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Insight into early precursors of proportional reasoning is necessary to further our theoretical understanding of mathematical development and to guide early interventions. Although several researchers have suggested patterning as a possible precursor for proportional reasoning, there is little empirical evidence to support this assumption, particularly at a young age. To address this gap, the current study explored if patterning in 4- to 5-year-olds (n = 346) is associated with proportional reasoning one and a half years later. Two measures of patterning ability (repeating and growing patterns) and two measures of proportional reasoning (one with discrete quantities and one with a discrete and a continuous quantity) were administered, together with measures addressing general cognitive and numerical abilities. Regression analyses showed that patterning is a unique predictor of proportional reasoning ability over and above sex and general cognitive and numerical abilities. An interaction effect between pattern types and the nature of the quantities was observed: Performance on repeating patterns was uniquely related to performance on proportional reasoning with two discrete quantities, whereas performance on growing patterns was uniquely related to performance on proportional reasoning with a discrete and a continuous quantity. Theoretical implications and suggestions for future studies are discussed.

The present study aimed to analyze the direction of the associations between repeating patterning, growing patterning, and numerical ability. Participants were 410 children who were annually assessed on their repeating patterning, growing patterning, and numerical ability, at ages 4, 5, and 6 years (i.e., spring 2017, 2018, and 2019). A cross-lagged panel model identified bidirectional associations between all three abilities from ages 4 to 5 years while taking into account spatial skills. From ages 5 to 6 years, both patterning abilities predicted later numerical ability, but the reverse was no longer true. Associations between performances on both pattern types also disappeared. Results highlight the unique associations between repeating patterning, growing patterning, and numerical ability, above spatial skills. ispartof: Child Development vol:92 issue:4 pages:1354-1368 ispartof: location:United States status: published

Children’s spontaneous focusing on Arabic number symbols (SFONS) has been identified as a relevant component of their early mathematical development. This study investigated whether SFONS is a sepa...

Young children show large individual differences in their tendency to focus spontaneously on numerical aspects (e.g., numerosities or Arabic number symbols) of their everyday environment. The origins of these individual differences are unclear. Given the role of the home numeracy environment (HNE) in children’s early mathematical development and the assumed link between children’s spontaneous number focusing tendencies and their numerical behavior in everyday life, it is plausible that children’s spontaneous focusing tendencies are related to their HNE. The present study aimed to test this hypothesis by longitudinally investigating children’s spontaneous focusing on numerosity (SFON) and spontaneous focusing on Arabic number symbols (SFONS) in relation to their HNE. Participants were 128 children (4- to 5-year-olds), who were followed from the second until the third year of Flemish kindergarten. In both kindergarten years, children completed a SFON and SFONS Picture task while their parents completed a home numeracy questionnaire. Correlation analyses and structural equation modeling revealed no significant associations between children’s spontaneous number focusing tendencies and their HNE, neither in second nor in third year of kindergarten. This finding suggests that children’s spontaneous number focusing tendencies are not per se related to their HNE. Various possible explanations for this unexpected finding are discussed and directions for further research on this relationship are suggested. ispartof: ZDM Mathematics Education vol:52 issue:4 pages:729-749 status: published

Background Early patterning competence has recently been identified as an important precursor of mathematical development. Whereas the focus of this research has been on children’s ability regarding repeating patterns, children might also differ in their spontaneous attention to patterns. Aims The present study aimed to explore 4‐ to 5‐year olds’ Spontaneous Focusing On Patterns (SFOP) and its association with their patterning and mathematical ability. Sample Participants were 378 children (Mage = 4 years 10 months; 191 boys) from 17 preschools. Methods Spontaneous Focusing On Patterns was measured with a construction task in which children had to build a tower with 15 blocks of three different colours. The constructions of the children were grouped into three categories (i.e., pattern, random, and sorting). We additionally administered tasks assessing their patterning ability, mathematical ability, spatial ability, and visuospatial working memory. Results When building a tower, 37% of the preschoolers spontaneously created a pattern, 49% made a random construction, and 14% sorted the blocks per colour. Preschoolers who spontaneously created a pattern had better patterning and mathematical ability than children in the random group. Group differences in patterning ability and spatial skills accounted for the difference in mathematical ability. Conclusions The current data suggest that children’s spontaneous attention to patterns is an important component of their mathematical ability. Children’s spontaneous pattern constructions may provide opportunities to discuss and practice patterns in preschool settings or at home, but more research is required to further analyse the role of SFOP in early mathematical development. ispartof: British Journal Of Educational Psychology vol:90 issue:3 pages:1-17 ispartof: location:England status: Published online

