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Adaptive serious mathematical games in kindergarten were used to investigate whether kindergarteners could grasp mathematics topics. A pretest–posttest-follow up design with two conditions. (Condition 1 educational kindergarten games on the computer, focusing on counting and comparison, Condition 2 educational kindergarten games on the computer, focusing on memory, counting and comparison) and one active control group (playing educational kindergarten games without mathematical content) was set up dealing with 45 preschoolers with a mean age of 68.78 months (SD = 4.46). Children were matched in kindergarten on their early mathematical and language skills as well as on their intelligence before the interventions took place. The study revealed that playing mathematical games in kindergarten had the potential to enhance the early mathematical skills. Children with initial weak mathematical skills in kindergarten caught up with their average performing peers, pointing to the importance of serious numerical games as “opportunities” in kindergarten. Both boys and girls benefitted, with a sustained effect in grade 1, revealing promising potential effects of offering opportunities to focus on mathematics even in very young children.

Several factors seem important to understand the nature of mathematical learning. Byrnes and Miller combined these factors into the Opportunity-Propensity model. In this study the model was used to predict the number-processing factor and the arithmetic fluency in grade 4 (n = 195) and grade 5 (n = 213). Gender, intelligence and affect (positive affect for arithmetic fluency and negative affect for calculation accuracy) predicted math learning, and pointed to the importance of the propensity factors. We have to be careful not to interpret gender differences, since this is a social construct, our analyses pointed to the relevance of including antecedent factors in the model as well . The Implications of the study for math learning will be discussed below.

Poor mathematical abilities have a substantial societal impact. This special issue includes contributions discussing learning of mathematics that have impact on educational policy or elementary school practice. All papers explore and illustrate recent studies and available literature in the field of understanding typical and atypical mathematics learning. They reflect on mechanisms of conceptual development, models of typical and atypical learning, individual quantitative and qualitative differences, strengths and weaknesses, factors that appear promising and positively influencing the learning process of students' learning of mathematics, and on interventions that aim to improve mathematics performance even in very young children. © 2022 Published by KURA Education & Publishing.

This special issue includes contributions discussing the assessment and training of metacognition that appear promising for the purpose of positively influencing the learning process of students’ learning of mathematics. More specifically, contributors explore, illustrate and scrutinize available research evidence for its relevance and effectiveness in the specific curricular field of mathematics education. After an introduction and discussion of the individual input, we explore the scientific progress in the area of the theoretical framework and conceptualizations of metacognition, the relationships between metacognition and mathematics performance, the various effects upon ability levels, the measures to assess metacognition, and the interventions that aim to improve mathematics performance. This special issue ends with a reflection on practical suggestions for mathematics education.

INTRODUCTION: Numerous life, peer, and school-related factors have been found to be associated with non-suicidal self-injury (NSSI) among adolescents; however, most studies have not explored the possible reciprocal nature of these associations. The aim of the current study was to examine bidirectional and longitudinal associations between NSSI and several life, peer, and school-related factors (i.e., stressful life events, peer relationships, academic achievement, and attitudes towards school). METHOD: Community-based adolescents completed questionnaires assessing the variables of interest at three time points; age 12 (T1; 55.09% girls), age 13 (T2; 56.95% girls), and ages 14-15 (T3; 57.41% girls). In total, 529 adolescents provided complete data across all three-time points. RESULTS: Analyses showed a bidirectional association between NSSI and both attitudes towards school and stressful life events. Specifically, stressful life events at T2 predicted engagement in NSSI at T3, and NSSI at T2 predicted increased risk of stressful life events at T3. Similarly, having negative attitudes towards school predicted NSSI at T2, which, in turn, predicted negative attitudes towards school at T3. Further, academic achievement at T1 was negatively associated with NSSI at T2. Peer relationships were neither a predictor nor a consequence of NSSI. CONCLUSIONS: Our results suggest that NSSI can be both a predictor and a consequence of various life, and school factors. Focus on these factors in prevention and intervention efforts for NSSI among adolescents may be warranted. ispartof: JOURNAL OF ADOLESCENCE vol:90 pages:100-108 ispartof: location:England status: published

The role of metacognitive postdiction accuracy and autonomous and controlled motivation in mathematics was explored in elementary school children (n = 208) within two perspectives, related to sample characteristics. A first study was set up in a population-based cohort. A second study was set up with children with and without a documented mathematical disability. Both studies revealed a concurrent relation between the metacognitive postdiction skills of children and their mathematical accuracy and speed, leading to the practical recommendation that teachers should pay attention to the accuracy of self-judgments of children. In addition, controlled motivation was negatively related to the speed and accuracy in study 2. Children with mathematical learning disabilities (MLD) differed from peers without mathematical learning disabilities on postdiction accuracy and autonomous motivation. However, they did not differ significantly on controlled motivation, suggesting the importance of differentiating between controlled and autonomous motivation when analyzing motivation in mathematics education.

In this paper, we investigate the role of metacognitive postdiction skills, intrinsic motivation and prior proficiency in mathematics as Propensity factors within the opportunity-propensity (O-P) model of learning. We tested Belgian children from Grade 1 till 6 in January and June. The study revealed overlapping yet different predictors for mathematical accuracy and fluency, which led us to the practical recommendation for teachers to pay attention to both aspects of mathematics. The metacognitive postdiction skills of children were related to accuracy in mathematics during the whole elementary school period. In addition, we observed that children evaluated their own performance as worse when they were slower in Grades 3 and 4. Intrinsic motivation was related to accuracy but not to fluency in Grade 3. Especially prior mathematical accuracy mattered as a propensity factor. More than half of the variance in accuracy and less than one-fifth of the variance in fluency in January predicted the performances of children for mathematics in June, a finding that highlights the importance of longitudinal designs including students' prior mathematical accuracy' as well. Finally, we observed that poor mathematics performers are less intrinsically motivated, and less metacognitively accurate. Moreover, they overestimate their performances more often than well-performing peers in all grades, stressing the importance of paying attention to these aspects in mathematics education.

