Mechanisms underlying the relations between parents' perfectionistic tendencies and young children's mathematical abilities.

BACKGROUND: Parents' high academic expectations are positively associated with young children's mathematical abilities. However, minimal attention has been devoted to whether, and how, different ways of conveying the performance targets would result in different outcomes. AIMS: The current study investigated whether and how parents' perfectionistic strivings and concerns were associated with young children's mathematical abilities through home mathematical activities, children's approach motivation to learn mathematics, and children's avoidance motivation to learn mathematics. SAMPLE: Participants included 211 kindergarteners in Hong Kong and their parents. METHODS: Data were collected through individual child tests and parent questionnaires. RESULTS: Structural equation modelling revealed that parents' perfectionistic strivings had a direct positive link with children's mathematical abilities, an indirect link via approach motivation to learn mathematics, and an indirect link via home mathematical activities, and then approach motivation. Parents' perfectionistic concerns had a direct negative link with children's mathematical abilities, an indirect link via approach motivation to learn mathematics, and an indirect link via avoidance motivation to learn mathematics. CONCLUSIONS: Early childhood practitioners are recommended to raise parents' awareness of how to communicate high-performance targets to children in a constructive manner.

Examining the learning effects of concrete and abstract materials among university students using a two-dimensional approach.

BACKGROUND: The debate on using concrete versus abstract materials in learning mathematics has been longstanding. For decades, research has focused on the physical characteristics of materials when defining them as concrete or abstract. AIMS: This study extends the field by proposing a two-dimensional classification, which defines materials as concrete or abstract based on the two dimensions of representation, namely object (i.e., appearance) and language (i.e., label). SAMPLE: A total of 120 university students participated in the study. METHODS: Participants were randomly assigned to learn the concept of modular arithmetic with one of four types of learning materials: concrete object labelled with concrete language, concrete object labelled with abstract language, abstract object labelled with concrete language and abstract object labelled with abstract language. They were also divided into high and low maths anxiety groups. RESULTS: Results showed that the students who learnt with abstract objects, regardless of the level of maths anxiety, outperformed their peers who learnt with concrete objects. However, for students with low maths anxiety only, those who learnt with materials labelled with abstract language showed better far-transfer performance compared with those who learnt with materials labelled with concrete language. CONCLUSIONS: The findings offer a new direction in the conceptualization of concrete and abstract learning materials by specifying the dimensions of representation.

The roles of different executive functioning skills in young children's mental computation and applied mathematical problem-solving.

This study investigated the relationships of four executive functioning skills (including verbal working memory, spatial working memory, inhibitory control, and cognitive flexibility) with young children's mental computation and applied mathematical problem-solving. Two hundred and twenty-five Chinese kindergarteners were tested with a battery of general cognitive, executive functioning and mathematics skills. Results showed that when children's age, gender, non-verbal intelligence, and listening comprehension skills were controlled, verbal working memory and cognitive flexibility were significant correlates of mental computation, whereas verbal working memory, spatial working memory, and cognitive flexibility were significant correlates of applied mathematical problem-solving. Inhibitory control was not significantly associated with the two domains of mathematics under investigation. The findings highlight the differential roles of different executive functioning skills in early mathematical skills and offer practical implication for helping young children in learning complex mathematical skills.

Next Directions in Measurement of the Home Mathematics Environment: An International and Interdisciplinary Perspective.

This article synthesizes findings from an international virtual conference, funded by the National Science Foundation (NSF), focused on the home mathematics environment (HME). In light of inconsistencies and gaps in research investigating relations between the HME and children's outcomes, the purpose of the conference was to discuss actionable steps and considerations for future work. The conference was composed of international researchers with a wide range of expertise and backgrounds. Presentations and discussions during the conference centered broadly on the need to better operationalize and measure the HME as a construct - focusing on issues related to child, family, and community factors, country and cultural factors, and the cognitive and affective characteristics of caregivers and children. Results of the conference and a subsequent writing workshop include a synthesis of core questions and key considerations for the field of research on the HME. Findings highlight the need for the field at large to use multi-method measurement approaches to capture nuances in the HME, and to do so with increased international and interdisciplinary collaboration, open science practices, and communication among scholars.

Effectiveness and Mechanisms of Mindfulness Training for School Teachers in Difficult Times: A Randomized Controlled Trial.

OBJECTIVES: Research in recent years has shown that mindfulness-based interventions can enhance teachers' mental and physical health. However, the existing studies were predominantly conducted in Western, educated, industrialized, rich, and democratic (WEIRD) societies. As a randomized controlled trial in a non-WEIRD society, the present study examined the effectiveness and mechanisms of mindfulness training for Hong Kong teachers in difficult times. METHODS: Teachers from primary and secondary schools (n = 186) were randomly assigned to mindfulness training (eight-week .b Foundations) or waitlist control condition. They completed online self-report surveys on measures of well-being, emotion management, and mindfulness in teaching at baseline, post-intervention, and two-month follow-up. RESULTS: The intervention group reported significantly higher levels of life satisfaction, positive affect, general health, along with significantly lower levels of insomnia, stress, and negative affect than the control group at post-test and two-month follow-up. The effect sizes were medium to large (η p 2 = 0.06 to 0.14). More importantly, teachers' baseline well-being had a significant moderating effect on the intervention effectiveness. Those with a lower baseline in well-being benefitted more than their counterparts with a higher baseline. In addition, teachers' emotion management was found to be the mediator through which mindfulness training enhanced teachers' well-being. Such improvement in well-being also predicted higher levels of mindfulness in teaching. CONCLUSIONS: This study provides evidence on the efficacy of mindfulness training for teachers beyond WEIRD societies. It suggests the universality and practicality of mindfulness training in enhancing teachers' well-being and reducing their distress in difficult times.