This study presents a patterning intervention for 5-year-olds, who were in their third year of preschool in Flanders (Belgium), with two key elements: A focus on the structure of patterns, and the inclusion of growing patterns (e.g., ABAABAAAB) in addition to repeating patterns (e.g., ABABAB). We evaluated the impact of this intervention on patterning and numerical ability in a quasi-experimental pretest-intervention-posttest design with a business-as-usual control group. The intervention consisted of a 20 week program with children in the patterning condition receiving weekly 30 min of patterning activities. After the intervention, the patterning group (n = 73) outperformed the control group (n = 74) on both repeating and growing patterns. We observed no transfer effect to children's numerical ability.

O objetivo deste estudo foi examinar as competências numéricas precoces de 355 crianças equatorianas no início do jardim de infância, considerando o tipo de escola que frequentam. As crianças resolveram um teste de habilidades numéricas precoces e um de foco espontâneo na numerosidade. Os resultados revelaram um nível baixo de habilidades numéricas precoces e de foco espontâneo na numerosidade. As crianças que frequentam escolas privadas superaram seus colegas de escolas públicas rurais em habilidades numéricas precoces, porém não no foco espontâneo na numerosidade. Esses achados são discutidos em função da importância de práticas de instrução diferenciadas em matemática precoce no jardim de infância equatoriano. ispartof: Cadernos de Pesquisa vol:51 pages:1-15 status: published

Young children’s early repeating patterning abilities are important foundations for their later mathematical development. Prior studies on young children’s repeating patterning abilities have been conducted exclusively in developed countries differing in economic, societal and educational characteristics from developing countries. In this study, we analyzed the performance and the errors of 4- to 5-year-olds on three repeating patterning tasks, and we investigated the association between children’s repeating patterning abilities and their early mathematical abilities in a developing country, Ecuador. A total of 60 preschoolers and 56 kindergartners completed a repeating patterning test and an early mathematics test at the end of the school year. Results first indicated rather low repeating patterning performances of both preschoolers and kindergartens, with large inter-individual differences in these performances. Kindergartners had significantly better patterning abilities than preschoolers. Second, error analyses indicated that children made different types of errors when solving the patterning tasks. The majority of errors were pattern-related errors, with preschoolers making more errors that were not pattern related than kindergarteners. Third, children’s patterning abilities were positively associated with early mathematical abilities in both grades. These results complement current theoretical models of young children’s mathematical development and inform educational policy and practices in this domain for developing countries. ispartof: European Journal Of Psychology Of Education vol:36 issue:4 pages:1-20 status: Published online

Teachers’ pedagogical content knowledge (PCK) importantly contributes to instructional quality and student outcomes. We aimed to complement the limited insights into preservice preschool teachers’ PCK, and its association with opportunities to learn (OTL), during teacher training. We offered 162 first-to-final-year preservice preschool teachers from two different teacher training institutes in Flanders (Belgium) a recently developed scenario-based instrument addressing students’ understanding of preschoolers’ (mis)conceptions and appropriate instructional strategies in the domain of early mathematics. Our findings revealed quantitative differences between first-year students’ PCK on the one hand and second-year and third-year students’ PCK on the other hand. We did not observe any quantitative differences in PCK between second-year and third-year students. Additional analyses on students’ errors pointed to qualitative differences between first-, second- and third-year students’ PCK. We interpret these findings in view of students’ OTL during teacher training, and discuss their theoretical and methodological implications for future work in the domain of teacher competence. ispartof: ZDM: The International Journal on Mathematics Education vol:52 issue:2 pages:1-12 status: Published online

