Early Number Knowledge Research Articles

Teachers’ Actions and Students’ Engagement Behaviors During Number System Knowledge Discussions: Implications for Enhancing Active Engagement

A critical challenge for elementary mathematics teachers is meeting the learning needs of all students, especially when there is variability in students’ number knowledge. Because young students’ number system knowledge (NSK) contributes to future success in mathematics, NSK activities must be designed to engage all students, particularly students who have struggled to engage in mathematics, to help students build early number knowledge. In this manuscript, we describe a quick images number sense intervention implemented across five second-grade teachers and 75 students, and examine outcomes related to teacher actions and student engagement behaviors. The results of our mixed-methods study indicate that the intervention provided multiple ways for students of varying abilities to engage with and learn the content. Our results provide practical implications for teachers, and prompt questions to evaluate in future research.

Children’s understanding of relational language for quantity comparisons

Numerical order and magnitude are important aspects of early number knowledge. We investigated children’s understanding of relational vocabulary for representing and communicating about order (before/after) and magnitude (bigger/smaller, more/less). In Experiment 1, 4- to 7-year-old children compared symbolic numbers, non-symbolic discrete quantities, and continuous amounts using relational words (N = 151). In Experiment 2, 4- to 6-year-old children made yes/no judgements of ordinal and magnitude relations between symbolic numbers (N = 60). Children showed lower performance with ordinal vocabulary compared to magnitude vocabulary (Experiment 1). Further, children were less likely to endorse the use of ordinal language for non-consecutive numbers than consecutive numbers, but showed no difference for magnitude language (e.g., 6 and 7 are bigger than 5, but only 6 comes after 5; Experiment 2). These results suggest a divergence in children’s understanding of magnitude and ordinal vocabulary, suggesting a dissociation between these two concepts and/or the language used to communicate about them.

Movement and Song Idiom Traditional to Enhance Early Mathematical Skills: Gelantram Audio-visual Learning Media

Movement and Song Idiom Traditional to Enhance Early Mathematical Skills: Gelantram Audio-visual Learning Media

Persistent Genetic and Family-Wide Environmental Contributions to Early Number Knowledge and Later Achievement in Mathematics

This study investigated the stable and transient genetic and environmental contributions to individual differences in number knowledge in the transition from preschool (age 5) to Grade 1 (age 7) and to the predictive association between early number knowledge and later math achievement (age 10–12). We conducted genetic simplex modeling across these three time points. Genetic variance was transmitted from preschool number knowledge to late-elementary math achievement; in addition, significant genetic innovation (i.e., new influence) occurred at ages 10 through 12 years. The shared and nonshared environmental contributions decreased during the transition from preschool to school entry, but shared and nonshared environment contributed to the continuity across time from preschool number knowledge to subsequent number knowledge and math achievement. There was no new environmental contribution at time points subsequent to preschool. Results are discussed in light of their practical implications for children who have difficulties with mathematics, as well as for preventive intervention.

The integration of symbolic and non-symbolic representations of exact quantity in preschool children

Preschoolers (n=62) completed tasks that tapped their knowledge of symbolic and non-symbolic exact quantities, their ability to translate among different representations of exact quantity (i.e., digits, number words, and non-symbolic quantities), and their non-symbolic, digit, and spoken number comparison skills (e.g., which is larger, 2 or 4?). As hypothesized, children's knowledge about non-symbolic exact quantities, spoken number words, and digits predicted their ability to map between symbolic and non-symbolic exact quantities. Further, their knowledge of the mappings between digits and non-symbolic quantities predicted symbolic number comparison (i.e., of spoken number words or written digits). Mappings between written digits and non-symbolic exact quantities developed later than the other mappings. These results support a model of early number knowledge in which integration across symbolic and non-symbolic representations of exact quantity underlies the development of children's number comparison skills.

An Analysis of an Assessment Tool for 5-year Old Students Entering Elementary School: The School Entry Assessment Kit

In the Western world, most 5 year old children begin their formal schooling, and do so with diverse proficiencies. A common aim is for teachers to quickly evaluate their proficiencies to identify strengths and gaps, and then begin the teaching of reading and number. This article reports two studies into the item and structural characteristics of a well used instrument administered in the first 6–8 weeks of the students’ school experience. The School Entry Assessment Kit consists of Concepts about Print (CAP) measure of early literacy, Tell Me procedures for oral language and story retelling, and Checkout game for early number knowledge and ability. The first study reviews the properties of these tests, and the second study relates the performance on the SEA with performance 1 and 5 years later. Implications for measuring progress, reviewing the tests, enhancing reporting, and reducing administration time are discussed.

