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The application of STEM (Science, Technology, Engineering, and Math) education in solving real-world problems is challenging. To tackle this challenge, a project-based learning approach that integrates robots with cost-effective self-made toys to problem-solving was adopted to assist rural primary school students to apply STEM skills. The purpose of this study was to evaluate the effects of the project-based learning approach which includes lecturing and hands-on activities on primary school students' STEM learning outcomes and attitudes. An experiment was conducted with 25 primary school students who voluntarily participated in a STEM summer-camp programme. Students were asked to assemble a paper house equipped with an IoT control module and LED light switches, and write and edit robot scripts to produce a robot-based storytelling narrative using the paper house they made as a context. The results show that the project-based learning approach was an effective approach for cultivating primary school students' STEM knowledge and skills as evidenced from the post-written test. The relationships between the students' STEM learning outcomes and attitudes were also confirmed by a clustering analysis. Students who had higher learning attitudes also achieved higher STEM learning outcomes; the findings are also supported by the feedback from the open-ended questionnaire items. This study suggests that integrating low-cost self-made toys and robots in project-based learning activities is an effective and practical approach to enhance primary school students' learning outcomes and learning attitudes in STEM education. [ABSTRACT FROM AUTHOR]

Based on the expectancy-value perspective on identity and identity formation, this paper explores the relationship between math identity (MI) and the dimensions of motivation (i.e. intrinsic value, attainment value, utility value and perceived competence) and math achievement in primary school. An additional aim of our research was to explore these relationships in different cultural contexts and investigate potential gender and grade differences concerning MI. The participants were 11,782 primary school students from Norway, Sweden, Estonia, Finland, Portugal and Serbia. All predictors from the motivation spectrum were significant for students' MI across the examined countries and had a stronger association with MI than math achievement. Among the motivational dimensions, intrinsic value had the strongest association with students' MI. Boys had significantly more positive math identities than girls in Estonia, Finland, Norway and Portugal. The results showed that the grade 4 students perceived themselves less as "math persons" than their grade 3 peers in all countries. [ABSTRACT FROM AUTHOR]

Background: Even though monitoring and control enactment are key aspects of self‐regulated learning (SRL), Adaptive learning technologies (ALTs) may reduce the need for learners to monitor and control their learning. Personalized dashboards are effective in supporting learners' monitoring and can potentially support control behaviour. Allowing learners to enact control over their learning process, seems to hold potential for increasing their motivation. Objectives: Therefore, this study's aim was to investigate the relation between control enactment and motivation. We examined how learners enacted control while learning with an ALT with personalized dashboards and examined the relation between learners' enactment of control and their motivation. Methods: Seventy‐eight primary school learners (Grade 5) participated. During the lesson, learners worked on mathematics in the ALT and concurrently were shown personalized visualizations that supported monitoring and enacting control over their learning process. Learners could enact control to change problems' difficulty to easy, medium, or hard. Motivation was measured before and after learning. Results: The SEM analyses showed that how learners enacted control was related to their motivation. Choosing difficult problems was related to more enjoyment and competence while choosing easy problems related to more pressure and tension. Learners who complied with the suggested difficulty level experienced less choice, but also less pressure/tension and more enjoyment and competence. Conclusions: These results provide avenues to account for broader learner characteristics like SRL and motivation to optimize learning. This way, hybrid systems in which control enactment is a shared responsibility of the system and learner, can be improved to support SRL development. Lay Description: What is currently known: Monitor and control enactment are key aspects of self‐regulated learning (SRL).Adaptive learning technologies may reduce the need for learners to monitor and control their learning.Personalized dashboards support learners' monitoring behaviour and can potentially also support control enactment.Enactment of control could positively affect learners' motivation. What does this paper add: There is a large variation in how learners enact control and whether they comply with the scaffold.Learners who chose more difficult problems experienced more enjoyment, while learners choosing easy problems, experienced more pressure.Learners complied with the scaffold, experienced less choice, but also less pressure and more enjoyment.This study provides avenues to account for broader learner characteristics like SRL and motivation to optimize learning. Practical implications: Support control enactment by actively involve learners in choice during the learning process.Offer monitor and enactment in conjunction, as learners can only make well‐founded choices if they can monitor their learning process.Intrinsically and extrinsically motivated learners showed different choice patterns and learning experience.It is important to have an understanding and monitoring of learners' motivation. [ABSTRACT FROM AUTHOR]