Working memory is important for a variety of life domains,. including for children's school functioning. As such, it is crucial to understand its development, antecedents and consequences. The current study investigates the development of different working memory components (phonological loop, visuospatial sketchpad, central executive), the influence of different aspects of the teacher-student relationship (closeness, conflict, dependency) and its predictive value for academic achievement (reading, spelling, mathematics) across the transition from kindergarten to first grade. The sample consisted of 107 kindergarten children. Working memory tasks were administered at the end of kindergarten and first grade. Teachers reported on teacher-student relationship quality in the middle of first grade. Standardized tests were used to assess academic achievement at the end of first grade. Results indicate moderate to large increases in the phonological loop and visuospatial sketchpad and large gains in the central executive. Dependency of the student towards the teacher significantly predicted visuospatial sketchpad performance at the end of first grade. Reading was significantly predicted by the visuospatial sketchpad and phonological loop in kindergarten, while for spelling the visuospatial sketchpad was important. Finally, mathematics was predicted by performance on the phonological loop and the visuospatial sketchpad. The current study indicates the importance of the affective quality of the teacher-student relationship for working memory performance, which in turn is important for academic achievement. It is therefore critical to attend to the early detection and prevention or intervention of working memory problems in the classroom in order to prevent future academic problems. Additionally, maintaining a positive relationship with students and encouraging their independent exploration may be important when preventing such problems, complementary to cognitive or other types of training and intervention.

This study examined number processing in 10-year-olds with developmental dyslexia (DD). The phonological deficit and double deficit hypotheses imply that children with DD might have a connection deficit that affects their ability to establish links between number symbols and magnitude representations. The double deficit hypothesis also posits that symbolic number difficulties may emerge due to difficulties with processes underlying rapid automatic naming (RAN). The DD group displayed difficulties with symbolic number processing but not with non-symbolic number processing. However, the underlying processes of this access or connection deficit appeared not to be related to phonological awareness or RAN. The DD group displayed impaired arithmetic fluency and calculation that were accounted for by defective processes underlying RAN. In view of the triple-code model, children with DD have impaired verbal number codes or defective access to verbal number codes but an intact core magnitude representation.

Participation, defined as 'involvement in life situations' according to the World Health Organisation, is a well-recognized concept and critical indicator of quality of life. In addition it has become an important outcome measure in child rehabilitation. However, little is known about the level of participation of young children with Developmental Disabilities. The aim of this study was to capture their subjective experiences of participation. An adapted informed consent based on a comic strip was used to get the children's assent. A Photo Elicitation study was used, in which photographs were taken by the children when they were involved in meaningful activities. The photographs were then used to facilitate communication with the children and to initiate in depth-interviews. Forty-seven interviews with 16 children between five and nine years were conducted based on their photographs. This method generated rich data, confirming that young children with Developmental Disabilities were able to inform us accurately on their experiences of participation. Data was analysed by means of an inductive thematic analysis. Results showed that children perceived their participation as satisfying when they can play, learn and join in family gatherings resulting in feelings of inclusion, recognition and belonging. When there are-on occasions-moments that their participation was obstructed, the children used two strategies to resolve it. Or they walked away from it and choose not to participate, or when autonomously motivated for the activity, they relied primarily on their context (i.e. mothers) as enabling their participation. Related to the data, children discussed themes related to their person, activities, connections and mediators between those themes. These themes fit well within earlier and current research on the subject of participation.

Studies on the predictors of mathematical learning and learning difficulties have been receiving growing attention. It is well established in the literature that IQ is a powerful predictor of several psychosocial outcomes, including school achievement. Other well-consolidated literature shows that cognitive–motivational effects exist but are rather small. There seems to be a big interaction between interest and specific knowledge in a domain (expertise). Variance is confounded. In this chapter, motivation and math anxiety are described within the opportunity–propensity (O-P) model including antecedent, opportunity, and propensity indicators to predict mathematical accuracy and fluency. Analyses on secondary data using this O-P model revealed that motivation as a propensity factor accounted for 10% of unique variance in addition to other predictors. Motivation and engagement were stronger predictors from kindergarten till second grade than from third till sixth grade. In addition, math anxiety might be considered a moderator of the relationship between mathematical achievement and motivation. Aside from acute effects, math anxiety might cause long-term negative impairments in mathematical performance that are kept up by a negative approach to mathematics and resulting avoidance behavior.

In November 2014 we had a wonderful possibility to organize a seminar International Seminar on Mathematical Learning Difficulties with our international colleagues in the field of mathematical learning difficulties. One of the main aims was to provide open lectures for the staff members and students in University of Helsinki. The meeting was supported by the Teachers’ Academy in University of Helsinki. We have collected extensive summaries of the presentations to form this special issue. The summaries are found in both English and Finnish. To sum up the main ideas from the presentations. Firstly, although mathematical learning difficulties are common, we do need more research to be able to understand the possible cognitive precursors or environmental issues affecting learning and causing problems. Secondly, we need more studies about intervention programmes designed to support the mathematical skills development in children having problems in learning mathematics. Thirdly, we also need more studies validating the positive findings in individual studies, using the same assessment and intervention tools.

