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1.
What developmental roles do nonsymbolic (e.g., dot arrays) and symbolic (i.e., Arabic numerals) magnitude comparison skills play in children's mathematics? We assessed a large sample in kindergarten, grade 1 and 2 on two well-known nonsymbolic and symbolic magnitude comparison measures. We also assessed children's initial IQ and developing Working Memory (WM) capacities. Results demonstrated that symbolic and nonsymbolic comparison had different developmental trajectories; the first underwent larger developmental improvements. Both skills were longitudinal predictors of children's future mathematical achievement above and beyond IQ and WM. Nonsymbolic comparison was moderately predictive only in kindergarten. Symbolic comparison, however, was a robust and consistent predictor of future mathematics across all three years. It was a stronger predictor compared to nonsymbolic, and its predictive power at the early stages was even comparable to that of IQ. Furthermore, the present results raise several methodological implications regarding the role of different types of magnitude comparison measures.  相似文献   

2.
Children show individual differences in their tendency to focus on the numerical aspects of their environment. These individual differences in ‘Spontaneous Focusing on Numerosity’ (SFON) have been shown to predict both current numerical skills and later mathematics success. Here we investigated possible factors which may explain the positive relationship between SFON and symbolic number development. Children aged 4–5 years (N = 130) completed a battery of tasks designed to assess SFON and a range of mathematical skills. Results showed that SFON was positively associated with children's symbolic numerical processing skills and their performance on a standardised test of arithmetic. Hierarchical regression analyses demonstrated that the relationship between SFON and symbolic mathematics achievement can be explained, in part, by individual differences in children's nonsymbolic numerical processing skills and their ability to map between nonsymbolic and symbolic representations of number.  相似文献   

3.
To examine the cross-lagged relationships between children's task motivation in mathematics and literacy, and their related performance, 139 children aged 5–6 years were examined twice during their kindergarten year. The results showed that only math-related task motivation and arithmetic performance showed cross-lagged relationship: the higher the math-related task motivation children reported in the beginning of the kindergarten year the higher the level of their arithmetic performance at the end of the kindergarten year. Moreover, the higher the level of children's arithmetic performance the more the interest in mathematics children reported later on. Literacy-related task motivation and literacy performance did not show a similar pattern of relations.  相似文献   

4.
Children's intuitive understanding of number, i.e. number sense, is associated with individual differences in mathematics achievement. To investigate the causal association between number sense, traditionally assessed with comparison or number line estimation tasks, and mathematics achievement, often assessed with an arithmetic test, an intervention study was conducted that aimed at training either comparison or number line estimation skills. We contrasted a comparison and number line estimation training. By doing so, we wanted to address the question which intervention had the largest effect on arithmetic. In addition, such a direct comparison between comparison and number line estimation trainings would allow us to get more insight in the association between both tasks. Participants were 151 five-year-olds that were randomly allocated to either an experimental condition (i.e. comparison or number line estimation) or one of the two control conditions (i.e., active control condition and empty control condition) in a pretest-posttest design measuring number knowledge, (non-)symbolic comparison and number line estimation and arithmetic. The results showed that both comparison and number line estimation trainings had a positive effect on arithmetic. However, the absence of transfer effects from one task to another, also suggested that comparison and number line estimation rely on different mechanisms and probably influence arithmetic through different mechanisms.  相似文献   

5.
Research Findings: The purpose of this study was to investigate the factorial structure of kindergarten children's mathematics and science process skills and the impact of children's competencies in process skills on their performance on mathematics and science achievement tests in 3rd grade. A subset of the Early Childhood Longitudinal Study–Kindergarten cohort data set (n = 8,731) was analyzed using multilevel structural equation modeling. Results demonstrated that science and mathematics process skills were highly related at the construct level but not at the indicator level, as was anticipated. Kindergarten children's competency in mathematics process skills was a strong predictor of their performance on science and mathematics achievement tests in the 3rd grade. However, children's competency in science process skills was only a significant predictor of their performance on a science achievement test in the 3rd grade. Moreover, socioeconomic status and gender were statistically significant predictors of process skills and performance on achievement tests. Practice or Policy: The findings of the present study suggest that the development of children's science and mathematics process skills should be supported utilizing integrated inquiry-based science and mathematics activities to help children recognize the connection between mathematics and science and to contribute to their science and mathematics achievement in later grades.  相似文献   

