In countries with a social pedagogic tradition for early childhood education, mathematical learning typically takes place in play-based situations. Preschool teachers’ ability to recognize ...mathematical content in children’s play is therefore an important prerequisite for educational quality. The present study examines how this ability relates to other aspects of preschool teachers’ professional competencies. Findings from regression analysis indicate that mathematical content knowledge (CK) predicts teachers’ sensitivity to mathematical content. However, further analyses reveal that this association is mediated by preschool teachers’ self-efficacy beliefs.
•We investigated preschool teacher’s mathematical competencies.•The competencies studied were professional knowledge, self-efficacy & self-concept.•Teacher’s math self-efficacy and self-concept were correlated.•Content knowledge (CK) predicted teachers’ sensitivity to mathematics.•Self-efficacy mediated the relationship between CK and teachers’ sensitivity.
•The present study was designed to investigate the best modeling procedure to teach the cardinality principle (CP).•Three intervention conditions involved: (a) label and then count (label-first), (b) ...count, label, and emphasize the last word (count-first), and (c) counting only.•How many—a direct measure of the CP was used as the main task to investigate CP understanding, and give-me-n—an indirect measure of the CP was used as transfer task to investigate meaningful application of the CP.•The count-first strategy provides a more efficacious way to model the CP, because it entails a closer temporal connection between the last number word of a count and the stated cardinal value of a collection.•Modeling the CP should capitalize on children’s subitizing ability to reinforce the purpose of counting for determining the number of objects in a collection and to promote understanding of the CP.
The cardinality principle (CP), which specifies that the last number word used in the counting process indicates the total number of items in a collection, is a critically important aspect of numeracy. Only one published study has focused on how best to teach the CP, and its results are uncertain (Mix, Sandhofer, Moore, & Russell, 2012). The present study was designed to investigate several modeling procedure to teach the CP. Forty-nine 2–5-year olds were randomly assigned to one of the three interventions: (a) label and then count (label-first), (b) count with an emphasis on the last word and label (count-first), and (c) counting only. At a delayed posttest, the count-first intervention was substantively more efficacious than the other interventions at promoting success on the CP task and a transfer task (as measured by effect size). The results underscore the need for early childhood educators and parents to reinforce the purpose of counting by building on children’s subitizing ability and explicitly labeling the total number of items after a collection is counted.
•Acquisition of the cardinality is crucial to the development of early numerical skills•The richness of number inputs children receive influences the acquisition of cardinality•A finger-based ...enriched intervention accelerated the understanding of cardinality in 3-year-olds•The intervention can be easily implemented into real-life learning settings
The acquisition of cardinal numbers represents a crucial milestone in the development of early numerical skills and more advanced math abilities. However, relatively few studies have investigated how children's grasping of the cardinality principle can be supported. It has been suggested that the richness of number inputs children receive influences the acquisition of cardinal numbers. The present study was designed to investigate whether canonical finger patterns representing numbers may contribute to this acquisition. Fifty-one 3-year-olds were randomly assigned to 1 of 2 training conditions: (a) a condition that involved counting and labeling, which has shown efficacy to support the acquisition of cardinality, and (b) a condition in which counting and labeling were enriched with finger patterns. Crucially, we aimed at providing evidence of both training programs in a real-life learning environment where teachers incorporated the training as a group-based activity into their regular schedule of daily activities. Children assigned to the finger-based condition outperformed those who received the counting-and-label training. Findings suggest that finger patterns may have a role in children's cardinality understanding. Furthermore, our study shows that instructional approaches for improving cardinality understanding can be easily and successfully implemented into real-life learning settings.
•Person-centered analysis captures variability in low-income preschoolers’ math.•Four profiles emerged with different patterns of strength and weaknesses.•Patterns of performance by profile varied ...across numerical skills assessed.•Age, working memory, inhibitory control predicted numerical skills profile.•Many children need more support in magnitude understanding.
On average, preschoolers from lower-income households perform worse on symbolic numerical tasks than preschoolers from middle- and upper-income households. Although many recent studies have developed and tested mathematics interventions for low-income preschoolers, the variability within this population has received less attention. The goal of the current study was to describe the variability in low-income children’s math skills using a person-centered analysis. We conducted a latent profile analysis on six measures of preschoolers’ (N = 115, mean age = 4.6 years) numerical abilities (nonsymbolic magnitude comparison, verbal counting, object counting, cardinality, numeral identification, and symbolic magnitude comparison). The results showed different patterns of strengths and weaknesses and revealed four profiles of numerical skills: (a) poor math abilities on all numerical measures (n = 13), (b) strong math abilities on all numerical measures (n = 41), (c) moderate abilities on all numerical measures (n = 35), and (d) strong counting and numeral skills but poor magnitude skills (n = 26). Children’s age, working memory, and inhibitory control significantly predicted their profile membership. We found evidence of quantitative and qualitative differences between profiles, such that some profiles were higher performing across tasks than others, but the overall patterns of performance varied across the different numerical skills assessed.