Extending previous research on the predictive value of large number discrimination, this study explored the role of infants' and toddlers' small number discrimination for numerical competencies in kindergarten (NCK). Although no significant relationship could be found between number discrimination in infancy (8 months, T1) and NCK (48 months, T3), the predictive value of toddlers' number discrimination (24 months, T2) for NCK could be demonstrated at least for some NCK. The finding that only toddlers' small number discrimination related to NCK raised thoughts about the task, age, set size, stability and development of number discrimination or other influencing factors. Future research should study all small set sizes (not only 1 vs. 3) and a broader range of NCK in a larger sample. Nevertheless, whereas infants' small number discrimination might be too early to predict NCK, performance in toddlerhood might be addressed in the future to establish a measure to detect at-risk mathematical development.

Introducción. Durante décadas el orden de nacimiento y las diferencias de género han atraído la atención de la investigación.Método. El orden de nacimiento, el tamaño de la familia y género, y la relación con el rendimiento aritmético es estudiada en 1152 alumnos de educación elemental (540 niñas, 612 niños) en Flanders. Los niños fueron seleccionados atendiendo al estatus socioeconómico de los padres y se les administró un test de cálculo mental y conocimiento de números.Resultados. Los hallazgos favorecen a los niños y sugieren que sólo los niños y nacidos en último lugar en familias extensas se muestran menos competentes en aritmética que los nacidos primero. En contraste con la predicción de Zajonc que señalaba que en familias con tres, cinco o más niños, eran los nacidos en medio quienes lo hacían mejor.Discusión. El estudio está parcialmente en línea con la hipótesis de confluencia y disolución. Las diferencias en función del orden de nacimiento pueden explicarse por la ventaja de la tutorización que los primogénitos realizan sobre los más pequeños ayudándoles en el procesamiento de la información. Sin embargo, nuestros datos proporcionan evidencias sobre que el orden de nacimiento explica sólo el 2% o 3% de la varianza. Los análisis muestran que los nacidos en último lugar presentan puntuaciones pobres tanto en familias pequeñas (dos elementos) como en familias grades (cinco o más elementos). Sin embargo, las desventajas de los benjamines y las ventajas de los primogénitos no están presentes en familias con tres o cuatro hijos.

Introducción. A pesar de todo el énfasis en la metacognición, los investigadores actualmente usan diferentes técnicas para evaluar la metacognición. El objetivo de esta contribución es el de ayudar a aclarar algunos de los paradigmas en la evaluación de la metacognición. El presente trabajo revisará además los estudios que intentan mejorar el proceso de aprendizaje a través de la metacognición.Método. Se realizó un estudio longitudinal con 32 niños para investigar el aprendizaje matemático y las habilidades metacognitivas en 3º y 4º curso de la educación primaria. Las habilidades metacognitivas fueron evaluadas a través de las calificaciones de los profesores, protocolos de pensamiento en voz alta, calificaciones infantiles del pasado y del futuro y la EPA 2000. Describimos además algunas maneras de optimizar el aprendizaje de las matemáticas a través de la metacognición.Resultados. A la hora de reflexionar sobre los resultados de este trabajo, existe evidencia de que la forma de evaluar determina lo que se va a conseguir. Cuestionarios infantiles no parecen reflejar sus habilidades en sí, pero son útiles para evaluar el ‘conocimiento’ y las ‘creencias’ metacognitivos de los niños. Los análisis de protocólos del pensamiento en voz alta resultaron ser técnicas precisas para evaluar las ‘habilidades’ metacognitivas de los niños con un nivel adecuado de fluidez verbal, pero requieren un tiempo excesivo. Los cuestionarios para los profesores muestran cierto valor añadido en la evaluación de las habilidades metacognitivas. Los datos mostraron que las habilidades metacognitivas evaluadas por calificaciones de profesores explicaron el 22,2% del rendimiento en las matemátics.Conclusión. Sugerimos que los profesores que estén interesados en la metacognición infantil empleen diseños de métodos múltiples, incluyendo los cuestionarios a profesores para obtener una visión completa de las habilidades metacognitivas. Teniendo en cuenta la naturaleza complicada del aprendizaje matemático, puede ser útil evaluar las habilidades metacognitivas en niños para enfocarse en estos factores y su función en el aprendizaje y desarrollo matemático. Los estudios también revelan que la metacognición puede ser entrenada y tiene algo de valor añadido en la intervención con niños en la resolución de problemas matemáticos. Nuestros datos sugieren que las habilidades metacognitivas deben ser enseñadas explícitamente para poder conseguir una mejora y no se puede suponer que se desarrollen por una experiencia libre de las matemáticas. Puede ser posible que al dedicar más tiempo a la instrucción metacognitiva, el proceso de enseñanza-aprendizaje mejoraría.