Acceptance of outgroup members in schools: Developmental trends and roles of perceived norm of prejudice and teacher support.

BACKGROUND: Schools around the world are increasingly diverse in ethnicity. Given the importance of peer acceptance in children's well-being and development, it is a pressing concern for educators to promote intergroup acceptance in schools. AIMS: First, to examine the developmental trends of acceptance of outgroup members in both the ethnic minority and majority students. Second, to investigate how outgroup acceptance is subject to the interplay between perceived norm of prejudice, a risk factor in the macrosystem, and teacher support, a protective factor in the microsystem. SAMPLE: The participants were 3,723 students (ethnic majority: 61%; boys: 51.9%; mean age: 13.7) at Grade 2, 5, 8, and 11 from 24 schools in Hong Kong. METHODS: The students were asked to complete a battery of questionnaires regarding their willingness to accept outgroup members in schools, perceived societal norm of prejudice against ethnic minority group, and teacher support they received in schools. RESULTS: It was found that ethnic minority students accepted outgroup members more than ethnic majority students accepted them. The difference was primarily driven by the low outgroup acceptance of ethnic majority students in Grades 2 and 5. The results of multi-level analysis revealed that outgroup acceptance was associated negatively with perceived norm of prejudice but positively with teacher support. The negative association between outgroup acceptance and perceived norm of prejudice was attenuated in schools with supportive culture. CONCLUSIONS: The results point to the need of early intervention and the importance of cultivating school culture with strong social emotional support.

Counting Enhances Kindergarteners' Mappings of Number Words Onto Numerosities.

We can make sense of how many a number represents by mapping the symbolic number word system onto the non-symbolic, approximate number system. This study adopted an intervention design to examine whether counting is essential in driving the formation of such symbolic-non-symbolic mappings. We compared kindergarteners' mapping ability after reading stories (1) without cardinal labels, or (2) with cardinal labels, or (3) with cardinal labels and verbal counting. Results showed that children who had counted when reading the stories showed better mapping between number words and their approximate representations than their peers in the other two conditions - suggesting that counting plays a role in developing early symbolic-non-symbolic mappings. Such findings provides empirical support for parents and early educators to enhance young children's mappings between numbers words and approximate representations through counting activities - such as counting the items in the story books while reading to children.

The underlying number-space mapping among kindergarteners and its relation with early numerical abilities.

People map numbers onto space. The well-replicated SNARC (spatial-numerical association of response codes) effect indicates that people have a left-sided bias when responding to small numbers and a right-sided bias when responding to large numbers. This study examined whether such spatial codes were tagged to the ordinal or magnitude information of numbers among kindergarteners and whether it was related to early numerical abilities. Based on the traditional magnitude judgment task, we developed two variant tasks-namely the month judgment task and dot judgment task-to elicit ordinal and magnitude processing of numbers, respectively. Results showed that kindergarteners oriented small numbers toward the left side and large numbers toward the right side when processing the ordinal information of numbers in the month judgment task but not when processing the magnitude information in the number judgment task and dot judgment task, suggesting that the left-to-right spatial bias was probably tagged to the ordinal but not magnitude property of numbers. Moreover, the strength of the SNARC effect was not related to early numerical abilities. These findings have important implications for the early spatial representation of numbers and its role in numerical performance among kindergarteners.

Developmental dyscalculia and low numeracy in Chinese children.

Children struggle with mathematics for different reasons. Developmental dyscalculia and low numeracy - two kinds of mathematical difficulties - may have their roots, respectively, in poor understanding of exact non-symbolic numerosities and of symbolic numerals. This study was the first to explore whether Chinese children, despite cultural and linguistic factors supporting their mathematical learning, also showed such mathematical difficulties and whether such difficulties have measurable impact on children's early school mathematical performance. First-graders, classified as dyscalculia, low numeracy, or normal achievement, were compared for their performance in various school mathematical tasks requiring a grasp of non-symbolic numerosities (i.e., non-symbolic tasks) or an understanding of symbolic numerals (i.e., symbolic tasks). Children with dyscalculia showed poorer performance than their peers in non-symbolic tasks but not symbolic ones, whereas those with low numeracy showed poorer performance in symbolic tasks but not non-symbolic ones. As hypothesized, these findings suggested that dyscalculia and low numeracy were distinct deficits and caused by deficits in non-symbolic and symbolic processing, respectively. These findings went beyond prior research that only documented generally low mathematical achievements for these two groups of children. Moreover, these deficits appeared to be persistent and could not be remedied simply through day-to-day school mathematical learning. The present findings highlighted the importance of tailoring early learning support for children with these distinct deficits, and pointed to future directions for the screening of such mathematical difficulties among Chinese children.

Exploring the developmental changes in automatic two-digit number processing.

Even when two-digit numbers are irrelevant to the task at hand, adults process them. Do children process numbers automatically, and if so, what kind of information is activated? In a novel dot-number Stroop task, children (Grades 1-5) and adults were shown two different two-digit numbers made up of dots. Participants were asked to select the number that contained the larger dots. If numbers are processed automatically, reaction time for dot size judgment should be affected by numerical characteristics. The results suggest that, like adults, children process two-digit numbers automatically. Based on the current findings, we propose a developmental trend for automatic two-digit number processing that goes from decomposed sequential (activation of decade digit followed by that of unit digit) to decomposed parallel processing (simultaneous activation of decade and unit digits).