Young children's symbolic magnitude understanding, or knowledge of how written numerals and number words can be ordered and compared, is thought to play an important role in their mathematical ...development. There is consistent evidence that symbolic magnitude skills predict mathematical achievement in later childhood and adulthood. Yet less is known about symbolic magnitude understanding before the start of formal schooling, a time when children are rapidly developing knowledge of small whole numbers. In this study, preschoolers (N = 140, Mean age = 4 years, 5 months) were assessed using measures of numerical skills (cardinality, symbolic magnitude, addition) and executive functioning (working memory, inhibitory control, attention shifting) in the winter and spring of the school year. Symbolic magnitude predicted later addition skills, fully mediating the relation between children's cardinality and addition skills. Moreover, children's domain-general executive functioning skills and domain-specific numeracy skills explained a similar amount of variability in children's later addition skills. Results highlight the role of symbolic magnitude in the development of children's understanding of mathematics.
How does improving children's ability to label set sizes without counting affect the development of understanding of the cardinality principle? It may accelerate development by facilitating ...subsequent alignment and comparison of the cardinal label for a given set and the last word counted when counting that set (Mix et al., 2012). Alternatively, it may delay development by decreasing the need for a comprehensive principle to understand and label exact numerosities (Piantadosi et al., 2012). In this study, preschoolers (N = 106, Mage = 4;8) were randomly assigned to one of three conditions: (a) count‐and‐label, wherein children spent 6 weeks both counting and labeling sets arranged in canonical patterns like pips on a die; (b) label‐first,wherein children spent the first 3 weeks learning to label the set sizes without counting before spending 3 weeks identical to the count‐and‐label condition; (c) print referencing control. Both counting conditions improved understanding of cardinality through increases in children's ability to label set sizes without counting. In addition to this indirect effect, there was a direct effect of the count‐and‐label condition on progress toward understanding of cardinality. Results highlight the roles of set labeling and equifinality in the development of children's understanding of number concepts.
In this study, preschoolers (N = 106, Mage = 4; 8) were randomly assigned to one of three conditions: (a) count‐and‐label, wherein children spent 6 weeks both counting and labeling sets arranged in canonical patterns like pips on a die; (b) label‐first, wherein children spent the first 3 weeks learning to label the set sizes without counting before spending 3 weeks identical to the count‐and‐label condition; (c) print referencing control. Both counting conditions improved understanding of cardinality through increases in children's ability to label set sizes without counting. In addition to this indirect effect, there was a direct effect of the count‐and label condition on progress toward understanding of cardinality.
This study examined the relation between the amount of mathematical input in the speech of preschool or day-care teachers and the growth of children's conventional mathematical knowledge over the ...school year. Three main findings emerged. First, there were marked individual differences in children's conventional mathematical knowledge by 4 years of age that were associated with socioeconomic status. Second, there were dramatic differences in the amount of math-related talk teachers provided. Third, and most important, the amount of teachers' math-related talk was significantly related to the growth of preschoolers' conventional mathematical knowledge over the school year but was unrelated to their math knowledge at the start of the school year.
This study analysed how preschool teachers differently enacted the same mathematical activity for preschool children to discern numbers, and how this affected the children’s learning opportunities ...during the activity. The analysis was based on variation theory and Chi’s taxonomy of learning activities. Two Swedish preschool teachers’ enactment of the same mathematical activity for 27 children aged 4–6 years was studied. Video recordings of what the children were offered to discern were used in the analysis. The results indicate that variations in how the teachers chose to enact the activity produced two different learning opportunities for the children. Differences in what aspects were made discernible were closely linked to the characteristics of the activity implemented. The enactments differed even if the same game was chosen and the same amount of time was used in the play-based activity. In one preschool group, there were few opportunities to discern more than the nominal form of numbers; the other preschool group had an activity focused on all number forms simultaneously. In addition, in the latter group, the children had the opportunity to develop equinumerosity. The results suggest that the activity with limited variation was more appropriate for learning with undeveloped knowledge; the children with more developed understanding required a more varied design. This study contributes to the knowledge of how the design of an activity affects children’s learning differently, which is important when planning learning-based preschool activities.
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