In this convergent mixed methods design study, single-subject and qualitative data were collected concurrently to provide an in-depth picture of the impact of a modified schema-based instructional intervention. The intervention was delivered using instructional trials embedded across general education math lessons and a modified concrete-semi-concrete-abstract instructional sequence. This study investigated the impact of the intervention on the word-problem-solving, strategy use, and concept acquisition of three students with extensive support needs. The paraprofessional-delivered intervention was implemented in elementary general education mathematics classrooms using embedded instruction and focused on teaching students to solve addition and subtraction word-problems. Single-subject data indicated that all three students learned to solve word-problems given concrete materials but needed more time to master the use of semi concrete supports. Qualitative data indicated that students used taught and untaught strategies to solve word-problems, and mastered addition word-problems before subtraction when they were taught simultaneously. Data were integrated in narrative format to explore how strategy use and concept acquisition related to student word-problem-solving performance. Limitations and implications for research are discussed. [ABSTRACT FROM AUTHOR]

This study extends prior research by manipulating both intervention and skill difficulty using a multiple baseline across participants design with changing phases in a virtual tutoring environment. Participants were four U.S. students from third and fifth grades for whom appropriate and challenging instructional targets were selected following diagnostic assessment using curriculum-based measurement. Instructional strategies were selected to align or misalign with those instructional targets. The multiple baseline design was used to determine the functional relationship between the instructional strategies (acquisition or fluency-building) with appropriate and challenging skills. Results suggested that indicated intervention strategies aligned with students' skill proficiency resulted in improvements but that contraindicated intervention strategies that were misaligned with students' skill proficiency did not. Furthermore, most students rated the contraindicated intervention strategies as less acceptable or reported higher levels of math anxiety. [ABSTRACT FROM AUTHOR]

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 (Mage = 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. Public Significance Statement: This research suggests that an optimal approach for parents in supporting early elementary children's numeracy learning is to use a combination of (a) prompts that reference relatively advanced numeracy concepts and (b) autonomy-supportive (vs. controlling) parenting practices in interacting with their children in the numeracy context. [ABSTRACT FROM AUTHOR]

Participating in classroom mathematics conversations, particularly engaging with the opinions of others, can improve learners' mathematical comprehension. Teachers can use a variety of invitation and follow-up moves to encourage student engagement. The study aimed to explore teacher follow-up on learners' initial responses to teacher questions and building on learner ideas in Grade 9 mathematics classrooms. A qualitative approach and descriptive case study design were utilised. Data were collected from three schools in the same circuit in South Africa through classroom lesson observations, face-to-face teacher interviews and researchers' field notes. Three Grade 9 mathematics teachers, one from each school, were purposively selected, and the selected teachers' already established Grade 9 classes, with a maximum of 30 learners each (owing to the COVID-19 health protocol), were automatically involved. Cognitively guided instruction, a learner-centred approach that uses social constructivism as a research paradigm, guided this study. The exploration was supplemented by Brodie's conceptual framework on teacher follow-up moves. The findings revealed that the three teachers followed up on learner contributions and used different follow-up moves, namely insert, elicit, press, maintain and confirm. The study showed hybrid teacher moves. Although more teacher moves were skewed towards elicit and insert, which are closer to traditional practices, there is an indication of moving towards the press, maintain and confirm, which are reform-oriented moves. In addition to these moves identified by Brodie, acknowledging or praising the learner for responding was another move that emerged in this study. [ABSTRACT FROM AUTHOR]

