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The aim of the present study was to address how to effectively predict mathematics learning disability (MLD). Specifically, we addressed whether cognitive data obtained during kindergarten can effectively predict which children will have MLD in third grade, whether an abbreviated test battery could be as effective as a standard psychoeducational assessment at predicting MLD, and whether the abbreviated battery corresponded to the literature on MLD characteristics. Participants were 226 children who enrolled in a 4-year prospective longitudinal study during kindergarten. We administered measures of mathematics achievement, formal and informal mathematics ability, visual-spatial reasoning, and rapid automatized naming and examined which test scores and test items from kindergarten best predicted MLD at grades 2 and 3. Statistical models using standardized scores from the entire test battery correctly classified ~80-83 percent of the participants as having, or not having, MLD. Regression models using scores from only individual test items were less predictive than models containing the standard scores, except for models using a specific subset of test items that dealt with reading numerals, number constancy, magnitude judgments of one-digit numbers, or mental addition of one-digit numbers. These models were as accurate in predicting MLD as was the model including the entire set of standard scores from the battery of tests examined. Our findings indicate that it is possible to effectively predict which kindergartners are at risk for MLD, and thus the findings have implications for early screening of MLD.

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... The learning difficulties in mathematics result from the lack of number sense skills (Gersten et al., 2005;Mazzocco & Thompson, 2005). Basic deficiencies in number sense (estimation, number line, counting operations, etc.) affect all activities, including quantities and the operation process (Butterworth, 2010), and constitute the reason for low mathematics achievement (Kuhn & Holling, 2014). ...

... It has been concluded that children with poor number sense have insufficient counting and operation skills, logical reasoning approaches, and understanding and using the relationships between numbers and operations (Burns, 2007). Thus, poor sense concerning numbers and operations leads to challenges in mathematics teaching (Baroody & Rosu, 2006) and learning (Landerl et al., 2004;Mazzocco & Thompson, 2005). ...

... Number sense that starts to be learned in early childhood and continues to develop in subsequent years of education is an important concept that should be learned and taught in mathematics education as it lays the foundation for learning mathematical concepts and establishing the relationships among them (Cheng & Wang, 2012;Mohamed & Johnny, 2010). Given the studies concluding that improvement of number sense skills increases GÖKÇE ET AL. | 3 mathematics achievements in years to come (Jordan et al., 2007;Mazzocco & Thompson, 2005;McGuire et al., 2012), lack of instruments that aim to identify number sense skills of primary school students raises concerns. ...

The purpose of this study is to develop tests for monitoring the number sense skills of primary school students based on proficiency definitions and to compare their number sense skills according to gender, school type, and mother's educational level. The first stage addressed to test development in which anchor items were used for vertical equating of number sense tests across grade levels. In the second stage, the number sense skills were compared in terms of student characteristics. The participants were 2034 primary school students. Reliable and valid number sense tests each consisting of 20 items were developed that allow comparison among Grades 2, 3, and 4. The findings indicated that number sense skills were not developed sufficiently in early childhood and had different trends in terms of gender through grades. Moreover, private schools outperformed public schools and the gap became higher in Grade 4. The results also showed that mother's education is an important factor for children to have higher number sense skills. Number sense is a prominent predictor of mathematics performance and monitoring number sense progress helps to evaluate the effectiveness of mathematics instruction.

... Most of children at risk of developing difficulties in mathematics show a profile characterized by poor performances in early math tasks (e.g., Mazzocco & Thompson, 2005) but also additional difficulties in domain-general processes, particularly memory processes (Raghubar, Barnes, & Hecht, 2010), with a stronger association with difficulties in visual-spatial memory (Szucs, Devine, Soltesz, Nobes, & Gabriel, 2013). This is particularly true for children that are at risk of developing specific learning disorders affecting math (Rosselli, Matute, Pinto, & Ardila, 2006;Szucs et al., 2013). ...