6.
Against the background of neuroimaging studies on how the brain processes numbers, there is now converging evidence that numerical magnitude representations are crucial for successful mathematics achievement. One major drawback of this research is that it mainly investigated mathematics performance as measured through general standardized achievement tests. We extended this research by investigating the association between numerical magnitude representations and children's strategy use during single‐digit arithmetic. Our findings reveal that children's symbolic but not nonsymbolic numerical magnitude processing skills are associated with individual differences in arithmetic. Children with better access to magnitude representations from symbolic digits retrieve more facts from their memory and are faster in executing fact retrieval as well as procedural strategies. These associations remain even when intellectual ability, digit naming, and general mathematics achievement are additionally controlled for. All this indicates that particularly the access to numerical meaning from Arabic symbols is key for children's arithmetic strategy development, which suggests that educators and remedial teachers should focus on connecting Arabic symbols to the quantities they represent.  相似文献   

7.
This study examined whether children's mathematics anxiety serves as an underlying pathway between parental involvement and children's mathematics achievement. Participants included 78 low-income, ethnic minority parents and their children residing in a large urban center in the northeastern United States. Parents completed a short survey tapping several domains of parental involvement, and children were assessed on mathematics anxiety, whole number arithmetic, word problems, and algebraic reasoning. Research Findings: The results indicated that parents influence children's mathematics achievement by reducing mathematics anxiety, particularly for more difficult kinds of mathematics. Specifically, the mediation analyses demonstrated that parental home support and expectations influenced children's performance on word problems and algebraic reasoning by reducing children's mathematics anxiety. Mathematics anxiety did not mediate the relationship between home support and expectations and whole number arithmetic. Practice or Policy: Policies and programs targeting parental involvement in mathematics should focus on home-based practices that do not require technical mathematical skills. Parents should receive training, resources, and support on culturally appropriate ways to create home learning environments that foster high expectations for children's success in mathematics.  相似文献   

8.
ABSTRACT

The author examined whether mathematics instruction provided by kindergarten teachers is related to children's mathematics learning during the kindergarten year based on the children's socioeconomic status and race. Hierarchical linear modeling was employed using a large sample of kindergarten students to estimate relationships between the teacher's instructional approach (e.g., concrete-spatial, interpersonal, linguistic) and children's mathematics skills. Results showed that the teacher's instructional approach was selectively related to children's mathematics learning. Students in classrooms where teachers frequently employed a concrete-spatial instructional approach learned more during the kindergarten year. Students from lower socioeconomic backgrounds benefitted more from teachers who often employed an interpersonal approach, and Black/African American students benefitted less from classrooms where teachers relied more on a linguistic approach. The findings suggest that kindergarten teachers’ instruction needs to employ varied methods that take into account students’ mathematics skills and background characteristics.  相似文献   

9.
This study investigated the longitudinal associations between children’s early mathematics and their home numeracy environment (HNE). Chilean children from families who varied widely in socioeconomic status were assessed at the beginning and end of prekindergarten in 2016 (N = 419, Mage = 4:7 [years:months]), and at the end of kindergarten in 2017 (N = 368, Mage = 5:10). Children whose parents provided frequent operational numeracy activities (e.g., learning simple sums) at prekindergarten showed better arithmetic performance and growth in nonsymbolic and symbolic number comparison at the end of kindergarten. Parents’ knowledge of number-related games predicted children’s arithmetic skills and growth in nonsymbolic number comparison. These findings underscore the persistent relations between the HNE and the development of children’s mathematical skills.  相似文献   

10.
There is an increasing emphasis in mathematics education on the importance of estimation abilities in children. This study investigates the role of context upon primary‐aged children's estimation skills. Children in three age groups (from aged 5 to 8 years) were asked to carry out a range of estimation tasks involving distance, area and volume measurements. The tasks varied in type and complexity and were either of a ‘real‐world’ or ‘mathematics task’ form. In addition to performance measures the children's answers to questions on how they carried out the estimates were recorded and analysed. Quantitative and qualitative analyses found significant effects for context and child strategy. Estimates in contexts perceived as mathematical were different, both in that they changed with age and in their error patterns, from contexts involving perceptual‐motor skills. The children's answers highlight the importance of imagery and classroom experience. The results are discussed within a model of estimating.  相似文献   

