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While symbolic number processing is an important correlate for typical and low mathematics achievement, it remains to be determined whether children with high mathematics achievement also have excellent symbolic number processing abilities. We investigated this question in 64 children (aged 8 to 10), i.e., 32 children with persistent high achievement in mathematics (above the 90th percentile) and 32 average-achieving peers (between the 25th and 75th percentile). Children completed measures of symbolic number processing (comparison and order). We additionally investigated the roles of spatial visualization and working memory. High mathematics achievers were faster and more accurate in order processing compared to average achievers, but no differences were found in magnitude comparison. High mathematics achievers demonstrated better spatial visualization ability, while group differences in working memory were less clear. Spatial visualization ability was the only significant predictor of group membership. Our results therefore highlight the role of high spatial visualization ability in high mathematics achievement.

This study examined adults’ frequent, efficient and adaptive use of direct subtraction (DS) and subtraction by addition (SBA) in mental multi-digit subtraction with the choice/no-choice method. Participants were offered subtractions in one choice condition (choice between DS and SBA) and two no-choice conditions (mandatory use of either DS or SBA). SBA was used as frequently as DS in the choice condition. DS was most accurate on subtractions with a large difference (e.g., 502 – 18), while SBA was fastest on subtractions with a small difference (e.g., 903 – 886). In general, participants were adaptive for task characteristics and their personal speed characteristics. We further analyzed task-based adaptivity on an individual level via a Latent Class Analysis. Results showed that two-thirds of the participants were adaptive to task characteristics, and that these adaptive participants were the most proficient in accuracy and speed in the choice condition. We further examined whether executive functions (updating, inhibition, shifting) were related to individual differences in strategy efficiency and task-based adaptivity. In line with our hypothesis, updating was related to strategy efficiency, such that participants with higher updating skills were more accurate. In contrast to our expectations, inhibition and shifting were not related to task-based strategy adaptivity. This study highlights adults’ efficient and adaptive use of arithmetic strategies, and its association with their proficiency and executive functions.

High-quality instruction in preschool is important for children's mathematical development. To date, the domain-specific elements constituting mathematics instruction quality and the factors associated with this quality are hardly studied, resulting in serious gaps in our insights into the topic. We aimed to address this gap by investigating (a) 43 preschool teachers' mathematical questioning behavior during shared picture book reading, and (b) its association with picture book and teacher characteristics. We analyzed the number and the level of abstraction of mathematical questions when sharing a mathematical (i.e., written with explicit mathematical aim and content) and a non-mathematical (i.e., written without explicit mathematical aim and content) picture book, and their associations with teachers' professional competence. For mathematical and non-mathematical picture books, teachers formulated mathematical questions, mainly at lower levels of abstraction. They formulated more, but proportionally less abstract, mathematical questions when sharing a mathematical versus a non-mathematical picture book. We found only limited evidence for associations between teachers' questioning behavior and their professional competence. Our findings indicate that preschool teachers offer opportunities to engage in mathematical interaction during shared picture book reading, pointing to the potential of this activity to implement high-quality mathematics instruction. They further show that mathematical picture books enable more mathematical interaction than non-mathematical picture books, but not at higher levels of abstraction. Future studies are needed to replicate and complement our findings, with special attention for the contribution of teacher professional competence and the fit to children's competency level.

El propósito del estudio fue examinar si los niños preescolares se enfocan espontáneamente en estructuras matemáticas –patrones y clasificación– y si dicho enfoque se asocia con sus habilidades para trabajar patrones. La metodología fue cuantitativa de tipo descriptivo y comparativo. Participaron en el estudio 60 preescolares que fueron evaluados al finalizar el año escolar. Los resultados indicaron que la mayoría de ellos se enfoca espontáneamente en crear una estructura matemática y que no existe asociación entre su tendencia a enfocarse en estructuras matemáticas y su habilidad para trabajar patrones. No se observaron diferencias en el enfoque espontáneo relacionadas al género ni al nivel socioeconómico. Se concluye que estos resultados permiten apuntar a la naturaleza universal del enfoque espontáneo en estructuras matemáticas.

