Prior research has shown that the home learning environment (HLE) is critical in the development of spatial skills and that various parental beliefs influence the HLE. However, a comprehensive analysis of the impact of different parental beliefs on the spatial HLE remains lacking, leaving unanswered questions about which specific parental beliefs are most influential and whether inducing a growth mindset can enhance the spatial HLE. To address these gaps, we conducted an online study with parents of 3- to 5-year-olds. We found that parents' growth mindset about their children's ability strongly predicted the spatial HLE after controlling for parents' motivational beliefs about their children, beliefs about their own ability, children's age, children's gender, and family SES. Further, reading an article about growth mindset led parents to choose more challenging spatial learning activities for their children. These findings highlight the critical role of parents' growth mindset in the spatial HLE. Crucially, these findings demonstrate that general growth mindset messages without specific suggestions for parental practices can influence parental behavior intentions. Further, these effects were also observed in the control domain of literacy, underscoring the broad relevance of the growth mindset in the HLE.

Research focusing on the home mathematics environment has shown mixed results across age groups. Using data from a large online survey, we explored parents' perceptions of the age appropriateness of home mathematics activities for their children. Children's ages ranged from one to 6 years old (N = 958). Activities spanned multiple domains of early mathematics including numeracy, geometry, patterning, spatial, and measurement domains. Descriptive statistics show there are clear developmental shifts in the appropriateness ratings for activities within and across these domains. Findings provide insight for future implications on the measurement of the home mathematics environment, as well as future research on age differences in the home mathematics environment.

Learning sciences are embracing the significant role technologies can play to better detect, diagnose, and act upon self-regulated learning (SRL). The field of SRL is challenged with the measurement of SRL processes to advance our understanding of how multimodal data can unobtrusively capture learners' cognitive, metacognitive, affective, and motivational states over time, tasks, domains, and contexts. This paper introduces a self-regulated learning processes, multimodal data, and analysis (SMA) grid and maps joint and individual research of the authors (63 papers) over the last five years onto the grid. This shows how multimodal data streams were used to investigate SRL processes. The two-dimensional space on the SMA grid is helpful for visualizing the relations and possible combinations between the data streams and how the measurement of SRL processes. This overview serves as an analytical introduction to the current special issue “Advancing SRL Research with Artificial Intelligence (AI)” and we encourage to position new research and unexplored frontiers. We emphasize the need for intensive and strategic collaboration to accelerate progress using new interdisciplinary methods to develop accurate measurement of SRL in educational technologies. © 2022 The Authors

Children tend to prioritize whole number information over relational information in proportional reasoning tasks, such that they judge a spinner with 4/10 red pieces as more likely to land on red than a spinner with 2/3 red pieces, because 4 > 2 (e.g., Hurst & Cordes, 2018a; Jeong et al., 2007). This whole number bias is hypothesized to be a driven by fluency in verbal counting in early childhood, which is thought to promote attention to whole number information. In this study, we explored (1) the relation between verbal counting abilities and whole number biases and (2) whether distinct framing contexts - either encouraging children to maximize the number of stickers won, or minimizing the number of stickers lost -differentially impact children's proportional reasoning. Three-to nine-year olds (N = 210, M-age = 5.7 years) chose which of two spinners they preferred to spin. Children in the Gain condition learned that if the spinner landed on red, they would win a sticker and if it landed on blue, nothing would happen; children in the Loss condition learned that if the spinner landed on red, nothing would happen, but if it landed on blue, they would lose a sticker. Counter to prior work, performance of both older (6-9 year olds) and younger (3-5 year olds) children revealed whole number biases. Notably, whole number biases were not related to counting abilities. Importantly, we find framing the task in a Loss scenario lessened whole number biases, suggesting that task framing can alter children's attention to whole number information in a proportional reasoning context.

It is widely recognized that debugging is challenging for novice programmers and, as such, computing educators and researchers have called for explicit debugging instruction. Debugging requires various knowledge and skills, and different students may show different strengths and weaknesses. An understanding of such individual differences is important as it may guide personalized instruction. The current study investigated individual differences in debugging in an undergraduate introductory computer science course. We extracted variables related to debugging from students' submission traces to programming problems in the first month of the course. We applied latent profile analysis to these variables and identified three distinctive profiles. Profile A showed higher debugging accuracy and speed. Profile B showed lower debugging performance in runtime and logic errors, while profile C had lower performance in syntactic errors and tended to make large code edit every submission. Students' gender and self-rated programming ability predicted profile membership. Moreover, profile A got higher scores than the others in the first exam, and this difference persisted in the second and third exam, even controlling for background variables and score on the first exam. We investigated how students transitioned across debugging profiles over the duration of the course. From the beginning to the end of the course, a large part of students stayed in lower performance profiles. Overall, these findings support the call that debugging should be taught at an early stage and suggest that different groups may need different debugging instructions or support.