Up till now, research evidence on the mathematical abilities of children with autism spectrum disorder (ASD) has been scarce and provided mixed results. The current study examined the predictive value of five early numerical competencies for four domains of mathematics in first grade. Thirty-three high-functioning children with ASD were followed up from preschool to first grade and compared with 54 typically developing children, as well as with normed samples in first grade. Five early numerical competencies were tested in preschool (5–6 years): verbal subitizing, counting, magnitude comparison, estimation, and arithmetic operations. Four domains of mathematics were used as outcome variables in first grade (6–7 years): procedural calculation, number fact retrieval, word/language problems, and time-related competences. Children with ASD showed similar early numerical competencies at preschool age as typically developing children. Moreover, they scored average on number fact retrieval and time-related competences and higher on procedural calculation and word/language problems compared to the normed population in first grade. When predicting first grade mathematics performance in children with ASD, both verbal subitizing and counting seemed to be important to evaluate at preschool age. Verbal subitizing had a higher predictive value in children with ASD than in typically developing children. Whereas verbal subitizing was predictive for procedural calculation, number fact retrieval, and word/language problems, counting was predictive for procedural calculation and, to a lesser extent, number fact retrieval. Implications and directions for future research are discussed.

A bulk of evidence supports the association of number line estimations using Arabic digits and dots with math learning. Surprisingly few studies have been conducted to explore the relationship between estimations using number words and mathematics. The present study expands previous findings by investigating estimations in three formats (Arabic digits, dots and number), adding language as predictor and by focusing at timed and untimed math learning. A sample of 132 children was followed from kindergarten till grade 2. Results reveal variability in estimation accuracy and errors declining with age and instruction in all children. In addition, our findings suggest that Arabic numerals have a more linear distribution than number words. Moreover, our findings suggest that language explains variation in kindergarten but not in evolution and, more in particular, untimed math achievement can be predicted by number line estimation. Implications for assessment, prediction of math learning and instruction are discussed.

Children in kindergarten were randomly assigned to adaptive computerised counting or comparison interventions, or to a business-as-usual control group. Children in both intervention groups, including children with poor calculation skills at the start of the intervention, performed better than controls in the posttest. However the effects of training held in grade 1, playing serious counting games improving number knowledge and mental arithmetic performances, and playing serious comparison games, only enhanced the number knowledge proficiency in grade 1. The value of these short periods of intensive gaming in kindergarten are discussed as a look-ahead approach to enhance arithmetic proficiency.

This research analyses preservice teachers' knowledge of fractions. Fractions are notoriously difficult for students to learn and for teachers to teach. Previous studies suggest that student learning of fractions may be limited by teacher understanding of fractions. If so, teacher education has a key role in solving the problem. We first reviewed literature regarding students' knowledge of fractions. We did so because assessments of required content knowledge for teaching require review of the students' understanding to determine the mathematics difficulties encountered by students. The preservice teachers were tested on their conceptual and procedural knowledge of fractions, and on their ability in explaining the rationale for a procedure or the conceptual meaning. The results revealed that preservice teachers' knowledge of fractions indeed is limited and that last-year preservice teachers did not perform better than first-year preservice teachers. This research is situated within the broader domain of mathematical knowledge for teaching and suggests ways to improve instruction and student learning.

article i nfo Article history: A large body of evidence supports the central influence of counting in the development of adequate arithmetic skills. Moreover a substantial amount of children with mathematical learning disabilities in elementary school can be correctly diagnosed in kindergarten by a combination of counting and magnitude estimation tasks. The present study expands previous findings, by adding language and logical thinking as predictors for arithmetic skills in kindergarten and grade 1. A sample of 63 children was tested in kindergarten on counting, logical thinking, estimation (number line estimation, number naming and number comparison), language and arithmetic skills. These children were tested again on arithmetic in grade 1. Results reveal that expressive language explains 24% of the variance in arithmetic skills among kindergarteners controlling for number naming and procedural counting knowledge as predictors. Moreover, language still predicts grade 1 arithmetic. In addition, our findings suggest that number naming and number comparison are better predictors than number line estimation of arithmetic skills in kindergarten.

The present paper investigates differences in the process of mastering the four basic arithmetic operations (addition, subtraction, multiplication and division) between Flemish and Chinese children from Grade 3 till Grade 6 (i.e. from 8 to 11 years old). The results showed, firstly, that Chinese students outperformed Flemish students in each grade but that difference in addition, subtraction and division skills between the groups decreased as grade increased. Secondly, the levels of mastery of the four skills varied between Chinese and Flemish students. Multiplication was relatively easier for Chinese students than for their Flemish peers as compared to the other skills (that is, the gap was larger). Third, low achievers experienced comparable learning difficulties in both countries, and higher achievers demonstrated their greater ability early on.

The efficacy of metacognition as theory-based instructional principle or technique in general, and particularly in mathematics, is explored. Starting with an overview of different definitions, conceptualizations, assessment and training models originating from cognitive information processing theory, the role of metacognition in teaching and learning is critically discussed. An illustrative training program in kindergarten demonstrates that explicit and embedded metacognitive training can have an effect on mathematics learning even in very young children. Theoretical and methodological issues for future research, and recommendations for mathematics educators, are analyzed within the framework of the Opportunity-Propensity and Universal instructional design framework, demonstrating the relevance of metacognition in the domain of mathematics teaching, impacting children’s learning of mathematics and their active involvement in their learning process.

1 Department of Education, Bar-Ilan University, 52100 Ramat-Gan, Israel 2 Department of Experimental Clinical and Health Psychology, Ghent University, Ghent, Belgium 3Department of Human-Computer Media, Wuerzburg University, Wuerzburg, Germany 4Department of Psychology, Technische Universitat Dresden, 01062 Dresden, Germany 5 Department of Educational &Counselling Psychology and Special Education, University of British Columbia, Vancouver, BC, Canada

Elementary school children with reading disabilities (RD; n = 17), mathematical disabilities (MD; n = 22), or combined reading and mathematical disabilities (RD+MD; n = 28) were compared to average achieving (AA; n = 45) peers on working memory measures. On all working memory components, 2 (RD vs. no RD) × 2 (MD vs. no MD) factorial ANCOVAs revealed clear differences between children with and without RD. Children with MD had lower span scores than the AA children on measures of the phonological loop and the central executive. A significant interaction effect between RD and MD was found only for listening recall and had a small, partial effect size. In addition, analyses showed that the best logistic regression model consisted of a visuospatial and a central executive task. The model significantly distinguished between the AA and clinical groups and between the MD and RD+MD groups. Evidence was found for domain-general working memory problems in children with learning disabilities. Management of working memory loads in structured learning activities in the classroom, at home, or during therapy may help these children to cope with their problems in a more profound manner.