During the COVID-19 pandemic, many online lessons for emergency remote teaching (ERT) were recorded. However, little is known about how these recordings can be reused as resources for students' active learning. This study aimed to design a post-video learning approach that uses recorded videos of lessons to remediate students' learning losses associated with the pedagogical challenges of ERT. Two classes (54 students in total) with two teachers of general studies and mathematics in a Hong Kong primary school participated in a quasi-experimental study in which they used an approach integrating video selection, visualizations of classroom dialogues, a discussion forum, and quizzes for 10 weeks. After the intervention, the students' mathematics knowledge had improved significantly relative to a comparison group, while the general studies class did not show significant changes. Eight students and two teachers were interviewed about their experiences with the post-video learning approach. The approach appeared to be a pedagogically meaningful way of engaging students in active learning activities and addressing the challenges raised by ERT by recycling recorded lessons. The results of this study also suggest that recorded lessons can be useful learning materials beyond tertiary education as they cater to younger learners' needs in video-based learning by, for example, segmenting class videos, using visualization for easier viewing, and including discussion forums and quizzes for enhanced interaction. The design implications of using video segments and visualized representations of classroom interactions as learning materials and how to foster knowledge co-construction through forums and quizzes are also discussed. [ABSTRACT FROM AUTHOR]

This study aims to analyze the influence of Habit of Mind, Mathematical Resilience, and Self-Confidence on the ability of fifth-grade students at SDN Gugus Gajah Mungkur, Gajah Mungkur District, Semarang City, to solve HOTS mathematics problems. Employing a quantitative approach with a correlational design, the research sample consists of 110 students, selected through proportional random sampling from a population of 136 students across five elementary schools within the Gajah Mungkur cluster. The research instruments include a mathematical reasoning ability test and a questionnaire to measure the independent variables. Data collection techniques involve tests and questionnaires, while data analysis employs descriptive analysis using Microsoft Excel 2016 and inferential analysis using statistical software such as SPSS. This includes conducting correlation tests, and regression tests, after verifying analysis requirements like normality, linearity, homoscedasticity, and autocorrelation. The results reveal a positive and significant relationship between Habit of Mind, Mathematical Resilience, and Self-Confidence, and the students' ability to solve HOTS Mathematics problems. Thus, this study highlights the importance of developing these three psychological aspects to enhance high-level mathematical problem-solving skills. Consequently, Habit of Mind, Mathematical Resilience, and Self-Confidence significantly contribute to improving students' abilities in solving HOTS Mathematics problems. [ABSTRACT FROM AUTHOR]

Kindergarteners' numerical abilities are fundamental to their future academic development. The cognitive correlates of numerical abilities remain in debate. The present study examined whether non-verbal number sense and literacy could persistently predict kindergarteners' numerical abilities. A large-scale sample consisting of 930 children aged from 5.0 to 6.9 years were assessed for numerical abilities (addition and subtraction), non-verbal number sense (numerosity comparison), literacy (character reading), and general cognitive processing (word span, rapid automatized naming, mental rotation, figure matching and rhythm). The results showed that, after controlling for all other aspects of cognitive processing available, non-verbal number sense did not correlate with numerical abilities, while literacy was a stable cognitive predictor of numerical abilities in both age groups. And rapid automatized naming (RAN) was the most powerful cognitive predictor in the 6 years of age group. Further dominance analysis also showed that literacy was the most important predictor of numerical performance in the 5 years of age group and was next only to RAN in the 6 years of age group. The results suggest that literacy rather than non-verbal number sense is a unique cognitive correlate for kindergartener's numerical abilities. We argue that increased focus on natural language, especially literacy, may help to improve kindergarteners' math ability. Highlights: A large-scale sample consisting of 930 Chinese children aged from 5.0 to 6.9 years were assessed for numerical abilities, non-verbal number sense, literacy, and general cognitive processing. The link between non-verbal number sense and children's numerical abilities did not survive after controlling for other cognitive processing. Literacy rather than non-verbal number sense is a stable cognitive correlate for kindergartener's numerical abilities in 5.0–6.9 years old kindergarteners. [ABSTRACT FROM AUTHOR]