Questions of high (vs. low) cognitive demand (CD), which encourage children to engage in abstract or critical thinking (e.g., problem solve, reason about cause-and-effect relations, make inferences), may drive relations between children's language exposure and early skills. The present study adopted a micro-analytic approach to examine caregivers' high-CD questioning with their preschool-aged children while viewing a wordless picture book (n = 121) and in the moment (e.g., interaction time, child responses) and global factors (e.g., caregiver education). The probability of caregivers' high-CD questioning increased with interaction time and caregiver education. Post-hoc exploratory analyses revealed that the relation between children's responses and caregivers' high-CD questioning depended on caregivers' perceptions of children's vocabulary skills. Specifically, the probability of caregivers' subsequent high-CD questioning was greater if their child did not respond previously and if caregivers perceived them to have high vocabulary skills. In contrast, caregivers' questioning remained relatively constant for responsive children across different vocabulary skills. Thus, caregivers may employ certain types of input during brief, informal learning interactions with their children by considering their own and their child's propensities and micro-level changes that occur during their conversations.

We developed a novel conceptualization of one component of creativity in narratives by integrating creativity theory and distributional semantics theory. We termed the new construct divergent semantic integration (DSI), defined as the extent to which a narrative connects divergent ideas. Across nine studies, 27 different narrative prompts, and over 3500 short narratives, we compared six models of DSI that varied in their computational architecture. The best-performing model employed Bidirectional Encoder Representations from Transformers (BERT), which generates context-dependent numerical representations of words (i.e., embeddings). BERT DSI scores demonstrated impressive predictive power, explaining up to 72% of the variance in human creativity ratings, even approaching human inter-rater reliability for some tasks. BERT DSI scores showed equivalently high predictive power for expert and nonexpert human ratings of creativity in narratives. Critically, DSI scores generalized across ethnicity and English language proficiency, including individuals identifying as Hispanic and L2 English speakers. The integration of creativity and distributional semantics theory has substantial potential to generate novel hypotheses about creativity and novel operationalizations of its underlying processes and components. To facilitate new discoveries across diverse disciplines, we provide a tutorial with code (osf.io/ath2s) on how to compute DSI and a web app (osf.io/ath2s) to freely retrieve DSI scores.

Teaching a particular subject provides rich opportunities for teachers to develop subject-specific knowledge and skills, especially for those who are in the early years of their career. Yet supporting evidence is scarce regarding the extent to which knowledge and skills teachers could gain from their teaching experience. This study aims to address this gap by collecting data from a from a national sample of 207 novice mathematics teachers for three years in a row to explore the development of two elements of teachers' pedagogical content knowledge (PCK) of mathematics: (1) knowledge of students' mathematical thinking and (2) knowledge of mathematics teaching. By using linear growth modeling to analyze the data derived from teachers' analyses of videos clips of mathematics classes, we found that teachers increased both elements of PCK, albeit at different rates. Further, the growth of these two important elements of PCK were associated with different teacher-related factors. Having a robust knowledge of mathematics played a key role in teachers' learning of students' mathematical thinking, whereas having a credential in mathematics teaching played a role in the development of teachers' knowledge of mathematics teaching. (c) 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

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.

Dual process theories of creativity suggest that creative thought is supported by both a generation phase, where unconstrained ideas are generated and combined in novel ways, and an evaluation phase, where those ideas are filtered for usefulness in context. Neurocognitively, both the default mode network (DMN) and the executive control network (ECN) have been implicated in generation and evaluation, respectively. Importantly, generating and evaluating ideas implies that the same information, reflected in patterns of neural activity, must be present in both phases, suggesting that information should be 'reinstated' (i.e. multidimensional patterns must reappear) within and/or between network nodes. In the present study, we used representational similarity analysis (RSA) to investigate the extent to which nodes of the DMN and ECN reinstate information between a generation phase, in which participants generated novel or appropriate word associations to single nouns, and an evaluation phase, where we presented the associations back to participants to evaluate them. We showed strong evidence for reinstatement within the ECN dorsal lateral prefrontal cortex during the novel association task, and within the DMN medial prefrontal cortex during the appropriate association task. We additionally showed between network reinstatement between the ECN dorsal lateral prefrontal cortex and the DMN posterior parietal cortex during the novelty task. These results demonstrate the importance of both within- and between-informational reinstatement for generating and evaluating ideas, and implicate both the DMN and ECN in dual process models of creativity.