memory network structure as a potential shared mechanism of Gc and creativity. Across two studies (N = 506 and N = 161) participants completed Gc tests of vocabulary knowledge and were divided into low, medium, and high Gc groups. They also completed two alternate uses task, to assess verbal creativity, and a semantic fluency task, to estimate semantic memory networks. Across both studies, the semantic memory network structure of the high Gc group was more flexible-less structured, more clustered, and more interconnected-than that of the low Gc group. The high Gc group also outperformed the low Gc group on the creativity tasks. Our results suggest that flexible access to semantic memory supports both verbal intelligence and creativity. Educational relevance statement: Crystallized intelligence (Gc)-knowledge acquired through education and experience-supports creativity, yet whether Gc contributes to creativity beyond providing access to more knowledge (semantic memory), remains unclear. In this two-part study, we find that individuals with higher Gc tended to have a more flexible semantic memory structure, which in turn supported greater verbal creativity. This finding suggests that building students' vocabulary knowledge and verbal skills may not just expand their knowledge base, but also increase creativity through enabling more flexible access to that knowledge. If supported by further research, this could mean educational interventions targeting growth in Gc and semantic flexibility may foster students' creative capacities beyond just improving content mastery. Overall, this research highlights the interplay between building domain knowledge and cultivating creative thinking, suggesting educators should aim to develop both abilities in tandem rather than treating them separately.

We investigated whether and to what extent U.S. kindergarten children ' s executive functions, oral vocabularies, and early literacy skills mediate relations between their sociodemographic background characteristics (i.e., family socioeconomic status, race or ethnicity, biological sex) and stable between-individual levels of mathematics and science achievement across kindergarten to 4th grade. We did so by fitting a random intercept crosslagged panel model to nationally representative data ( N = 9081, M age = 92.4 months). Cross-lagged relations were relatively stronger from mathematics to science achievement than from science to mathematics achievement. These relations were weaker in earlier grades and stronger in later grades. Autoregressive coefficients were stronger for mathematics than for science and much stronger for each domain during the upper elementary grades. Children ' s working memory abilities and early literacy skills were the strongest mediators of the relations between their socioeconomic backgrounds and over-time mathematics or science achievement. Educational relevance statement: We observed cross-lagged relations between mathematics and science achievement, particularly during the upper elementary grades and from mathematics to science achievement. We also observed that kindergarten children ' s executive functions, oral vocabularies, and early literacy skills mediate relations between their sociodemographic background characteristics and mathematics and science achievement. Results suggest that multi-component interventions designed to facilitate learning of both mathematics and science skills might be especially effective if introduced by the upper elementary grades. These multi-component interventions might also be designed to support children ' s executive functions, oral vocabularies, and early literacy skills instead of only teaching mathematics and science skills. Our findings add to the limited existing work examining over-time relations between mathematics and science achievement and the extent to which executive functions, oral vocabularies, and early literacy skills help to explain sociodemographic gaps in elementary schoolchildren ' s mathematics and science achievement.

Primarily studying executive functions of children from low-income backgrounds in comparison to more affluent peers can promote a deficit perspective that they are uniformly lacking in skills. We used latent profile analysis to investigate patterns of heterogeneity in executive functions in a sample of 232 preschoolers (Mage = 52.15 months, SDage = 6.70 months; 50 % female; 34 % Latine, 31 % White, 10 % Asian, 7 % Black, 14 % Multiracial, and 4 % other) from low-income backgrounds in the Midwestern United States. Five executive functions (working memory, inhibitory control, cognitive flexibility, complex planning, and behavioral self-regulation) were used as indicators. We found evidence of four latent profiles including three profiles with consistently below average, above average, and high executive functions. A fourth discordant profile had high executive functions but below average behavioral self-regulation. We also estimated relations among executive function profiles and concurrent numeracy, vocabulary, and geometry; patterns of relations differed by pre-academic skill. Educational relevance and implications: Primarily studying executive functions of children from low-income backgrounds in comparison to more affluent peers can promote a deficit perspective that they are uniformly lacking in skills. Using a statistical method that allowed us to explore sub-groups of children based on their executive function skills, we found evidence of four distinct sub-groups in a sample of preschoolers from lowincome backgrounds. One sub-group scored high in executive functions but lower in incorporating them into gross motor behavior, which may be particularly important for early math. Results disrupt deficit perspectives and point to future areas of research for designing targeted and differentiated instruction.

While research has shown that students benefit from student-centered pedagogies, few studies have considered the benefits of this pedagogical approach for educators as they learn through teaching. In response to this need, we analyzed interviews, lesson plans, and video observations from five teachers in elementary schools across the United States who varyingly engaged student-centered and teacher-centered pedagogies. Our analyses revealed that the participating teachers developed a wide breadth of teacher knowledge regardless of their pedagogical approach. However, the teachers who employed student-centered teaching reported more pedagogical content knowledge gains for themselves than the teachers who used direct teaching.

Fostering creativity is vital for tackling 21st-century challenges, and education plays a key role in nurturing this skill. According to the associative theory, creativity involves connecting distant concepts in semantic memory. Here, we explore how semantic memory changes following an educational intervention intended to promote creativity. Specifically, we examine how a scientific education curriculum-Scientific Creativity in Practice (SCIP) program-impacts the semantic memory networks of 10-18-year-old students in a chemistry class (n = 176). Students in an Intervention group who received the SCIP intervention, and a Control group who did not, completed creative thinking tests, as well as verbal fluency tasks to estimate semantic networks in science-specific (chemistry) and domain-general (animal) categories. Results showed that the SCIP intervention enhanced performance on one test of scientific creative thinking but showed no significant difference on another. Using network science methods, we observed increased interconnectedness in both science-specific and domain-general categories, with lower path distances between concepts and reduced modularity. These traits define a 'small-world' network, balancing connections between closely related and remote concepts. Notably, the chemistry semantic network showed substantially more reorganization, consistent with the chemistry contents of the SCIP intervention. The findings suggest that semantic memory reorganization may be a cognitive mechanism underlying successful creativity interventions in science education.

Drawing on the situated expectancy-value, dimensional comparison theories, and the intersectionality approach, this article examined the changes in adolescents' math and science motivational beliefs, the parental and college correlates of those beliefs, and the differences at the intersection of gender and college generation status (i.e., female and male first- and continuing-generation college students). Findings based on the nationally representative high-school longitudinal study data (N = 12,070; M-age = 14 years; 54% female students; 28% first-generation college students; and 14% Latinx, 9% Black, 10% Asian, and 57% White) suggest that although adolescents' math and science ability self-concepts declined during high school, their science interest remained stable, and their math and science utility values increased. Adolescents' motivational beliefs in ninth grade and the changes from ninth to 11th grade positively predicted whether they declared a science, technology, engineering, and mathematics (STEM) college major. Parents' ninth-grade STEM support was more consistently associated with adolescents' concurrent beliefs compared to the changes in their beliefs. Finally, we found that female first-generation college students, who were more likely to be Latinx and Black students, tended to have lower math and science motivational beliefs, received less parental STEM support, and were less likely to choose a STEM major than their peers. The findings of this study indicate adolescents' math and science motivational development in high school matters for their college majors and that certain understudied groups, including female first-generation college students, may experience acute marginalization in STEM and warrant further attention.