The current study examined whether sport participation in preschool was related to executive functioning (EF) and academic outcomes (i.e., math, language, literacy) in the fall and spring of kindergarten, as well as whether EF in the fall of kindergarten mediated the relation between sport participation in preschool and academic outcomes in the spring of kindergarten. The sample was drawn from a state-funded prekindergarten program evaluation (n = 120 children; mean age at baseline = 57.63 months, female = 47%, mean monthly family income = $1636.92). Parents reported on child sport participation in the spring of the child's preschool year. Children were directly assessed on EF and academic achievement in the fall and spring of kindergarten. Results revealed that sport participation in preschool only predicted literacy in the spring of kindergarten. There was no evidence that EF mediated the relation between sport participation and academic outcomes. Implications and future directions are discussed. Highlights: Preschool sport participation may predict specific academic skills in kindergarten. Executive functioning did not mediate the relation between sport and academic skills. Varied conceptualizations of sport may inform relations between sport and cognition. [ABSTRACT FROM AUTHOR]

The purpose of this study was to investigate the effects of the concrete-representational-abstract–integrated (CRA-I) sequence on students with learning disabilities' performance when learning fraction and decimal concepts. Three elementary-level students in Grades 4 and 6 participated in a single-case multiple probe across behaviors study. The intervention involved explicit use of fraction blocks, coins, base ten blocks, number lines, pictures, and abstract symbols to teach unit fractions, fraction and decimal equivalence, addition of fractions with unlike denominators, and writing fractions as decimals. The researchers demonstrated a functional relation between CRA-I and three different behaviors related to fraction concepts: decreased error in estimating fraction magnitude, addition of unlike fractions, and writing fractions as decimals. The findings show promise in the use of CRA-I for teaching fraction concepts to students with learning disabilities. [ABSTRACT FROM AUTHOR]

Math anxiety is widespread problem described as worry and tension while doing mathematics. The aim of research is to determine whether there is a correlation between math anxiety and the performance of elementary school students in solving mathematical problems at the second level. . The theoretical part of the thesis contains information and empirical findings about math anxiety and solving mathematical problems. The research sample was comprised of 138 (46,38 % girls and 53,62 % boys) 9th grade elementary learners from Slovak republic. The data were collected by the questionnaire of our own design comprising : the modified abbreviated math anxiety scale, the state-trait anxiety inventory, and the math test. Quantitative data analysis methods included descriptive statistics and Spearman coefficient as a measurement of correlation between variables. The results have revealed that mathematics anxiety has significant correlation (R = - 0.401; p = 1,09216.10-6, p < 0.01) with the success of mathematical problems and significant correlation (R = 0.608; p = 2,44249.10-15, p < 0.01) with the mathematics achievement. 36,23 % of the participants reported high math anxiety, and a further 18% were at least somewhat affected by it. The results confirm that the mAMAS questionnaire is an appropriate tool for determining the level of mathematical anxiety among pupils in Slovakia. [ABSTRACT FROM AUTHOR]

Increasing evidence suggests that success in science, technology, engineering, and math (STEM) fields is not only dependent upon one's actual STEM-relevant abilities but also upon one's STEM-relevant attitudes—in particular, math and spatial attitudes. Here, we examine whether simply mentioning the math or spatial relevance of a task affects children's performance and the moderating role of children's math and spatial attitudes. Further, we examine gender differences in performance given pervasive gender gaps in STEM and early-emerging gender differences in math and spatial attitudes. Participants (221 first- to fourth-grade children from the United States; 113 girls, 108 boys; 52% White, 16% Black, 14% Asian, 9% Hispanic or Latinx, 18% multiple races/ethnicities) were introduced to a novel task framed as tapping into math or spatial abilities (or no framing [control condition]). Children then completed math and spatial anxiety and self-concept measures. Results indicate that children who heard the math task framing were less accurate relative to children in the control condition, and the effect was larger for those with higher math anxiety or lower math self-concept, but it was not different for boys and girls. Children who heard the spatial task framing, however, performed comparably to children in the control condition. Though both math and spatial attitudes revealed identical patterns of gender differences (with higher anxiety and lower self-concept in girls than boys), there were no gender differences in performance. This study highlights the salient role of math attitudes early in development and provides key insights for future work aimed at increasing STEM outcomes. Public Significance Statement: Findings reveal that children perform worse on a novel task when it is described as being related to math—but not spatial—skills, and this effect is strongest for children with more negative math attitudes. Moreover, girls had more negative math and spatial attitudes than did boys, but gender differences were not observed in performance on the task. Findings provide key insights into processes implicated in science, technology, engineering, and math outcomes. [ABSTRACT FROM AUTHOR]