The role of indigenous traditional counting systems in children's development of numerical cognition: results from a study in Papua New Guinea

The Government of Papua New Guinea undertook a significant step in developing curriculum reform policy that promoted the use of Indigenous knowledge systems in teaching formal school subjects in any of the country's 800-plus Indigenous languages. The implementation of the Elementary Cultural Mathematics Syllabus is in line with the above curriculum emphasis. Given the aims of the reform, the research reported here investigated the influence of children's own mother tongue (Tok Ples) and traditional counting systems on their development of early number knowledge formally taught in schools. The study involved 272 school children from 22 elementary schools in four provinces. Each child participated in a task-based assessment interview focusing on eight task groups relating to early number knowledge. The results obtained indicate that, on average, children learning their traditional counting systems in their own language spent shorter time and made fewer mistakes in solving each task compared to those taught without Tok Ples (using English and/or the lingua franca, Tok Pisin). Possible reasons accounting for these differences are also discussed.

Early number knowledge and cognitive ability affect early arithmetic ability

Previous literature suggests that early number knowledge is important for the development of arithmetic calculation ability. The domain-general ability of verbal working memory also has an impact on arithmetic ability. This longitudinal study tested the impact of early number knowledge and verbal working memory on the arithmetic calculation ability of children in preschool (N=315) and then later in Grade 1 using structural equation modeling. Three models were used to test hypotheses drawn from previous literature. The current study demonstrates that both early number knowledge and the domain-general ability of verbal working memory affect preschool and Grade 1 arithmetic ability. Early number knowledge had a direct impact on the growth of arithmetic ability, whereas verbal working memory had only an indirect effect via number knowledge and preschool arithmetic ability. These results fit well with von Aster and Shalev’s developmental model of numerical cognition (Developmental Medicine & Child Neurology, 2007, Vol. 49, pp. 868–873) and highlight the importance of considering arithmetic ability as independent from early number knowledge. Results also emphasize the importance of training early number knowledge before school entry to promote the development of arithmetic ability.

The relation between spatial skill and early number knowledge: the role of the linear number line.

Spatial skill is highly related to success in math and science (e.g., Casey, Nuttall, Pezaris, & Benbow, 1995). However, little work has investigated the cognitive pathways by which the relation between spatial skill and math achievement emerges. We hypothesized that spatial skill plays a crucial role in the development of numerical reasoning by helping children to create a spatially meaningful, powerful numerical representation-the linear number line. In turn, a strong linear number representation improves other aspects of numerical knowledge such as arithmetic estimation. We tested this hypothesis using 2 longitudinal data sets. First, we found that children's spatial skill (i.e., mental transformation ability) at the beginning of 1st and 2nd grades predicted improvement in linear number line knowledge over the course of the school year. Second, we found that children's spatial skill at age 5 years predicted their performance on an approximate symbolic calculation task at age 8 and that this relation was mediated by children's linear number line knowledge at age 6. The results are consistent with the hypothesis that spatial skill can improve children's development of numerical knowledge by helping them to acquire a linear spatial representation of numbers.

"The relation between spatial skill and early number knowledge: The role of the linear number line": Correction to Gunderson et al. (2012).

"The relation between spatial skill and early number knowledge: The role of the linear number line": Correction to Gunderson et al. (2012).

Cardinal number and its representation: skills, concepts and contexts

Surprisingly little is known about the extent of children’s knowledge about number beyond their ability to recite, read and write numbers and count quantities of objects. There is little information on the extent to which children are aware of how number is used in their everyday environment or of how much they gain from such early exposure. The extent to which current curriculum frameworks build upon early number knowledge and provide early experience of practical problem‐solving is also unknown. Comparative research was carried out with children in the period before they begin their formal education. The findings suggest that young children may not be equipped with the concepts essential for representing number in the domains of counting and cardinality. The results have implications for early years curricula to ensure a secure base on which to successfully teach number operations and problem‐solving.