Children's Number Sense Research Articles

Efficacy of Learning Disorder Treatment for Reading or Mathematics Disorders: An Open Study.

This study aimed to identify the effectiveness of treatment programs for children with reading (RD) or mathematics disorders (MD). Structured treatment programs were developed to improve phonological awareness and number sense among children and adolescents with RD or MD, respectively, and the effectiveness of the learning disorder treatment programs were evaluated. We used standardized, objective diagnostic, and evaluation tools not only to recruit participants with RD, MD, or comorbid attention deficit and hyperactivity disorder, but also to assess the effectiveness of the treatments regarding both improved core neurocognitive deficits of RD or MD and academic achievement. Forty children with RD or MD received one-on-one treatments from therapists. In the RD group, treatment effects were observed in all subtests. In the word and paragraph reading tests, the accuracy rates and fluency improved. The results of the phonological working memory test, word-sound correspondence test, and rapid automatic naming tests also improved. In the MD group, the accuracy rate and fluency on the arithmetic test improved. An increase in the accuracy rate in the size and distance comparison tests and a decrease in the error rate in the estimation test were also observed. However, there were no improvements in reaction time in these subtests. Learning disorder treatment programs that focus on improving phonological awareness or number sense in children with RD or MD improved achievement, phonological awareness, and number sense.

The relationship between family socioeconomic status and the young children's number sense development: The mediating role of parent-child activities.

This study examines the relationship between family socioeconomic status, parent-child activities, and young children's digital development. Using the Family SES questionnaire, the parent-child activities questionnaire, and the 5 to 6 year old children's number sense development scale as research instruments, 314 young children (M = 70.42, SD = 3.47). The results show that: (1) Family Socioeconomic Status can significantly positively predict the young children's number sense development; (2) Parent-child activities play a partial mediating role in the relationship between family socioeconomic status and the young children's number sense development. This study provides specific guidelines and recommendations for improving the young children's number sense development.

Age-related trends of number sense in children with and without neurodevelopmental disorders

Age-related trends of number sense in children with and without neurodevelopmental disorders

Multiplication facts and number sense in children with mathematics learning disabilities and typical achievers

Two age groups of children with math learning disabilities (MLD) (mean age (years; months): 12;2 [sixth graders], and 13;10 [eighth graders]) and four age groups of typically achieving (TA) children (mean age: 7;8, 8;9, 9;7 and 11;9, for second, third, fourth, and sixth graders, respectively) as well as adults performed a simple multiplication production test. Four aspects of performance were compared: retrieval vs. procedural frequency, accuracy, response times, and error plausibility (implausible errors were defined as either far, five- or parity-rule violating, non-table, or decade inconsistent errors). MLD sixth graders performed similar to TA second graders. MLD eighth graders improved only on easy problems (i.e., problems involving numbers ≤5 and duplicate numbers) and performed similar to TA fourth graders. Number sense development in children with MLD is discussed.

Validity and Reliability Study for the Turkish Version of Number Sense Screener for 60-71 Months Old Children

In this study, it was aimed to carry out the validity and reliability study of Number Sense Screener (NSS)’s Turkish version for 60-71 year-old children. The universe of the study in which general survey model was used consists of children at 60-71 years of age, who were continuing their education during the spring term of academic year 2017-2018 in public and private kindergartens under the Ministry of National Education within the central district of Aydin/Turkey. As for the sample of the study, 658 children contunuing their education in 12 different preschools pre-determined according to socioeconomic status (low-middle-high) were included through systematic sampling method. Validity and reliability studies were carried out using data from the NSS application. Drawing from the analyses, it was determined that item difficulty values of the assessment tool ranged between 0.08 and 0.96, item discrimination indices ranged between 0.17 and 0.53 and item infit and outfit values ranged between 0.50-1.50. Having used Guttman's lambda-2, Alpha coefficient, Feldt-Gilmer coefficient, Feldt-Brennan coefficient and Raju's beta coefficient, it was determined that reliability coefficient calculated for the entire assessment tool varied between .826 and .837. Following DIF analysis, it was concluded that assessment tool items were not biased towards gender. According to the results of the study, it was concluded that the Turkish version of NSS is a valid and reliable assessment tool for assessing the number sense of children at 60-71 months of age.