Anemia is a global public health problem, especially common among children in developing countries, which affects their physical and mental health development. However, there is currently a lack of research on the relationship between anemia and academic performance. The objective of this study was to explore the association between anemia and academic performance, and the possible factors mediating this association among Chinese children. The data for this study came from the baseline survey of the Chinese Education Panel Survey Elementary School Cohort. The cohort was conducted from September 2018 to June 2019 in 160 elementary schools, covering 20 provinces and 40 counties/districts throughout China. Paper-based questionnaires were used, completed by 4th grade students, parents, head teachers, main teachers, and principals. The data used included questionnaire responses, physical measurements, and academic performance of 17,695 students. Based on students' hemoglobin levels and school altitude data, we grouped them into anemia and nonanemia categories using WHO criteria. The anemia group had 1,154 individuals, while the nonanemia group had 16,541 individuals. An ordinary least squares regression and mediation effect analysis were conducted. Our findings found the prevalence of anemia was 6.52% among Chinese Grade 4 students. Students without anemia had a higher average test score for three academic subjects than students with anemia (P < 0.001); their test scores for Chinese, Mathematics, and English were also higher (P < 0.05). Multivariate regression analysis showed a negative association between anemia and average test scores as well as individual test scores for the three subjects. Mediation analysis found that anemia affected academic performance directly (P < 0.05), and indirectly by decreasing the cognition score (P < 0.05). The indirect effect was 19.9% of the total effect. Findings highlighted anemia affected academic performance both directly and indirectly. Nutrition-related interventions should be implemented to prevent a decrease in academic performance among students with anemia. [ABSTRACT FROM AUTHOR]

Teacher innovative behavior is one of the vital factors, affecting student engagement, addresses diverse needs, promotes critical thinking, fosters lifelong learning, and contributes to educational research and development. By encouraging and supporting teacher innovation, we may can ensure that education remains relevant, effective, and impactful in preparing students for the future. Teacher innovative behavior is also needed to improve the mathematics skills of elementary school students, and it is important to determine the predictors that significantly affecting Teacher innovative behavior. Therefore, this study aimed to develop a model that predicted possible factors affecting mathematics teachers' innovative behavior based on Social Cognitive Theory (SCT). Data were collected from 132 elementary school teachers in China to verify the model, and the analysis was conducted using a structural equation modelling approach. Theoretically, 10 of the 15 hypotheses were found to be significant. The results showed that facilitating conditions and self-efficacy significantly affect mathematics teachers' innovative behavior. Meanwhile, Technological, Pedagogical and Content Knowledge (TPACK) knowledge, Social Influences, Rewards, Work engagement and anxiety did not show any effect. The contribution developed a model and provided new knowledge about the factors affecting elementary school teachers' innovative behavior. Practically, this could be used to improve teachers' innovative behavior. [ABSTRACT FROM AUTHOR]

Task-related change in physiological arousal is suggested to reflect active involvement with the task. While studies often examine such task-related changes in arousal as averaged across the entire task, the present study focused on temporal changes in arousal during a task. More specifically, we investigated changes in elementary school students' physiological arousal during an arithmetic task and associations between these changes and students' mindset, performance on the task, and math grades. We used a person-oriented approach to analyze the tonic electrodermal activity of 86 fourth graders, recorded while they were working on an arithmetic task. With model-based clustering of students' on-task electrodermal activity, we identified three groups of students with differing temporal dynamics of physiological arousal during the task: Increasing Arousal, Decreasing Arousal and Decreasing and Increasing Arousal. The Decreasing Arousal profile contained more students classified as holding a Fixed Mindset Tendency than would be expected if physiological profile membership and mindset tendency were independent. The Increasing Arousal profile performed better on the task than the Decreasing Arousal profile. No association was found with math grades. These results provide a new insight into individual differences in temporal patterns of on-task physiological arousal. [ABSTRACT FROM AUTHOR]