Many studies have investigated the association between children’s spontaneous attention to number and their early mathematical abilities. This work has presented number in a non-symbolic format by exclusively using numerosities as their stimuli. Therefore, little is known about children’s spontaneous attention for Arabic number symbols. We aimed to address this gap by exploring, for the first time, whether we can observe individual differences in young children’s tendency to spontaneously focus their attention on Arabic number symbols (SFONS) using a newly developed Picture task. We investigated SFONS and its association with spontaneous focusing on numerosity (SFON), numerical abilities, and teacher ratings of mathematical competence in the three years of Flemish kindergarten. One hundred and eleven kindergartners (2 years 4 months – 6 years 2 months of age) completed a battery of tasks to measure their SFONS and SFON, as well as a range of numerical abilities (i.e., Arabic numeral identification, verbal counting, and counting objects). Kindergarten teachers were asked to rate their children’s mathematical competence on a 4-point Likert scale. Findings revealed that children in the three kindergarten years under study largely differed in their tendency to spontaneously attend to Arabic number symbols in the pictures they had to describe. We also observed differences in the levels of SFONS and SFON between the three kindergarten years. Although SFONS and SFON were not strongly associated in the three kindergarten years, significant associations were found between children’s SFONS and their numerical abilities in kindergarten year 1 and 2, and teacher ratings of their mathematical competence in kindergarten year 3. Together, these results suggest that SFONS is a relevant component of children’s early mathematical development. ispartof: Early Childhood Research Quarterly vol:48 pages:111-121 status: published

We investigated the use of the subtraction by addition strategy, an important mental calculation strategy in children with different levels of mathematics achievement. In doing so we relied on Siegler’s cognitive psychological model of strategy change (Lemaire & Siegler, 1995), which defines strategy competencies in terms of four parameters (strategy repertoire, distribution, efficiency and selection), and the choice/no-choice method (Siegler & Lemaire, 1997), which is essentially characterized by offering items in two types of conditions (choice and no-choice). Participants were 63 11-12-year-olds with varied mathematics achievement levels. They solved multi-digit subtraction problems in the number domain up to 1,000 in one choice condition (choice between direct subtraction or subtraction by addition on each item) and two no-choice conditions (obligatory use of either direct subtraction or subtraction by addition on all items). We distinguished between two types of subtraction problems: problems with a small versus large difference between minuend and subtrahend. Although mathematics instruction only focused on applying direct subtraction, most children reported using subtraction by addition in the choice condition. Subtraction by addition was applied frequently and efficiently, particularly on small-difference problems. Children flexibly fitted their strategy choices to both numerical item characteristics and individual strategy speed characteristics. There were no differences in strategy use between the different mathematical achievement groups. These findings add to our theoretical understanding of children’s strategy acquisition and challenge current mathematics instruction practices that focus on direct subtraction for children of all levels of mathematics achievement. ispartof: Journal of Numerical Cognition vol:4 issue:1 pages:215-234 status: published

The number line estimation task is widely used to investigate mathematical learning and development. The present meta-analysis statistically synthesized the extensive evidence on the correlation between number line estimation and broader mathematical competence. Averaged over 263 effect sizes with 10576 participants with sample mean ages from 4 to 14 years, this correlation was r = .443. The correlation increased with age, mainly because it was higher for fractions than for whole numbers. The correlation remained stable across a wide range of task variants and mathematical competence measures (i.e., counting, arithmetic, school achievement). These findings demonstrate that the task is a robust tool for diagnosing and predicting broader mathematical competence and should be further investigated in developmental and experimental training studies. ispartof: Child Development vol:89 issue:5 pages:1467-1484 ispartof: location:United States status: published

We examined children's number-based and digit-based strategy use profiles on multi-digit subtraction problems in relation to task performance and individual (gender, grade, mathematical achievement level) and contextual (country) characteristics. 318 third- to sixth-graders solved a multi-digit subtraction strategy use task, where half of the subtraction problems had number characteristics that stimulated the number-based compensation strategy. First, latent class analyses revealed five strategy use profiles. Most children consistently relied on one strategy (either digit-based strategies or the number-based decomposition or sequential strategies) across problems. Only a minority of children demonstrated strategy variety and flexibility – more often high achievers and children from higher grades. Second, children's strategy instruction history was related to their profile of strategy use, but this relation was less straightforward than generally assumed. Finally, consistent digit-based strategy users were more accurate than consistent decomposition strategy users and varied number-based strategy users.