An Exploratory Study of a Story Problem Assessment: Understanding Children's Number Sense

The purpose of this study was to identify and describe students' use of number sense as they solved story problem tasks. Three 8- and 9-year-old students participated in clinical interviews. Through a process of holistic and qualitative coding, researchers used the number sense view as a theoretical framework for exploring how students' number sense was reflected in their numerical reasoning and verbal explanations of strategies for solving story problems. The results suggest that students' coordination of number sense constructs affords flexibility in problem-solving and deeper understanding of place value. Implications for classroom practice and mathematics education research are discussed.

Developing Children's Number Sense Using Calculators

In the past, most people believed that calculators were useful only for obtaining or checking answers to computation problems. Therefore, in many ways they have often been ignored as a teaching resource. Based on the lack of interest, some parents and teachers have shied away from calculator's use, especially in primary mathematics. Many researchers have also found that using calculators as a teaching aid is most useful and effective in developing number sense and mental computation. The Calculator-Aware Number (CAN) project in Britain found that children develop their own strategies for carrying out calculations and achieve a high level of numeracy when using calculators

Calling for the development of children's number sense in primary schools in Malaysia

ABSTRACTAlthough 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.

Pathways of Number Line Development in Children

Dyscalculia, or mathematics learning disability, has received growing attention in recent years. Working memory and number sense are hypothesized to form important determinants of dyscalculia, but longitudinal assessments of number sense in children with or at-risk for dyscalculia are scarce. The current study investigated number line development in first and second grade, in addition to kindergarten predictors and mathematical proficiency as an outcome. Children (n = 396) could be divided into three latent growth classes: at-risk, catch-up, and typical, based on their number line development. Growth was predicted by kindergarten number sense and verbal working memory. According to the class to which they were assigned, children differed in mathematical proficiency at the end of grade 2. The current study makes an important contribution to the understanding of risk for dyscalculia, showing that children at-risk can be distinguished based on their number line development, and that kindergarten variables are predictive of subsequent development.

Evaluation of a Parent Training Program for Promoting Filipino Young Children's Number Sense with Number Card Games

Not all parents are skilled in scaffolding their young children’s numeracy learning. The present study investigated the effectiveness of a parent training program in promoting Filipino young children’s number sense via card game playing at home. Participants were 161 young children and their parents; families were of a relatively low socioeconomic status. During the 10-week intervention period, parents in the experimental group received training on how to use number game cards to help their children acquire various numeracy concepts; parents in the control group received no special instructions. Children in the experimental group showed greater improvements in their performance on six number sense tasks (namely numeral identification, object counting, rote counting, missing number, numerical magnitude comparison, and addition) over the intervention period than did children in the control group. Findings of the present study suggest that providing simple training to parents on strategies for fostering their young children’s number sense at home is important for giving children a good early start in basic number knowledge.

Numerical landmarks are useful—except when they’re not

Placing landmarks on number lines, such as marking each tenth on a 0–1 line with a hatch mark and the corresponding decimal, has been recommended as a useful tool for improving children’s number sense. Four experiments indicated that some landmarks do have beneficial effects, others have harmful effects, and yet others have no effects on representations of common fractions (N/M). The effects of the landmarks were seen not only on the number line task where they appeared but also on a subsequent magnitude comparison task and on correlations with mathematics achievement tests. Landmarks appeared to exert their effects through the encodings and strategies that they promoted. Theoretical and educational implications are discussed.

Cognitive phenotype of mathematical learning disabilities: What can we learn from siblings?