In recent years, an increasing number of studies have examined the association between mathematical abilities and executive functions (EFs). However, it remains unknown via which mechanisms' mathematical performance is associated with EFs. The current study examined the associations of overall task proficiency, strategy selection, and strategy execution when solving multi-step subtraction problems with three EFs (i.e., updating, inhibition, and shifting). With a choice/no-choice design, 150 fifth-graders' (M[subscript age] = 10 years, 11 months) direct subtraction (DS; e.g., 712 - 346 = ?; 712 - 300 = 412, 412 - 40 = 372, and 372 - 6 = 366) and subtraction by addition (SBA; e.g., 712 - 346 = ?; 346 + 54 = 400, 400 + 300 = 700, 700 + 12 = 712, and 54 + 300 + 12 = 366) use to solve multi-step subtractions was examined. Participants were offered ten subtractions in one choice condition (free choice between DS and SBA), based on which we obtained data about task proficiency and strategy selection, and in two no-choice conditions (mandatory use of either DS or SBA), which were used to examine strategy execution. The results showed that task proficiency in the choice condition was associated with updating and inhibition but not with shifting. Furthermore, strategy selection was associated with updating but not with inhibition and shifting. Strategy execution was associated with updating but not with inhibition and shifting. The inclusion of separate strategy selection and execution parameters helped to unravel how arithmetic performance and EFs are associated.

Resumen El objetivo de este estudio fue examinar las competencias numéricas tempranas de 355 niños ecuatorianos al iniciar el jardín infantil, teniendo en cuenta el tipo de escuela a la que asisten. Los niños resolvieron una prueba de habilidades numéricas tempranas y una de enfoque espontáneo en la numerosidad. Los resultados revelaron un nivel de habilidades numéricas tempranas y de enfoque espontáneo en la numerosidad bajos. Los niños que asisten a escuelas privadas superaron a sus compañeros de escuelas públicas rurales en habilidades numéricas tempranas, pero no en su enfoque espontáneo en la numerosidad. Se discuten estos hallazgos en vista de la importancia de prácticas de instrucción diferenciadas en matemática temprana en el jardín infantil ecuatoriano.

Selecting a large and diverse sample of 5–6-year-old preschool children (179 boys and 174 girls; Mage = 70.03 months, SDage = 3.43), we aimed to extend previous findings on variability in children’s home math environment (i.e., home math activities, parental expectations, and attitudes) and its association with children’s mathematical skills. We operationalized mathematics in a broader way than in previous studies, by considering not only children’s numerical skills but also their patterning skills as integral components of early mathematical development. We investigated the effects of children’s gender and socioeconomic status (SES) on their home math environment, examined the associations between children’s home math environment and their mathematical skills, and verified whether these associations were moderated by children’s gender and/or SES. Parents of 353 children completed a home math environment questionnaire and all children completed measures of their numerical (e.g., object counting) and patterning skills (e.g., extending repeating patterns). Results indicated no effect of children’s gender on their home math environment. There was no effect of SES on the performed home math activities, but small SES differences existed in parents’ math-related expectations and their attitudes. We found no evidence for associations between children’s home math environment and their mathematical skills. Furthermore, there were no moderating effects of gender or SES on these associations. One explanation for these findings might relate to the characteristics of the general preschool system in the country of the present study (Belgium). Future studies should consider the effect of the preschool learning environment because it might explain differences between studies and countries with regard to the home math environment and its association with mathematical skills.

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.

This study is the first to examine the associations between the occurrence, frequency, and adaptivity of children's subtraction by addition strategy use (SBA; e.g., 712 - 346 = ?; 346 + 54 = 400, 400 + 300 = 700, 700 + 12 = 712, and 54 + 300 + 12 = 366) and their underlying conceptual knowledge. Specifically, we focused on two rarely studied components of conceptual knowledge: children's knowledge of the addition/subtraction complement principle (i.e., if a + b = c, then c - b = a and c - a = b) and their knowledge of different conceptual subtraction models (i.e., understanding that subtraction can be conceived not only as "taking away" but also as "determining the difference"). SBA occurrence was examined using a variability on demand task, in which children had to use multiple strategies to solve a subtraction. SBA frequency and strategy adaptivity were investigated with a task in which children could freely choose between SBA and direct subtraction (e.g., 712 - 346 = ?; 712 - 300 = 412, 412 - 40 = 372, and 372 - 6 = 366) to solve 15 subtractions. We measured both children's knowledge of the addition/subtraction complement principle, and whether they understood subtraction also as "determining the difference." SBA occurrence and frequency were not related to conceptual knowledge. However, strategy adaptivity was related to children's knowledge of the addition/subtraction complement principle. Our findings highlight the importance of attention to conceptual knowledge when teaching multi-digit subtraction and expand the literature about the relation between procedural and conceptual knowledge.