... Around 15-35 % of preschoolers can be classified as low achievers for early mathematical skills and are at an increased risk of being diagnosed with mathematical learning difficulties in school age (Mazzocco & Thompson, 2005). It is therefore necessary to define early training programs that may benefit children with this weakness. ...

... Additionally, the RM-S group also performed significantly better than the RM-NS group in rapid calculation. Mathematics achievement, particularly calculation skills here tested with both written and mental calculation tasks, are predicted by basic addition and subtraction abilities in kindergarten (Chard et al., 2005;Mazzocco & Thompson, 2005), counting skills (Koponen, Salmi, Eklund, & Aro, 2013) as well as numerical knowledge (Peng et al., 2016), all skills trained in our symbolic training. Therefore, we could assume that working on these skills at preschool age led to an adequate mathematics achievement in 1st grade. ...

Background: Children’s understanding of symbolic (e.g., Arabic digits) and non-symbolic (e.g., sets of dots) magnitudes plays a key role in their mathematics achievement, but only a few studies directly compared the effects of symbolic and non-symbolic interventions on mathematical abilities.
Aims: This longitudinal study compared the impact of symbolic and non-symbolic trainings in a group of preschoolers at risk of developing difficulties in mathematics (RM), analyzing their post-intervention performance both in early math skills (last preschool year) and in mathematics achievement in 1st grade.
Methods: Eighty-nine RM children and 66 typically developing controls were selected from among 604 preschoolers. RM children were assigned to three intervention conditions: no intervention, symbolic or non-symbolic intervention.
Results: Results showed specific effects on tasks related to the training (e.g., effects of symbolic training on symbolic tasks) and some effects of generalization (e.g., effects of symbolic training on non-symbolic tasks). In 1st grade, children attending the symbolic intervention showed a mathematics achievement profile similar to that of typically developing peers.
Conclusions: These results suggest the importance of training the symbolic processing of numbers at preschool age, allowing at risk children to catch up with their peers before entering formal schooling.
https://authors.elsevier.com/a/1cZXo3Ahveqzxb

... As argued by Bisanz, Sherman, Rasmussen, and Ho (2005), the acquisition of arithmetic is informative about how children develop knowledge in a specific domain. Moreover, acquiring more information on the mental process involved in arithmetic tasks may support educators in identifying useful educational activities and enhance our preschool years are predictive of their later math achievement (Jordan, Kaplan, Ramineni, & Locuniak, 2009;Mazzocco & Thompson, 2005;Östergren & Träff, 2013); in fact, previous studies (Jordan, Kaplan, Ramineni, & Locuniak, 2009;Mazzocco & Thompson, 2005) have demonstrated that five-year-old children who had a better grasp of basic arithmetic were more likely to achieve better math fluency by second and third grade. ...

... As argued by Bisanz, Sherman, Rasmussen, and Ho (2005), the acquisition of arithmetic is informative about how children develop knowledge in a specific domain. Moreover, acquiring more information on the mental process involved in arithmetic tasks may support educators in identifying useful educational activities and enhance our preschool years are predictive of their later math achievement (Jordan, Kaplan, Ramineni, & Locuniak, 2009;Mazzocco & Thompson, 2005;Östergren & Träff, 2013); in fact, previous studies (Jordan, Kaplan, Ramineni, & Locuniak, 2009;Mazzocco & Thompson, 2005) have demonstrated that five-year-old children who had a better grasp of basic arithmetic were more likely to achieve better math fluency by second and third grade. ...

... The definition of learning disability in mathematics is not agreed upon within professionals, and it creates an ongoing debate about how much difficulties in calculation and numeral understanding are specific difficulties in mathematical functioning (Augustyniak et al., 2006;Landerl et al., 2004;Mazzocco & Thompson, 2005), or do they reflect difficulties in general cognitive functioning, that are at the basis of mathematical functioning (Ardila & Rosselli, 2002;Geary, 1993;Shalev et al., 1997), such as language, memory, sequence perception and abstraction. The research about the causes of learning difficulties in mathematics is in progress, and mostly documents difficulties in specific subjects (National Mathematics Advisory Panel's task group, 2008). ...