In a sample of 39 children with mathematical learning disabilities (MLD) and 106 typically developing controls belonging to three control groups of three different ages, we found that visual perception, motor skills and visual-motor integration explained a substantial proportion of the variance in either number fact retrieval or procedural calculation. Furthermore, children with MLD performed significantly worse on visual perception, motor skills and visual-motor integration in comparison with age-matched control children. A mild developmental delay in visual perception, visual-motor integration and (fine) motor coordination and a severe delay in motor skills were found in children with MLD. However, not all children with MLD have problems on these domains. They seem to be a heterogeneous group, not only with respect to their mathematical profile but also with respect to their visual perceptual, motor and visual-motor integration skills. Diagnostic implications are discussed.

Background. The ability to compare numbers, as the most basic form of number sense, has been related to arithmetical achievement. Aims. The current study addressed the predictive value of non-symbolic and symbolic (number word (NW) and Arabic number (AN)) comparison for arithmetics by means of a longitudinal design. Sample. Sixteen children with mathematical disabilities (MD), 64 low achievers (LA), and 315 typical achieving (TA) children were followed from kindergarten till grade 2. Method. The association of comparison skills with arithmetical skills in grades l and 2 was studied. The performances of MD, LA and TA children were compared. Results. Regression analyses showed that non-symbolic skills in kindergarten were predictively related to arithmetical achievement 1 year later and fact retrieval 2 years later. AN comparison was predictively related to procedural calculation 2 years later. In grade 2, there was an association between both symbolic tasks and arithmetical achievement. Children with MD already had deficits in non-symbolic and symbolic AN comparison in kindergarten, whereas in grade 2 the deficits in processing symbolic information remained. Conclusions. The combination of non-symbolic and symbolic deficits represents a risk of developing MD.

Since the 1920s researchers have been studying children's temporal concepts, concluding that the concept of time is complex and difficult to teach children. This research literature review aims to provide a theoretical framework to guide future research about time‐related teaching in primary school. After preliminary considerations about the potential of instructional interventions in this context, this review analyses the position of time‐related conceptions within primary school curricula and explores which factors exert an influence on the concept of time. Finally, clock reading is discussed as a key time‐related skill in primary education that mirrors the complexity of time conceptions in general.

article i nfo Arithmetic abilities Counting principles Cardinality principle Kindergarten predictors Multilevel

In a 2-year longitudinal study, 66 children were assessed in Grades 3 and 4 with a within-method-and-time design on metacognition (including the computerized Evaluation and Prediction Assessment [EPA2000]) and mathematics. Moreover, half of the children were trained in Grade 3 in the metacognitive skill of predicting their abilities in solving mathematics tasks. All children completed mathematics tests before and after the training took place. Results showed that there was progress in metacognition and in mathematics skills. Moreover, children in the metacognitive group did better than the children in the control group. Conclusions are drawn on the relationship between metacognition and mathematics abilities.

Arithmetic abilities acquired in kindergarten are found to be strong predictors for later deficient arithmetic abilities. This longitudinal study ( N = 684) was designed to examine if it was possible to predict the level of children's arithmetic abilities in first and second grade from their performance on preparatory arithmetic abilities in kindergarten. Furthermore, the role of intelligence in the assessment of developing mathematical reasoning and numerical facility was investigated. The results showed that good predictions of beginning arithmetic abilities can be made. Even in the long term, it was possible to make predictions of later arithmetic performances, especially for the domain of arithmetical reasoning. Logic thinking abilities such as seriation and classification and counting knowledge may be assessed in kindergarten as possible markers for at-risk development. Furthermore, it is important to take into account intelligence when looking for useful predictors of arithmetical reasoning.

Previous research stresses the importance of seriation, classification, and counting abilities that should be assessed in kindergarten, when looking for crucial predictors of mathematical learning disabilities in Grade 1. This study examines ( n = 158) two-year-long predictive relationships between children's seriation, classification, procedural counting knowledge, and conceptual counting knowledge, and their numerical facility and arithmetical achievement in Grades 3, 4, and 5. Path analyses reveal a relationship between procedural counting knowledge in Grades l and 3 and numerical facility, and between conceptual counting knowledge in Grade l and arithmetical achievement in Grades 1 and 2. In addition, procedural counting knowledge correlates with seriation, and conceptual counting knowledge correlates with classification as well as with seriation in Grade 1. Clinicians are encouraged to select early arithmetic subtests with caution when assessing and predicting arithmetic and arithmetical disabilities.

