Multimedia hints are widely used in educational materials to support conceptual learning, yet their comparative effectiveness across modalities remains underexplored. Prior studies suggest that graphical hints can enhance learners' performance on physics problems, but it is unclear how they interact with other modalities such as text and voice. Understanding these interactions is essential for designing effective instructional tools. In this study, we investigated the effects of graphical, typographic, and vocal hints, individually and in combination, on students' problem-solving performance. A total of 162 students from a conceptual physics course participated in individual interviews and solved four sets of isomorphic problems. Each set included an initial problem (pretest), six training problems, a near transfer problem, and a far transfer problem. We employed a 2 × 2 × 2 between-subject quasi-experimental design to examine the effects of the three hint modalities. Results from paired-sample t-tests showed significant performance gains from pretest to both near and far transfer tasks, indicating that solving isomorphic problems with hints promotes learning. Among modalities, graphical hints led to better training performance than typographic or vocal hints. Notably, combining typographic and vocal hints produced worse outcomes than using either modality alone, contradicting the auditory superiority effect and suggesting potential cognitive overload. These findings highlight the effectiveness of visual support and caution against indiscriminate integration of multiple hint modalities. We provide evidence-based recommendations for designing multimedia instructional materials that optimize cognitive processing and support conceptual problem solving in physics.

Parents are considered a major resource in children's numeracy development. The relative role of cognitive and motivational parenting practices, however, is unclear given that the two types of practices have largely been studied in isolation. The current study simultaneously estimated the contributions of several cognitive and motivational parenting practices hypothesized to be important, but which may have overlapping effects. To capture parents' cognitive practices, the level and structure (i.e., prompts vs. statements) of 529 American parents' (80% mothers; 65% White, 20% Black; 33% less than a bachelor's degree) numeracy talk was coded during a challenging numeracy activity. Parents' motivational practices were assessed by coding their autonomy support and control in the activity. Children's (M-age = 7.5 years; 49% girls) engagement of numeracy strategies was also coded. Multilevel minute-to-minute modeling predicting children's engagement from both cognitive and motivational parenting practices indicated that parents' cognitive practices, particularly advanced prompts, predicted children's subsequent engagement of numeracy strategies, which were often advanced. Parents' motivational practices, as reflected in their autonomy support (vs. control), also foreshadowed children's engagement. These effects of the two types of practices were independent of one another. Taken together, the findings are consistent with the idea that cognitive and motivational parenting practices provide distinct resources that can benefit children's math learning.

A parent-directed intervention designed to foster growth-oriented mindsets about math was evaluated in a longitudinal randomized-control trial. Parents (N = 615; 61% White, 22% Black; 63% with at least a bachelor's degree) participated in the intervention or an active control condition in which they learned about the Common Core math curriculum. Parents reported on their math mindsets and parenting practices (e.g., autonomy-supportive math homework assistance) over 15-18 months; their young elementary school children's (M-age = 7.17 years; 50% girls) math adjustment (e.g., mindsets and achievement) was also assessed. The intervention (vs. control) led to sustained increases in parents' beliefs that math ability is malleable and math failure is beneficial for learning. The intervention, however, did not improve their math parenting practices or children's math adjustment relative to the control. Instead, there were generally improvements in math parenting practices and children's math adjustment over the course of the study regardless of condition, perhaps because the control condition provided parents with useful information about the Common Core math curriculum. Overall, the findings indicate that although the mindset intervention was effective in instilling stronger growth-oriented mindsets about math in parents, this did not translate into benefits for children's math learning over and above the active control condition.