11.
This study examined the role of verbal counting skill as an early predictor of math performance and difficulties (at or below −1.5 standard deviation in basic math skills) in middle school. The role of fourth-grade level arithmetical skills (i.e., calculation fluency, multi-digit arithmetic i.e. procedural calculation, and word problem solving) as mediators was also investigated. The participants included 207 children in central Finland who were studied from kindergarten to the seventh grade. Path modeling showed that verbal counting in kindergarten is a strong predictor for basic math performance in seventh grade, explaining even 52% of the variance in these skills after controlling for the mothers’ education levels. This association between early verbal counting skill and basic math performance was partly mediated through fourth-grade procedural calculation and word problem solving skills. Furthermore, verbal counting had an unique predictive relation to middle school math performance above and beyond the basic arithmetical and problem solving skills in fourth grade. Poor kindergarten verbal counting skill was a significant indicator for later difficulties in mathematics.  相似文献   

12.
Research Findings: Children from families of lower socioeconomic status (SES) enter kindergarten with less developed mathematical knowledge compared to children from middle SES families. This discrepancy is present at age 3 years and likely stems from differences in the home learning environment. This study reports SES-related differences both in the quantity and quality of mathematical support children receive in the home and in parent beliefs about early mathematical development and then compares both with children's performance on a comprehensive mathematics assessment. Participants included 90 children in their 1st year of preschool (2 years before kindergarten entry) and 88 children in their prekindergarten year (the year just prior to kindergarten entry). Both cohorts were balanced for SES and gender. The results suggested minimal SES-related variation in mathematical support received in either cohort but clear SES differences in parents’ beliefs about early mathematical development. Middle SES parents of children in both cohorts held higher expectations in terms of skills they expected children to possess by age 5, as well as a more accurate understanding of which skills are within the developmental range of most children by age 5. These differences accounted for unique variance in children's scores on the mathematics assessment. Practice or Policy: Implications are discussed.  相似文献   

13.
This study investigated whether different types of ordering skills were related to mathematics achievement in children (n = 100) in middle childhood, after the effects of age, socio-economic status, IQ, and processing speed were taken into account. The relations between ordering skills and magnitude processing were also investigated, as well as the possibility that some of the shared variance between math and reading is explained by ordering abilities. The ordering tasks included the ordering of familiar numerical and non-numerical sequences, a parental report of children’s everyday ordering skills, and an order working memory task. Three magnitude processing tasks (symbolic and non-symbolic comparison and number line estimation), were also administered, as well as measures of inhibition and spatial working memory. From this set of measures, number ordering, order working memory and number line estimation emerged as the most important predictors of mathematics skills. We found that number ordering mediated the effect of both symbolic and non-symbolic comparison skills on mathematics, further confirming that this task captures some essential skills related to mathematics. Additionally, order working memory mediated the effect of both number comparison and reading skills on math. Finally, whereas non-symbolic comparison and number line estimation are considered important indicators of magnitude processing skills, there was no relationship between these abilities, but there was a correlation between each of these abilities and reading skills, with number line estimation also mediating the effect of reading skills on math. These novel findings could contribute to a better understanding of the basic processes underlying math ability, and why math and reading are strongly related in typical populations and in children with learning difficulties.  相似文献   

14.
The present study investigated whether kindergarten teachers' causal attributions would predict children's reading‐related task motivation and performance, or whether it is rather children's motivation and performance that contribute to teachers' causal attributions. To investigate this, 69 children (five to six years old at baseline) and their teachers were examined twice during the kindergarten year. Teachers filled in a questionnaire measuring their causal attributions twice during the kindergarten year. Information about the children's reading‐related task motivation and performance was gathered at the beginning of and at the end of the kindergarten year. The results showed that the higher the task motivation and performance in reading the children showed, the more the teachers attributed their success to ability and effort, and the less they attributed it to teachers' help. Teachers' ability and effort attributions for success, in turn, predicted a high level of children's subsequent task motivation in reading. Moreover, teachers seldom attributed high‐achieving children's failure to lack of ability or effort.  相似文献   