The sensitivity of number sense as cognitive phenotype for mathematical learning disabilities (MLD) was assessed in siblings of children with MLD (n = 9) and age matched children without family members with MLD (n = 63). A number line estimation paradigm was used as a measure of children's early number sense. In line with the triple code model of Dehaene (1992), three different presentation formats were presented. The results of the study confirmed that number line estimation was related to early arithmetic achievement in kindergarten. In addition siblings were less proficient in number line placements compared to non-siblings, with a larger effect size for symbolic and especially number word estimation compared to the non-symbolic results. Siblings also differed from non-siblings on procedural and conceptual counting skills and logical thinking in kindergarten. Moreover MLD had a familial aggregation, since about three out of five sibling girls had clinical scores on an Early Numeracy Test in kindergarten, pointing to a risk to develop MLD themselves. Implications of the study to our understanding of MLD are discussed.

Development and Validation of a Computer‐Administered Number Sense Scale for Fifth‐Grade Children in Taiwan

To investigate the structure of number sense and then to assess its uses in fifth‐grade children's number sense development, a computerized number sense scale was developed and evaluated. The findings of the study indicate that the newly developed scale, with four dominant factors identified and reconfirmed, is internally consistent and substantially valid. It can be reliably used as a screening measure for a quick check of students' number sense development via online self‐assessment. Compared with our previous study, both qualitative and quantitative changes were detected in students' number sense development at different grades. The qualitative change in number sense development is manifested in different numbers of factor components produced at different grades. The quantitative change is manifested in different amounts of factor variance explained at different grades. Furthermore, among the four aspects of number sense, Taiwanese students perform best on recognizing the relative number size yet relatively worse on judging the reasonableness of computational results.

Mental number line, number line estimation, and mathematical achievement: Their interrelations in grades 5 and 6.

As indicated by the distance effect and the spatial-numerical association of response codes (SNARC) effect, natural numbers are mentally represented on a number line, Purportedly, this number line underlies children's number sense, which supports the acquisition of more advanced mathematical competencies, In 3 studies with a total of 429 fifth and sixth graders, the authors compared the influences of each child's distance effect, SNARC effect, conceptual knowledge about decimal fractions, and numerical intelligence on mathematical school achievement. Additionally, they tested using decimal fractions whether number line estimation competence mediates the influence of the internal number line. In all, the results, found with path models, revealed that domain-specific conceptual knowledge, numerical intelligence, and number line estimation each were good predictors of achievement, while distance and SNARC effects were virtually unrelated to all other variables. Individual differences in the use of the internal number line, as assessed by these 2 effects, seem to be of little importance when it comes to the acquisition of the content of 5th- and 6th-grade mathematics lessons. The results instead highlight the importance of conceptual understanding and estimation competence

Using Kindergarten Number Sense to Predict Calculation Fluency in Second Grade

Children's number sense in kindergarten was used to predict their calculation fluency in second grade (N = 198). Using block entry regression, usual predictors of age, reading, memory, and verbal and spatial cognition were entered in the first block and number sense measures were added in the second block. Number sense measures contributed a significant amount of variance over and above the more general predictors (26%—42%). Uniquely predictive subareas were active memory for numbers, number knowledge, and number combinations, with number combinations standing out as the strongest single predictor. Number sense screening in kindergarten, using “at-risk” versus “not-at-risk” criteria, successfully ruled out 84% of the children who did not go on to have calculation fluency difficulties and positively identified 52% of the children who later showed fluency difficulties. The relation of early number skills to later calculation fluency has important implications for math screening and intervention.

The primary mathematics curriculum: enhancing its potential for developing young children's number sense in the early years at school

A sense of number is now generally recognised as a central factor in learning, and later applying, mathematics. Consequently, number sense is increasingly emphasised in curriculum documentation related to mathematics. The Primary School Curriculum: Mathematics, published by the Government of Ireland in 1999, is no exception. It implicitly stresses the importance of number sense and draws teachers’ attention to a range of key aspects. This article examines how numbers sense is defined generally, how it is explicated in the curriculum for the youngest children at primary school, and the nature of the guidance that curriculum documentation provides to teachers in relation to developing young children's number sense. The curriculum documentation is examined in terms of a socio-culturally related framework which the author developed for considering number sense as it pertains to young children. This framework has four aspects: pleasure and interest in number; understandings of the purposes of number; quantitative thinking; and awareness/understanding of numerals. A number of areas of omission were identified in the teacher guidelines that accompany the curriculum documents. Implications are drawn with respect to a review of the current documents related to early years mathematics, and areas for potential development are outlined.