Success in science, technology, engineering, and mathematics (STEM) fields is often believed to require intellectual talent ("brilliance"). Given that many cultures associate men more than women with brilliance, this belief poses an obstacle to women's STEM pursuits. Here, we investigated the developmental roots of this phenomenon, focusing specifically on young children's beliefs about math (N = 174 U.S. students in Grades 1–4; 93 girls, 81 boys; 52% White, 17% Asian, 13% Hispanic/Latinx). We found that field‐specific ability beliefs (FABs) that associate success in math (vs. reading/writing) with brilliance are already present in early elementary school. We also found that brilliance‐oriented FABs about math are negatively associated with elementary school students' (and particularly girls') math motivation—specifically, their math self‐efficacy and interest. The early emergence of brilliance‐oriented FABs about math and the negative relation between FABs and math motivation underscore the need to understand the sources and long‐term effects of these beliefs. Research Highlights: Field‐specific ability beliefs (FABs) are beliefs about the extent to which intellectual talent (or "brilliance") is required for success in a particular field or context.Among adults, brilliance‐oriented FABs are an obstacle to diversity in science and technology, but the childhood antecedents of these beliefs are not well understood.The present study (N = 174) found that FABs that associate success in math (vs. reading/writing) with brilliance were already present in Grades 1−4.Brilliance‐oriented FABs about math were negatively associated with elementary school students' (and particularly girls') math motivation—specifically, their math self‐efficacy and interest. [ABSTRACT FROM AUTHOR]

The present study aimed to examine the mediating role of parental involvement in the association between parental attitudes toward their own mathematics and reading abilities and children's learning interests in the Chinese context. Participants included 395 Chinese elementary students whose ages ranged from 6.53 to 12.82 years (mean = 9.68 years) and their caregivers. The results showed that parental attitudes toward their own mathematics and reading not only had a domain-specific effect on parent-reported children's learning interests in these subjects but also had a cross-domain effect on other subjects. Furthermore, parental home- and school-based involvement mediated the association between parental attitudes toward mathematics and reading and parent-reported children's learning interests in these subjects. At the domain-specific level, parental home-based involvement, rather than school-based involvement, mediated the relation between parental attitudes and children's learning interests in mathematics and reading. At the cross-domain level, both home- and school-based involvement mediated the association between parental attitudes toward their own reading and children's mathematics interests. The findings underline the relevance of parental attitudes toward their own mathematics and reading and parental home- and school-based involvement in the development of Chinese elementary school students' learning interests. • Parental attitudes toward math and reading had domain-specific and cross-domain effects on children's learning interests. • Parental home- and school-based involvement mediated the link between parental attitudes and children's learning interests. [ABSTRACT FROM AUTHOR]

• Corrective feedback influenced children's in-the-moment math problem solving. • Feedback with verification reduced persistence relative to the correct answer alone. • Feedback with verification enhanced reliance on entrenched incorrect strategies. • Feedback from a person reduced accuracy relative to computer feedback alone. The current study examined how different features of corrective feedback influenced children's performance and motivational outcomes on a mathematics task. Elementary school-aged children from the United States (N = 130; M age = 7.61 years; 35% female; 60% White) participated in a Zoom session with a trained researcher. During the learning activity, children solved a series of mathematical equivalence problems and were assigned to different feedback conditions that varied in feedback content (correct answer alone vs. correct answer with verification) and feedback source (computer alone vs. computer with person). In terms of content, feedback with verification cues led to decreased persistence, decreased strategy variability, and higher reliance on entrenched strategies relative to feedback that contained the correct answer alone. In terms of source, feedback from the computer alone enhanced children's accuracy; however, the most resilient children received feedback from the computer and a person. Findings are discussed in light of existing feedback theories. [ABSTRACT FROM AUTHOR]