Pre-school teachers' competence to see and decide to use learning opportunities in informal play-based situations (i.e. situation-specific skills) is key for high-quality pre-school instruction. Current insights into pre-school teachers' situation-specific skills and their association with underlying teacher disposition and instructional materials are limited. We aimed to complement existing findings by systematically analysing pre-service and in-service pre-school teachers' situation-specific skills in association with their underlying disposition and the type of instructional material in the domain of early mathematics. We assessed 274 pre-service and in-service pre-school teachers' mathematical content and pedagogical content knowledge (MCK, MPCK), beliefs and situation-specific skills, operationalised as the mathematical questions they formulate during simulated shared picture book reading activities. Logistic multilevel regression analyses revealed a complex interplay between pre-service and in-service pre-school teachers' disposition, the type of instructional material and situation-specific skills, pointing to the need for future studies on the topic.

Abstract This study aimed at analyzing the development of Ecuadorian children’s early numerical abilities during the Kindergarten year in relation to their SES, the quality of their early mathematics education, and the attended school type. 179 Ecuadorian Kindergartners (18 classrooms, 6 classrooms per school type) were offered a standards-based early numeracy test at both the start and the end of the Kindergarten year. In all classrooms, the quality of early mathematics education was assessed twice via the COEMET instrument. Results first showed rather low scores on the early numeracy test, with only 50% (at the start) up to 70% (at the end) of the items solved correctly, along with large inter-individual differences in these scores. Second, the quality of early mathematics education in the participating classrooms was also rather low. Third, children’s early numerical abilities at Kindergarten entry, SES, and school type predicted children’s early numerical abilities at the end of the school year. The quality of early mathematics education did not contribute to children’s numerical development. We critically discuss our findings in view of optimizing the quality of Ecuadorian early mathematics education as a stepping stone towards enhanced numerical development.

There is abundant evidence that young children are capable of developing mathematical knowledge and that the arithmetic skills of young children are a predictor of their future academic achievement. There is also a common agreement that the quality of early mathematical instruction has an important influence on children´s subsequent learning. In Ecuador studies on young children´s early mathematical competencies and instruction are scare. Therefore a study was initiated to (1) assess the numerical competencies of preschoolers and kindergartners (first year of elementary education) attending a public school in Cuenca, with the objective to critically analyze their numerical thinking and reasoning, and (2) examine teachers’ practices and believes regarding early mathematical instruction and children´s mathematical competencies. An application of the Number Knowledge Test (Griffin, 2005) demonstrated that most of the participating children had not developed basic numerical competencies. In addition, teachers strongly believe that young children are incapable of carrying out mathematical thoughts. As a consequence, mathematical activities in which children and teachers are engaged are insufficiently developed. The scientific and practical implications of these results are discussed.

Hace algunos años, Hatano diferenció entre el nivel de experto de aprendizaje de rutina y el adaptativo e impulsó el desarrollo y la implementación de ambientes de aprendizaje que tengan como objetivo el tipo adaptativo de experiencia por sobre el de rutina. En esta contribución, nos enfocamos en un aspecto de la adaptabilidad, la llamada adaptativa del uso de estrategias de solución en aritmética de educación primaria. En la primera parte de este artículo, brindamos algunos enfoques conceptuales y metodológicos en los asuntos de adaptabilidad. Más específicamente, hacemos una revisión crítica de las definiciones y operacionalizaciones de estrategias de adaptabilidad que solo toman en cuenta tareas y características del sujeto. Argumentamos la necesidad de un concepto y un enfoque que también incluya el contexto sociocultural. La segunda parte, comprende algunas consideraciones educativas con respecto a las preguntas de porque, cuando, para quien o cómo se procura la búsqueda de nivel de experto adaptativa en la educación de las matemáticas para la escuela primaria.