El objetivo del presente estudio fue examinar la influencia del nivel socioeconómico de los niños de jardín infantil en el desarrollo de sus habilidades numéricas tempranas y su enfoque espontáneo en el número (SFON), después de controlar por variables cognitivas de dominio general, como inteligencia y memoria de trabajo, y por edad. Al iniciar el jardín infantil, 355 niños y niñas resolvieron una batería de pruebas para evaluar sus habilidades numéricas tempranas, SFON, inteligencia y memoria de trabajo. Los resultados indican que existen diferencias individuales en las habilidades numéricas tempranas y el SFON de los niños ecuatorianos al iniciar el jardín infantil. Además, el nivel socioeconómico se correlacionó positivamente con las habilidades numéricas tempranas, pero no con el SFON. Al final se discuten las implicaciones teóricas, metodológicas y prácticas del estudio.

Despite the general agreement regarding the importance of stimulating young children’s early mathematical skills, mathematical learning opportunities in preschool are limited. Educational technology (ET) may be an effective tool to address this problem. Taking into account the weaknesses of previous reviews, we conducted a systematic and comprehensive review of the research literature on the effectiveness of ET in early mathematics education, critically analyzing the findings of studies adhering to a media comparison approach (comparing an ET condition to a non-ET condition or another ET condition) versus studies following a value-added approach (comparing at least two ET conditions which only differ with respect to one feature in the ET or in its implementation). Reviewing 54 studies, we systematically analyzed (1) the effectiveness of ET, (2) the features of the ET and ET implementation associated with ET effectiveness, and (3) child characteristics associated with ET effectiveness. Our analyses indicated that media comparison studies comparing an ET to a non-ET condition provide evidence for the effectiveness of ET for enhancing young children’s mathematical competencies. Second, value-added studies pointed to ET implementation features associated with ET effectiveness, namely teacher support during ET use and an individual grouping structure. Finally, both media comparison and value-added studies revealed that ET effectiveness is associated with children’s performance in the ET and with their prior knowledge. To further advance the field, value-added studies on features of the ET and its implementation are required, as well as studies focusing on important child characteristics that are associated with ET effectiveness. ispartof: International Journal of Child-Computer Interaction vol:27 pages:1-26 status: published

Mathematics-related affect comprises an individual’s attitudes, beliefs, emotions and motivations towards mathematics. These affective constructs have been widely studied in mathematics education and cognitive psychology and have been shown to be related to cognitive outcomes such as performance on a range of mathematical tasks. However, it is not yet clear how these constructs develop, or how they relate to cognitive factors in young children who are in the early stages of learning mathematics. As such, the current special issue focuses on mathematics-related affect in primary school children aged 4 to 10 years. It brings together five recent empirical studies and two discussant articles looking at the development of attitudes, beliefs, emotions and motivations towards mathematics, and the relations between affective and cognitive factors in these young age groups. In this introductory paper, we provide some brief historical context, followed by a rationale for the special issue, and an overview of its structure and scope. ispartof: Educational Studies in Mathematics vol:100 issue:3 pages:201-209 status: published

Recent evidence indicates that young children's spontaneous focusing on numerosity (SFON) uniquely contributes to their early numerical abilities. This study complements previous findings by validating the relation between young children's SFON and their early numerical abilities in a developing country, namely Ecuador. We analysed 355 Ecuadorian 5- to 6-year-olds' SFON in relation to their early numerical abilities at the start of kindergarten, controlling for children's socio-demographic (socio-economic status, age) and general cognitive (working memory, intelligence) characteristics. Our results evidence the unique contribution of Ecuadorian kindergartners' SFON to their early numerical abilities, controlling for children's working memory, intelligence, socio-economic status, and age. Our findings support the validity of previous findings on the unique contribution of SFON to young children's early numerical abilities in developed countries for developing countries. Additionally, they raise timely questions for further theoretical and methodological studies on young children's numerical development worldwide, in developing and developed countries. Statement of contribution What is already known? SFON uniquely contributes to early numerical abilities. However, this is only documented in Finnish samples. Previously only limited control for domain-general cognitive and socio-demographic characteristics. What does the study add? SFON uniquely contributes to early numerical abilities in Ecuadorian 5- to 6-year-olds. This unique contribution remains after controlling for WM, IQ, SES, and age. Evidence for the universal nature of the association between SFON and early numerical ability.