Third grade elementary school children solved tests on mathematical reasoning and numerical facility. Metacognitive skillfulness was assessed through think aloud protocols, prospective and retrospective child ratings, teacher questionnaires, calibration measures and EPA2000. In our dataset metacognition has a lot in common with intelligence, but planning measured with teacher ratings plays a role above and beyond IQ. Moreover, we found that skills are generally related, but that it is more appropriate to assess them separately. In addition, results show the value of an experienced teacher as actual measure of metacognitive planning skills. Our dataset suggests convergent validity for prospective and retrospective child ratings, but no significant relationship with the other metacognitive measures. Metacognitive skillfulness combined with intelligence accounts for between 52.9% and 76.5% of the mathematics performances. The choice of diagnostic instruments highly determines the predicted percentage. Consequences for the assessment of metacognitive skills are discussed.

This paper presents an overview of two studies in which the co-morbidity of clinical disorders in mathematical learning disabilities (MLD) in elementary school children has been examined. MLD were reported in children with differ- ent levels of intelligence. About 54% did not meet the discrepancy-criterion. The proportions of reading (32%), spelling (21%), visuo-spatial (11%) and language disabilities (10%) were higher than that found in the general population. The proportion of ADHD (42%) was also higher than that found in the general proportion. Comorbid heterotypic depression and anxiety rates were 8% and 6% respectively. Furthermore a proportion of motor problems (15%) and ODD problems (5%) were reported. This study indicates that co-morbidity with clinical disorders is more a rule than exception in children with MLD. In addition, there may be different patterns of symptoms between genders. Girls more often had an average- intelligent but non-discrepant intelligence profile with less co-morbid problems.

Homework aims to improve variables and processes related to academic achievement. In China, homework assignments are not only given by teachers, but also by parents and students themselves. In present study we focus on the impact of additional homework developed by parents and learners. The data comes from 10,959 students enrolled in Chinese primary schools. The results reveal that parents and students from disadvantaged families approach homework as a way to compensate for an unprivileged background. Students develop homework assignments depending on the extent to which their parents develop homework. It shows that the learning performance of students improves significantly when their parents with low level jobs assign a moderate level of homework. In contrast, student achievement is significantly lower when their parents with high level jobs don't assign any homework. Students from disadvantaged families benefit largely from homework involvement. Although there is a certain compensatory impact of homework, educational authorities should provide additional support to students from disadvantaged families.

Many studies tested the association between numerical magnitude processing and mathematical achievement with conflicting findings reported for individuals with mathematical learning disorders. Some of the inconsistencies might be explained by the number of non-symbolic stimuli or dot collections used in studies. It has been hypothesized that there is an object-file system for ‘small’ and an analogue magnitude system for ‘large’ numbers. This two-system account has been supported by the set size limit of the object-file system (three items). A boundary was defined, accordingly, categorizing numbers below four as ‘small’ and from four and above as ‘large’. However, data on ‘small’ number processing and on the ‘boundary’ between small and large numbers are missing. In this contribution we provide data from infants discriminating between the number sets 4 vs. 8 and 1 vs. 4, both containing the number four combined with a small and a large number respectively. Participants were 25 and 26 full term 9-month-olds for 4 vs. 8 and 1 vs. 4 respectively. The stimuli (dots) were controlled for continuous variables. Eye-tracking was combined with the habituation paradigm. The results showed that the infants were successful in discriminating 1 from 4, but failed to discriminate 4 from 8 dots. This finding supports the assumption of the number four as a ‘small’ number and enlarges the object-file system’s limit. This study might help to explain inconsistencies in studies. Moreover, the information may be useful in answering parent’s questions about challenges that vulnerable children with number processing problems, such as children with mathematical learning disorders, might encounter. In addition, the study might give some information on the stimuli that can be used to effectively foster children’s magnitude processing skills.

This paper presents a study on mathematical problem solving in third-grade pupils. The relationship between mathematics, metacognition and intelligence was investigated in children with (n = 191) and without mathematical learning disabilities (n = 268). A significant relationship was found between prediction, evaluation, intelligence, procedural and mathematical fact retrieval skills in children without mathematical learning disabilities. In the children with mathematical learning disabilities a relationship was found between metacognitive and procedural skills. No such relationship was found between intelligence and metacognition or between metacognition and mathematical fact retrieval skills. In addition it was investigated if children with mathematical learning disabilities had less adequate metacognitive skills than peers without learning problems. At group level significant differences were found between both groups. However on analyzing these results further, it was found that four out of five children with combined mathematical learning disabilities, half of the children with procedural disabilities and only 5% of the children with a retrieval deficiency had low metacognitive skills. Furthermore, metacognitive problems were found in one out of five children without learning disabilities. Moreover, a majority of the children with mathematical learning disabilities and inadequate metacognitive skills had problems with prediction and evaluation skills. Most third graders with low metacognitive skills only appeared to have problems predicting the level of difficulty of tasks. Inaccurate evaluations were found on a more regular basis in children with mathematical learning disabilities and inadequate metacognitive skills as opposed to the sample of children with inadequate metacognitive skills but without learning difficulties, where their occurrence was rather a one off. The implications of this study for diagnosis and treatment will be discussed later in this paper.

This paper focuses on the role of evaluation in mathematics in 749 elementary school children. The macroevaluative skills and calibration scores of high versus low mathematical problem solvers were contrasted as measures of metacognition. No relevant calibration differences were found for gender. In addition, the performances of children with mathematics learning disabilities could not be explained according to the maturational lag hypothesis. Finally, although macrometacognitive evaluation and calibration seem attractive alternatives for time-consuming on-line metacognitive assessment techniques, our data show that a global and retrospective assessment of the macroevaluation is not always enough to get the picture of mathematical problem solving in young children.