UMBC) and an M.S. in Mechanical Engineering from the

Although the belief that ability can change, a growth mindset, has been identified as beneficial for motivation and challenge seeking, recent criticisms of mindset theory have argued that mindset is a weak predictor of achievement in some circumstances. Meanwhile, researchers have qualitatively described adults who agree with growth mindset, but do not behave as though they believe ability can change (e.g., praise children for their intelligence), suggesting they may hold a false growth mindset. In three studies with US adults (N = 294), undergraduate students (N = 214), and elementary school teachers (N = 132), we used cluster analyses to identify individuals with a false growth mindset. Mindset groups were identified based on participants' combinations of responses to the traditional mindset measure and two alternative mindset measures. Five groups were identified in each study: fixed mindset, moderate mindset, false growth mindset, effort mindset, and extreme flexibility mindset. The mindset groups differed in their perceived competence in math (Studies 1-3), preference for challenge (Study 1), challenge seeking on optional math problems and math value (Study 2), and beliefs that only some students can do math and math anxiety (Study 3). Findings suggest that holding an inconsistent set of beliefs, like a false growth mindset, might contribute to the disconnect between mindset theory and practice and that consistent responses across a variety of growth mindset measures may prove to be the most adaptive. We conclude with words of caution to the many researchers and educators who hope that growth mindset interventions can improve student outcomes.

This research examines whether prior research may not have detected cultural-specificity in the role of controlling and autonomy-supportive parenting in children's adjustment because of reliance on between-individual analyses. In two longitudinal studies (Ns = 825 and 934) of early adolescents, within-individual analyses were conducted to examine the reciprocal pathways between children's reports of parenting and their reports of their adjustment in the United States and China. Increments in controlling parenting predicted decrements in children's emotional and behavioral, but generally not academic, adjustment over time, with little evidence that this was stronger in the United States than in China. Decrements in children's emotional and behavioral, but generally not academic, adjustment predicted increments in controlling parenting over time similarly in the two countries. There were few overtime pathways involving autonomy-supportive parenting in either direction in either country.

This research examined how parents' math anxiety is associated with their controlling and autonomy-supportive involvement in children's math learning; the contribution of such involvement to children's math achievement was also evaluated. Parents (N = 562; 62% White, 21% Black; 65% with at least a bachelor's degree) of young elementary school children (M-age = 7.48 years; 50% girls) reported on their math anxiety as well as controlling and autonomy-supportive involvement in children's math learning; observations were also made. At the same time and a year later, children's math achievement was assessed. Parents with higher math anxiety were more controlling (in both parents' reports and the observations) and less autonomy supportive (only in the observations) with children who had poorer math achievement. Notably, controlling parenting (in both parents' reports and the observations) was most likely to predict lower math achievement a year later among such children. The findings suggest math-anxious parents are prone to using practices with children struggling in math that further undermine their math achievement, which can create an unconstructive cycle for children's math learning.

This research examined parents' involvement in children's math homework and activities. During 2017 to 2019, American parents (N = 483; 80% mothers; 67% white) of young elementary school children (M-age = 7.47 years; 50% girls) reported on their math helping self-efficacy; they also reported on their involvement in children's math homework and activities daily for 12 days. At this time and a year later, children's math motivation and achievement were assessed. Parents' involvement in homework (vs. activities) was more affectively negative (d = .34), particularly among parents low in self-efficacy (d = .23). The more affectively negative parents' involvement, particularly in homework, the poorer children's later math motivation and achievement (beta s = -.09 to .20).

A new parent-report measure was used to examine parents' person and process responses to children's math performance. Twice over a year from 2017 to 2020, American parents (N = 546; 80% mothers, 20% other caregivers; 62% white, 21% Black, 17% other) reported their responses and math beliefs; their children's (M-age = 7.48 years; 50% girls, 50% boys) math adjustment swas also assessed. Factor analyses indicated parents' person and process responses to children's math success and failure represent four distinct, albeit related, responses. Person (vs. process) responses were less common and less likely to accompany views of math ability as malleable and failure as constructive (|r|s = .16-.23). The more parents used person responses, the poorer children's later math adjustment (|beta|s = .06-.16).

This research examined parents' restriction of children's peer relationships in the United States and China. American and Chinese children (N = 934; M-age = 12.67 years) reported on their parents' peer restriction (e.g., limiting children's time with peers) and their behavioral and psychological adjustment 3 times over a year. Increments in parents' peer restriction predicted decrements in children's adjustment over time to a similar extent in the United States and China. However, decrements in children's adjustment predicted increments in parents' peer restriction over time to a greater extent in the United States (vs. China). Thus, it is possible that culture contributes to the socialization process involving parents' restriction of children's peer relationships but only via child-driven pathways.