15.
The current study investigated the development of children's performance on tasks that have been suggested to underlie early mathematics skills, including measures of cardinality, ordinality, and intelligence. Eighty‐seven children were tested in their first (T1) and second (T2) school year (at ages 5 and 6). Children's performance on all tasks demonstrated good reliability and significantly improved with age. Correlational analyses revealed that performance on some mathematics‐related tasks were nonsignificantly correlated between T1 and T2 (number line and number comparison), showing that these skills are relatively unstable. Detailed analyses also indicated that the way children solve these tasks show qualitative changes over time. By contrast, children's performance on measures of intelligence and nonnumerical ordering abilities were strongly correlated between T1 and T2. Additionally, ordering skills also showed moderate to strong correlations with counting procedures both cross‐sectionally and longitudinally. These results suggest that, initially, mathematics skills strongly rely on nonmathematical abilities.  相似文献   

16.
Although the early development of children's number sense is a strong predictor of their later mathematics achievements, it has been overlooked in primary schools in Malaysia. Mainly attributable to underdeveloped number sense of Malaysian primary and secondary school children, their inability to handle simple mathematics tasks, which require the understanding of basic mathematical concepts, numerical estimation, and mental computation, is a cause for worry. To enhance the perception of curriculum designers and mathematics teachers about why and how number sense ought to be developed, this article serves as a review of essential components, theoretical framework, and test of number sense.  相似文献   

17.
The aim of the present longitudinal study was to investigate factors contributing to mothers' and fathers' teaching of reading and mathematics to their children during kindergarten and Grade 1. It was assumed that mothers' and fathers' teaching during kindergarten would be influenced by their socioeconomic status and their own learning difficulties, whereas during Grade 1 by their children's academic performance. A total of 189 mothers and 165 fathers filled in questionnaires regarding their teaching of reading and mathematics twice, once in kindergarten and once in Grade 1. Children's reading and mathematics performance was also examined twice, once in kindergarten and once in Grade 1. The results showed that the lower the socioeconomic status of mothers and fathers, the more teaching of reading and mathematics they reported. Moreover, the lower the children's academic performance in reading and mathematics in the beginning of Grade 1, the more teaching by mothers and fathers reported later on. Overall, the results suggest that mothers and fathers adjust their teaching to the actual skill level of their children when their children enter primary school.  相似文献   

18.
Children's symbolic number sense was examined at the beginning of first grade with a short screen of competencies related to counting, number knowledge, and arithmetic operations. Conventional mathematics achievement was then assessed at the end of both first and third grades. Controlling for age and cognitive abilities (i.e., language, spatial, and memory), number sense made a unique and meaningful contribution to the variance in mathematics achievement at both first and third grades. Furthermore, the strength of the predictions did not weaken over time. Number sense was most strongly related to the ability to solve applied mathematics problems presented in various contexts. The number sense screen taps important intermediate skills that should be considered in the development of early mathematics assessments and interventions.  相似文献   

19.
In this study, we examine whether preventive enrichment of pre-math skills has an influence on number knowledge in preschool children from low income families. Our data analyses use two methods to examine the influence of two independent programs implemented during junior kindergarten and kindergarten. The first implies the traditional approach comparing the self-selected treated group to a self-selected comparison group. The second approach uses a self-selected dosage approach to the treatment condition, considering that implementation of the program varied across teachers. The results regarding the enrichment program in kindergarten were inconclusive. Nevertheless, the pre-math program implemented in junior kindergarten showed a positive influence on children’s core requisite skills for later learning of arithmetic. Although children were receptive during both preschool years, a junior kindergarten program that elaborates upon conceptual issues beyond the number line appears both feasible and beneficial over the short-term.  相似文献   

20.
Children struggle with exact, symbolic ratio reasoning, but prior research demonstrates children show surprising intuition when making approximate, nonsymbolic ratio judgments. In the current experiment, eighty-five 6- to 8-year-old children made approximate ratio judgments with dot arrays and numerals. Children were adept at approximate ratio reasoning in both formats and improved with age. Children who engaged in the nonsymbolic task first performed better on the symbolic task compared to children tested in the reverse order, suggesting that nonsymbolic ratio reasoning may function as a scaffold for symbolic ratio reasoning. Nonsymbolic ratio reasoning mediated the relation between children’s numerosity comparison performance and symbolic mathematics performance in the domain of probabilities, but numerosity comparison performance explained significant unique variance in general numeration skills.  相似文献   

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