This study investigated the relationship between kindergartners’ Spontaneous Focusing on Numerosity (SFON) and their number-related utterances during numerical picture book reading. Forty-eight 4- to 5-year-olds were individually interviewed via a SFON Imitation Task and a numerical picture book reading activity. We expected differences in the frequency of number-related utterances during picture book reading between children with a higher SFON score, providing more number-related utterances, and children with a lower SFON score. Our results showed large inter-individual differences in both kindergartners’ SFON and the frequency of their number-related utterances during picture book reading, yet SFON was not related to the frequency of number-related utterances. This unexpected result is discussed in terms of its scientific, methodological, and educational implications.

Numerical competencies acquired in preschool are foundational and predictive for children's later mathematical development. It remains to be determined whether there are gender differences in these early numerical competencies which could explain the often-reported gender differences in later mathematics and STEM-related abilities. Using a Bayesian approach, we quantified the evidence in favor of the alternative hypothesis of gender differences versus the null hypothesis of gender equality. Participants were 402 4- to 5-year-old children attending preschool in Flanders (Belgium). Children were selected via stratified cluster sampling to represent the full range of socioeconomic backgrounds. All children completed eight numerical tasks (verbal counting, object counting, numeral recognition, symbolic comparison, nonsymbolic comparison, nonverbal calculation, number order, dot enumeration). Results supported the gender equality hypothesis, and this evidence was substantial for seven of the eight numerical tasks. Preschoolers' early numerical competencies are characterized by gender equality. They probably do not explain later-reported gender differences.

Young children’s spontaneous focusing on numerosity (SFON) predicts their later mathematical competencies. In this study we investigated the development of SFON in Ecuadorian kindergartners as well as the contribution of early numerical abilities and the quality of mathematics education to this development. The participants were 100 kindergartners drawn from 10 classrooms. Children received two SFON tasks, one at the beginning and one at the end of the school year, and an early numerical abilities achievement test at the beginning of the school year. The quality of mathematics education was assessed twice via the COEMET instrument. Results demonstrated limited SFON development during the kindergarten year, with large individual differences in and highly consistent SFON performances. Additionally, children’s SFON development during the kindergarten year was predicted by their SFON tendency and early numerical abilities at the start of the year. The quality of mathematics education did not contribute to children’s SFON development. The scientific and practical implications of these results are discussed.

Children’s Spontaneous Focusing On Numerosity (SFON) predicts later mathematics performance. This association is assumed to rely on children’s self-initiated practice in number recognition during everyday activities, which would enhance their further mathematical development. Consequently, SFON in experimental tasks should be associated with SFON during everyday activities. The present contribution aims to enhance our understanding of this association by critically discussing the major results of two recently conducted studies on the association between SFON in experimental tasks and SFON during picture book reading. Study 1 revealed no association between children’s SFON in an Imitation task and their number-related utterances during numerical picture book reading. Study 2, in which we contrasted two different SFON tasks and their association to picture book reading, revealed a positive association between children’s SFON in the Picture task (but not in the Imitation task) and their number-related utterances during picture book reading. Theoretical, methodological, and educational implications are discussed.

© 2017 The British Psychological Society. We aimed to investigate upper elementary children's strategy use in the domain of multidigit division in two instructional settings: the Netherlands and Flanders (Belgium). A cross-sectional sample of 119 Dutch and 122 Flemish fourth to sixth graders solved a varied set of multidigit division problems. With latent class analysis, three distinct strategy profiles were identified: children consistently using number-based strategies, children combining the use of column-based and number-based strategies, and children combining the use of digit-based and number-based strategies. The relation between children's strategy profiles and their instructional setting (country) and grade were generally in line with instructional differences, but large individual differences remained. Furthermore, Dutch children more frequently made adaptive strategy choices and realistic solutions than their Flemish peers. These results complement and refine previous findings on children's strategy use in relation to mathematics instruction. Statement of contribution: What is already known? Mathematics education reform emphasizes variety, adaptivity, and insight in arithmetic strategies. Countries have different instructional trajectories for multidigit division. Mixed results on the impact of instruction on children's strategy use in multidigit division. What does this study add? Latent class analysis identified three meaningful strategy profiles in children from grades 4-6. These strategy profiles substantially differed between children. Dutch and Flemish children's strategy use is related to their instructional trajectory. ispartof: British Journal of Developmental Psychology vol:36 issue:2 pages:169-187 ispartof: location:England status: published