Young Children's Number Sense in China and Finland

This study examined the influence of nationality, age and gender on Chinese (N = 130) and Finnish (N = 203) pre‐schoolers' number sense. Two highly correlated aspects of number sense were extracted: one reflecting the children's ability to organise and compare quantities (i.e. relational skills), and another pertaining to their ability to operate with number‐word sequence (i.e. counting skills). The results showed a significant age‐related gain in both aspects of number sense, whereas no gender differences were found. With respect to counting skills, the Chinese children outperformed the Finnish children irrespective of age, whereas in relation to relational skills, this was true only among the older children. Differences in language, teaching and cultural ethos are considered as alternative explanations for the findings.

The development of young children's number sense through participation in sociocultural activity: Profiles of two children

SUMMARY Children's accounts of their participation in sociocultural activity related to number are essential for their teachers in order that they can assist children in building their formal learning in number on informally acquired numerical understandings. Children's participation in sociocultural activity related to number will differ from child to child. This study explores some of those differences as conveyed by children who, from their own perspectives, recount their experiences with number. Individual experience-based flexible focused clinical interviews were held with a number of children. In discussion, children in the study tell the story of their participation in numerical learning, the guidance they received, their collaboration with others and the extent to which they suggest that they control their own learning. Individual profiles were drawn up from the interview data and these portray how children appeared to participate in numerically-related learning, how they appeared to be supported in that participation and how participation in such events appeared to prepare them for their participation in the interviews. The two profiles discussed in this paper show the importance of affect in relation to children's cognitive development in the domain of number. Implications are drawn for curriculum, assessment and pedagogy. The data presented here are part of a larger study related to number sense as it pertains to young children at the point of entry to school in Ireland.

Young children's number sense in Finland, Hong Kong and Singapore

This study examines young children's number sense in subjects from Finland (n=254), Hong Kong (n=246), and Singapore (n=130). Chinese, English and Finnish versions of the Early Numeracy Test (ENT; Van Luit et al., 1994) were used. Two highly correlated aspects of number sense were measured, one reflecting children's abilities to organize and compare quantities (i.e. relational skills), and the other pertaining to their ability to operate with number-word sequence (i.e. counting skills). The results showed significant age-related gain on the relational and counting scales. No gender or language differences were found. The children in Hong Kong and Singapore outperformed those in Finland in relational and counting tasks starting at the age of four years. The children in Singapore also had better relational and counting skills than those in Hong Kong. Differences in teaching were assumed to explain the findings.

Teaching and Learning Number Sense – An Intervention Study of Fifth Grade Students in Taiwan

Two classes (one experimental and one control) in a public elementary school located in southern Taiwan participated in this study. Number sense activities were conducted in the experimental class as supplementary teaching materials, while the control class followed the standard mathematics curriculum. Data indicate that there are statistically significant differences between pretest and posttest (pretest and retention-test) scores for the experimental and control classes at the 0.01 level. The scores for the experimental class increased 44% after instruction (the mean score went from 12.35 to 17.81), while the scores for the control class increased only 10% after instruction (the mean score went from 11.29 to 12.42). Compared to the control class, the experimental class made much more progress on number sense tests. Results indicate that students in the teaching class (not including the students in the low level) advanced in their use of number sense strategies when responding to interview questions. The data demonstrate that the teaching of number sense activities, executed in the experimental class, is effective in developing children's number sense. Furthermore, the results of retention demonstrate that the students' learning was meaningful and significant.