A longitudinal study was conducted on 82 children to investigate, firstly the numerical competence of young children and the predictive value of (pre)-numerical tests in kindergarten, and, secondly, whether children's knowledge of the numerical system and representation of the number size is related to their computation and logical knowledge and to their counting skills. In an additional cross-sectional study on 30 children with a clinical diagnosis of mathematical learning disability (MLD) of 8,5 years, age- and ability-matched with 2 x 30 children the same parameters of numerical competence were assessed. The longitudinal data showed individual differences in numerosity, as well as the relationship between a delay in arithmetics in grade I and problems on numerosity in kindergarten. In the cross-sectional results some evidence was found for the independence of numerical abilities in MLD-children. About 13% of them had still severe pre-numerical processing deficits (in number sequence production, cardinality skills and logical knowledge) in grade 3. About 67% had severe difficulties in executing calculation procedures and a lack of conceptual knowledge. A feature of 87% of the NILD-children was severe translation deficits, with a significantly worse knowledge of number words compared with the knowledge of Arab numerals. Finally a severe deficit in subitizing was found to be present in 33% of the MLD children. On a group level the processing deficits were linked to understanding numerosity, since the ability-matched younger children and the MLD-children had the same pre-numerical and numerical profile. Implications for the assessment of mathematical disabilities and the value of TEDI-MATH((R)) as an instrument in this process are discussed. (c) 2007 Elsevier Inc. All rights reserved.

In Belgium, between 3% and 8% of the children in elementary schools have mathematics learning disabilities (MLD). Many of these children have less developed linguistic, procedural, and mental representation skills. Moreover, a majority of the children have been found to show inaccurate prediction and evaluation skills in Grade 3. MLD often become obvious in elementary school. Whereas some children are retained, others are referred to special education. During the last 10 years, the number of children in special education and the number of children with learning disabilities who are following a special guidance program in general education (inclusive education) have increased. Children in Belgium with MLD can get therapy for about 2 years. Nevertheless, many problems continue unresolved even in high school and adulthood.

The effectiveness of a short metacognitive intervention combined with algorithmic cognitive instruction was assessed in an elementary school setting. Two hundred thirty-seven 3rd-grade children were randomly assigned to a 5-session metacognitive strategy instruction, an algorithmic direct cognitive instruction, a motivational program, a quantitative-relational condition, or a spelling condition. Children in the metacognitive program achieved significant gains in trained metacognitive skills compared with the 4 other conditions. Moreover, the children in the metacognitive program performed better on trained cognitive skills than children in the algorithmic condition, with a follow-up effect on domain-specific mathematics problem-solving knowledge. Despite the consistency of findings, no generalization effects were found on transfer of cognitive learning. (PsycINFO Database Record (c) 2016 APA, all rights reserved)

Research Findings: To date, studies comparing the mathematical abilities of children with autism spectrum disorder (ASD) and typically developing children are scarce, and results remain inconclusive. In general, studies on this topic focus on mathematical abilities learned from elementary school onward, with little attention for possible precursors at younger ages. The current exploratory study focused on the important developmental period of preschool age, investigating 5 early numerical competencies in 30 high-functioning children with ASD and 30 age-matched control children: verbal subitizing, counting, magnitude comparison, estimation, and arithmetic operations. Children were examined at 5 or 6 years of age, attending the 3rd and final year of preschool. Overall, rather similar early number processing was found in children with and without ASD, although marginally significant results indicated a weaker performance of children with ASD on verbal subitizing and conceptual counting. Practice or Policy: Given the pervasiveness and impact of ASD on other domains of functioning, it is important to know that no general deficits in early numerical competencies were found in this study. However, some downward trends in mathematics performance were identified in children with ASD, which can serve as the basis for additional research in this field.

Off-line metacognition (prediction and evaluation) was assessed in 437 normally intelligent children with or without learning disabilities in grades 2 and 3. Children with specific mathematics learning disabilities were compared with peers with specific reading disabilities, children with combined learning disabilities, age-matched peers and younger children matched at mathematical problem-solving level. Our results indicate that offline metacognition cannot be reduced to a demonstration of intelligence. Moreover, the off-line metacognitive scores of children with reading disabilities were comparable to those of age-matched peers without learning disabilities. Furthermore, significantly lower prediction and evaluation scores were found for children with specific or combined mathematics learning disabilities compared with age-matched peers. In addition, our data showed a different metacognitive profile for children with specific or combined mathematics learning disabilities, not comparable on all aspects to the profile of younger children, as suggested by the retardation or maturational-lag hypothesis. The educational implications of these results are discussed.

The present study aims at exploring predictors influencing mathematics performance. In particular, the study focuses on internal students' characteristics (gender, age, metacognitive experience, mathematics self-efficacy) and external contextual factors (GDP of school location, parents' educational level, teachers' educational level, and teacher beliefs). A sample of 1749 students and 91 teachers from Chinese primary schools were involved in the study. Path analysis was used to test the direct and indirect relations between the predictors and mathematics performance. Results reveal that a large proportion of mathematics performance can be directly predicted from students' metacognitive experiences. In addition, other student characteristics and contextual variables influence mathematics performance in direct or indirect ways.