This study explored the development of Ecuadorian Kindergartners’ spontaneous focusing on numerosity (SFON) during the Kindergarten year, as well as the contribution of early numerical abilities to this development. 100 Kindergartners coming from 10 classrooms received two SFON tasks, one at the beginning and one at the end of the school year, and an early numerical abilities achievement test at the beginning of the school year. Results first demonstrated limited SFON development during the Kindergarten year, with inter-individual differences in and intra-individual stability of children’s SFON tendency. Second, both children’s SFON tendency and their early numerical abilities at the start of the Kindergarten year were predictively related to their SFON tendency at the end of the year. Our results do not only add to our theoretical understanding of SFON in young children, but also inform educational policy and practices in the domain of early mathematics education in Ecuador, as they provide building blocks for optimizing the educational goals and curricula for Kindergarten mathematics. ispartof: European Journal of Psychology of Education vol:32 issue:3 pages:449-462 status: published

BACKGROUND: Young children's spontaneous focusing on numerosity (SFON) as measured by experimental tasks is related to their mathematics achievement. This association is hypothetically explained by children's self-initiated practice in number recognition during everyday activities. As such, experimentally measured SFON should be associated with SFON exhibited during everyday activities and play. However, prior studies investigating this assumed association provided inconsistent findings. AIMS: We aimed to address this issue by investigating the association between kindergartners' SFON as measured by two different experimental tasks and the frequency of their number-related utterances during a typical picture book reading activity. SAMPLE: Participants were 65 4- to 6-year-olds in kindergarten (before the start of formal education). METHODS: Kindergartners individually participated in two sessions. First, they completed an action-based SFON Imitation task and a verbal SFON Picture task, with a short visuo-motor task in between. Next, children were invited to spontaneously comment on the pictures of a picture book during a typical picture book reading activity. RESULTS: Results revealed a positive association between children's SFON as measured by the Picture task and the frequency of their number-related utterances during typical picture book reading, but no such association for the Imitation task. CONCLUSIONS: Our findings indicate that children with higher SFON as measured by a verbal experimental task also tend to focus more frequently on number during verbal everyday activities, such as picture book reading. In view of the divergent associations between our SFON measures under study with everyday number activities, the current data suggest that SFON may not be a unitary construct and/or might be task-dependent. ispartof: British Journal of Educational Psychology vol:88 issue:4 pages:550-565 ispartof: location:England status: published

Background. In the last decades, children’s understanding of mathematical principles has become an important research topic. Different from the commutativity and inversion principles, only few studies have focused on children’s understanding of the addition/subtraction complement principle (if a − b = c, then c + b = a), mainly relying on verbal techniques. Aim. This contribution aims at deepening our understanding of children’s knowledge of the addition/subtraction complement principle, combining verbal and non-verbal techniques. Sample. Participants were 67 third- and fourth-graders (9-10-year-olds). Methods. Children solved two tasks in which verbal reports as well as accuracy and speed data were collected. These two tasks differed only in the order of the problems and the instructions. In the looking back task children were told that sometimes the preceding problem might help to answer the next problem. In the baseline task no helpful preceding items were offered. The looking back task included 10 trigger-target problem pairs on the complement relation. Results. Children verbally reported looking back on about 40% of all target problems in the looking back task; the target problems were also solved faster and more accurately than in the baseline task. These results suggest that children used their understanding of the complement principle. The verbal and non-verbal data were highly correlated. Discussion. This study complements previous work on children’s understanding of mathematical principles by highlighting inter-individual differences in 9-10-year-olds’ understanding of the complement principle and indicating the potential of combining verbal and non-verbal techniques to investigate (the acquisition of) this understanding. ispartof: British Journal of Educational Psychology vol:86 issue:3 pages:382-396 ispartof: location:England status: published