Does mathematical vocabulary predict the change in students' performance on mathematical tasks from one academic year to the next? Chilean Spanish-speaking students (N = 87) completed measures of mathematical vocabulary, mathematical skills (i.e., arithmetic fluency, calculation, and applied problems), receptive vocabulary, and working memory in Grade 2 (T1, M age = 7:11 years:months, SD = 0:5, 46% girls). One year later (T2) they completed the same mathematical measures. Concurrent relations were found between mathematical vocabulary and the three mathematical skills at both time points. Together, general and mathematical vocabulary at T1 explained significant unique variance in the change in applied problems and calculation from T1 to T2. For calculation however, only mathematical vocabulary predicted significant unique variance in the change from T1 to T2. Change in arithmetic fluency was only predicted by working memory. These results address the roles of general and mathematical vocabulary in students' mathematical development in elementary school. • We evaluated changes in mathematical vocabulary and mathematical skills. • We studied Spanish-speaking students in early elementary school. • Mathematical vocabulary predicted students' change in calculation skills. • Domain-general and domain-specific skills differentially support mathematical development. [ABSTRACT FROM AUTHOR]

• Teacher expectations and student motivation decrease at the end of second grade. • Changes in teacher expectations and student motivation are correlated. • Teacher expectations influence subsequent change of student motivation. While teacher expectations are known to influence students' academic achievement, they may also exert significant influences on student motivation, which is a precursor to a student's achievement as well. A number of previous studies have demonstrated that motivation affects a student's achievement. There is, however, a dearth of longitudinal research examining the relation between teacher expectations and students' motivational variables. In this article, we examine the relations between teacher expectations of students' mathematics ability, students' mathematics-related competence beliefs, and students' mathematics-related intrinsic task-values. Our sample consisted of 796 second-grade students and their 50 teachers; the data collection was conducted at three points within a school year. Longitudinal latent change score analyses yielded three main results: First, teacher expectations of students' mathematics ability and both students' mathematics-related competence beliefs and intrinsic task values decreased significantly in the second half of the school year. Second, regarding correlated changes, students who experienced larger increases in teacher expectations also demonstrated higher increases in competence beliefs and intrinsic task values in mathematics. Third, after controlling for students' initial mathematics achievement, effects of teacher expectations of students' mathematics ability at the beginning of the school year on subsequent changes in students' mathematics-related competence beliefs and intrinsic task values were revealed. Our study highlights the important role of teacher expectations in shaping students' motivational variables, which underscores the need for teacher training programs and policy interventions aimed at increasing teachers' awareness of their expectations and how they can foster a positive learning environment for their students. [ABSTRACT FROM AUTHOR]

Understanding relative quantities is crucial for many formal mathematical and everyday experiences, and its development has been examined using both probability judgment and proportion matching frameworks. The current study examines individual difference and developmental patterns that emerge within and between these frameworks, using computerized tasks administered within-subjects to a socio-demographically diverse sample of elementary school students (N = 96, 52 female, M age = 8.56-years, 5.1–12.4) between kindergarten and fifth-grade. The results indicate that performance between the two task frameworks was correlated, and that age was significantly correlated with performance on both tasks. There were also differences across tasks, and children were overall more successful in their probability judgements than proportion matching. The findings, therefore, indicate some individual difference and cognitive developmental commonality across frameworks, but also that they are differentially effective in prompting relative quantity problem-solving strategies, which has implications for developmental research and theory and suggests a more nuanced approach to when children understand relative quantities is needed. • Probability judgment and proportion matching are vital and likely related. • Children completed probability and proportion tasks as concurrent measures. • Measures were correlated but differentiable. • Findings support a common foundation but differences in relative quantity prompting. [ABSTRACT FROM AUTHOR]