We examined whether academic and professional bachelor students with dyslexia are able to compensate for their spelling deficits with metacognitive experience. Previous research suggested that students with dyslexia may suffer from a dual burden. Not only do they perform worse on spelling but in addition they are not as fully aware of their difficulties as their peers without dyslexia. According to some authors, this is the result of a worse feeling of confidence, which can be considered as a form of metacognition (metacognitive experience). We tried to isolate this metacognitive experience by asking 100 students with dyslexia and 100 matched control students to rate their feeling of confidence in a word spelling task and a proofreading task. Next, we used Signal Detection Analysis to disentangle the effects of proficiency and criterion setting. We found that students with dyslexia showed lower proficiencies but not suboptimal response biases. They were as good at deciding when they could be confident or not as their peers without dyslexia. They just had more cases in which their spelling was wrong. We conclude that the feeling of confidence in our students with dyslexia is as good as in their peers without dyslexia. These findings go against the Dual Burden theory (Krüger & Dunning, 1999), which assumes that people with a skills problem suffer twice as a result of insufficiently developed metacognitive competence. As a result, there is no gain to be expected from extra training of this metacognitive experience in higher education students with dyslexia.

Introduction. In the present study we used a metaphorical representation in order to stimulate the numerical competences of six-year-olds. It was expected that when properties of physical action are used for mathematical thinking or when abstract mathematical thinking is grounded in sensorimotor processes, learning gains should be more pronounced in children with stronger motor capacities than in children with rather low motor capacities. Method. Thirty-four first grade children with a mean age of 6 years and 6 months participat-ed in the experiment with a pre and posttest design. Therefore mouse handling precision, gross and fine motor performances and number line estimation was administered before and after the intervention with a digital number line. Results. In contrast to what was expected, children that performed below the median in a gross motor task benefitted significantly more from the intervention compared to children with scores above the median for such gross motor tasks. Discussion and Conclusion. These results do not only highlight the relationship between motor development and math learning but they also show that children with lower motor ca-pacities are possibly more in need of a strong physical appearance whereby the possibilities for action are clearly visible, even in digital tools. ispartof: Electronic Journal of Research in Educational Psychology vol:12 issue:1 pages:61-82 status: published

This research analyzed how fractions are taught in the fourth grade of elementary school in Flanders. Analysis centered on the presence of five features of instruction recommended by research on teaching and learning fractions (i.e., multiple solution pathways, linking representations, estimation and justification of the solution, collaboration, embedment in a realistic context). Our sample consisted of 88 instructional episodes that were selected out of 24 videotaped lessons and the corresponding lessons in the teacher’s guide. Analysis related to instruction as described in the teacher’s guide, instruction during the whole group phase of teaching, and instruction during the individual practice phase of teaching. The study revealed (1) that the observed lessons reflected to a limited extend the recommended instructional features and (2) factors that contributed to a departure from these recommendations. This research is situated in the domain of teaching and learning fractions and within the broader domain of curriculum implementation. ispartof: The Elementary School Journal vol:116 issue:1 pages:49-75 status: published

A relationship between motor and mathematical skills has been shown by previous research. However, the question of whether subtypes can be differentiated within developmental coordination disorder (DCD) and/or mathematical learning disability (MLD) remains unresolved. In a sample of children with and without DCD and/or MLD, a data-driven model-based clustering was used to identify subgroups of individuals with relatively homogeneous profiles on measures associated with motor and mathematical skills. One subgroup of children with motor problems was found based on motor variables. Based on mathematical variables, two clinical clusters were found: a subtype with number fact retrieval problems and a subtype with procedural calculation problems. Clustering with motor and mathematical skills revealed two clinical clusters: a cluster with number fact retrieval as well as procedural calculation problems and below average motor and visual-motor integration skills. A second cluster of children had only procedural calculation and visual-motor problems. Our results raise questions about the usefulness of placing children who have below average mathematical skills into a single diagnostic category. Furthermore, we inform ongoing debates about the overlap between DCD and MLD, as below average motor skills were found in both MLD subgroups, although a different motor profile is linked to a different mathematical profile.

The accuracy and speed in an enumeration task were investigated in adolescents with typical and atypically poor development of arithmetic skills. The number naming performances on small and large non-symbolic numerosities of 18 adolescents with mathematical learning disorders (MLD) and 28 typically achieving age-matched (TA) adolescents were compared. A mixed logistic regression model showed that adolescents with MLD were not significantly less accurate on numbers within the subitizing range than control peers. Moreover, no significant differences in reaction times were found between both groups. Nevertheless, we found that within the control group adolescents with higher ability tended to respond faster when taking into account the whole range (1-9) of numerosities. This correlation was much weaker in the MLD group. When looking more closely at the data, however, it became clear that the correlation between accuracy and speed within the control group differed in direction dependent on the range (subitizing or counting) of the numerosities. As such, our findings did not support a limited capacity of subitizing in MLD. However, the data stressed a different correlation between speed and accuracy for both groups of adolescents and a different behavioral pattern depending on the numerosity range as well. Implications for the understanding and approach of MLD are considered. © 2013 The Authors.

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.

Recent studies have shown that children with mathematics difficulties (MD) have weaknesses in multiple areas of mathematics. Andersson (2008), for example, recently found that children with MD perform significantly worse than other children on clock reading tasks. The present study builds on this recent finding and aims at a more profound understanding of the difficulties that children with MD experience with telling time. Therefore, clock reading abilities of 154 children with MD were compared to the ability of 571 average achieving children and a qualitative error analysis was performed. The results of this study confirm the earlier finding of Andersson (2008) that children with MD perform worse on clock reading than average achieving children, and additionally shows that children with MD are especially struggling the combination of procedural and retrieval strategies that are needed to read complex five minute and one minute clock times. Children with MD make more errors that reflect immature counting strategies and deficits in memory retrieval. This finding is in line with Geary’s (2005) theory of subtypes in MD, that argues that children with MD have problems with mathematical procedures and semantic memory retrieval.