This study analyzed children’s use of mental computation strategies and the standard algorithm on multi-digit subtractions. Fifty-eight Flemish fourth-graders of varying mathematical achievement level were individually offered subtractions that either stimulated the use of mental computation strategies or the standard algorithm in 1 choice and 2 no-choice conditions. In the choice condition, children could apply their preferential strategy on each item; in the no-choice conditions, they had to solve all items with mental computation and the standard algorithm, respectively. Results revealed that children of all achievement levels applied the standard algorithm remarkably frequently and efficiently, even on subtractions that were intended to evoke mental computation. Moreover, children did not fit their strategy choices to the numerical characteristics of the items, but high and above-average achieving children based their strategy choices on their individual mastery of the different strategies. We discuss the theoretical, methodological, and instructional implications of these results. ispartof: European Journal of Psychology of Education vol:31 issue:2 pages:99-116 status: published

This article describes a limited longitudinal European study of young children’s early numeracy development within three testing cycles, onaverage, at the mid-point and towards the end of their fifth to sixth year and again at the mid-point of their sixth to seventh year. Assessment was carried out using the Utrecht Early Numeracy Test (ENT) (Van Luit, Van de Rijt and Pennings, 1994). The multilevel modelling method of analysis used for the study provided an extension of multiple regression to incorporate the hierarchical structure of the data collected, with boys and girls of different social-economic status, nested within different institutions within different countries. The results showed that the ENT was a useful tool for international comparison. The finding that differences between countrieswere negligible was surprising bearing in mind that the English pupils werein formal schooling throughout the testing cycle, the Belgian, German, Greek and Dutch children from the mid-point, and the Slovene children, not at all.

There are two well-known computation methods for solving multi-digit subtraction items, namely mental and algorithmic computation. It has been contended that mental and algorithmic computation differentially rely on numerical magnitude processing, an assumption that has already been examined in children, but not yet in adults. Therefore, in this study, we examined how numerical magnitude processing was associated with mental and algorithmic computation, and whether this association with numerical magnitude processing was different for mental versus algorithmic computation. We also investigated whether the association between numerical magnitude processing and mental and algorithmic computation differed for measures of symbolic versus nonsymbolic numerical magnitude processing. Results showed that symbolic, and not nonsymbolic, numerical magnitude processing was associated with mental computation, but not with algorithmic computation. Additional analyses showed, however, that the size of this association with symbolic numerical magnitude processing was not significantly different for mental and algorithmic computation. We also tried to further clarify the association between numerical magnitude processing and complex calculation by also including relevant arithmetical subskills, i.e. arithmetic facts, needed for complex calculation that are also known to be dependent on numerical magnitude processing. Results showed that the associations between symbolic numerical magnitude processing and mental and algorithmic computation were fully explained by individual differences in elementary arithmetic fact knowledge.

This study investigated the strategy characteristics and development of children with mathematical disabilities (MD) in the domain of simple addition and subtraction, in terms of Lemaire and Siegler’s model of strategic change, using the choice/no-choice method and the combined chronological-age (CA)/ability-level (AL)–match design. Four groups of children, matched on either CA or mathematical AL, solved a series of 36 problems with the bridge over 10 in four conditions. In the choice condition, children could choose between retrieval, decomposition to 10, and counting on to solve each problem. In the retrieval, decomposition, and counting conditions, they had to answer the same 36 problems using retrieval, decomposition to 10, and counting on, respectively. The results revealed clear differences in the frequency, efficiency, and adaptiveness with which the CA-matched children applied the available strategies. In contrast, we observed no differences in strategy frequency, efficiency, and adaptiveness between the AL-matched children. These results support the hypothesis that the strategy development of children with MD is marked by a delay rather than a specific deficit. Moreover, this study further documents the value of the methodology used to study children’s strategy use and development in the domain of simple arithmetic. Centrum voor Instructiepsychologie en -technologie. Leuvens Instituut voor onderwijsonderzoek (LIVO) Departement Pedagogische wetenschappen. Afdeling Didactiek. Centrum voor Orthopedagogiek. ispartof: Journal of Learning Disabilities vol:37 issue:2 pages:119-131 ispartof: location:United States status: published