... In the 3rd program they used conceptual explanations, such as: ʺcannot tell the story presented before him, therefore doesnʹt understand which number operation he should useʺ, and in addition, procedural explanations, such as: ʺdifficulty in connecting the words and numbers, that is he has difficulty identifying from the problem which number operations he is required to performʺ. These findings strengthen the importance of the distinguishing between mathematical functioning difficulties and general cognitive functioning difficulties (Augustiniak, Murphy & Phillips, 2006;Landerl et al., 2004;Mazzocco & Thompson, 2005). Geary (2005) and Strang and Rourke (1985) claim that students who have difficulties acquiring mathematical knowledge have a variety of learning disabilities. ...

... Early mathematics is a potent predictor of later school achievement, as many researchers have demonstrated to date (Duncan et al., 2007;Geary, 2013;Mazzocco & Thompson, 2005). The associations between early and later mathematics achievement are particularly noteworthy, in view of the association school mathematics achievement has with a wide range of quality of life outcomes ranging from career success (Ritchie & Bhatia, 1999) to health and financial outcomes and decision making (Adams, 2002). ...

... The associations between early and later mathematics achievement are particularly noteworthy, in view of the association school mathematics achievement has with a wide range of quality of life outcomes ranging from career success (Ritchie & Bhatia, 1999) to health and financial outcomes and decision making (Adams, 2002). The trajectory of mathematics achievement levels begins even before school entry, and unfortunately for many U.S. students, it begins with poor numeracy skills at kindergarten entry (Duncan et al., 2007;Mazzocco & Thompson, 2005) and continues with underachievement in school mathematics through high school (Geary, 2013). Altering persistently low mathematics achievement trajectories requires instructional support or intervention (Aunola et al., 2002) in the early grades, and an academically productive first-grade experience may provide a foundation for children's continued mathematics success throughout school (Watts et al., 2014). ...

To investigate whether child × instruction effects contribute to mathematics gains in first grade, we conducted a cluster randomized controlled trial with 454 (205 treatment; 249 control) students in 28 classrooms. Classrooms were randomly assigned to implement Math Peer Assisted Learning Strategies (Math PALS) to supplement Saxon Math or Saxon Math alone. Teachers received professional development on either Math PALS (treatment) or individualized reading instruction (control). Intent-to-treat and treatment-on-the-treated results revealed no significant difference between the Math PALS and control groups in student mathematics gains. However, Math PALS effectiveness varied with initial math skills. Based on modeled results of the continuous fall math score, students who scored at the 75th percentile of the sample demonstrated significantly stronger mathematics outcomes compared with the treated control group; there was no significant treatment effect for students at the 50th percentile. For students with lower initial math skills (modeled at the 25th percentile of the sample), the effect of the treatment was negative. Students with lower initial mathematics skills made greater gains in the control group (Saxon Math alone) versus the Math PALS group.

... Children at risk of SLD may experience preliminary symptoms in math skills early in childhood. These may include problems with recognition, counting numbers, and arithmetic problems (Mazzocco & Thompson, 2005). These math difficulties can be a sign of the difficulties children may face in their future learning. ...

The assessment of teachers' perceptions can lead to findings on the need for teacher training and information. The purpose of the research is to determine the perceptions of teachers regarding knowledge and perceptions about the early detection of learning difficulties in early childhood and can lead to findings of the necessity of information and training of teachers as this is usually considered necessary in order for teachers to keep up with the renewed social conditions. The survey was conducted in March 2023 with an electronic distribution of a questionnaire to 68 preschool teachers. The findings that emerged are generally consistent with findings of previous research and highlight the importance of early detection of learning difficulties and link it to language disorders in students. However, they face difficulties as they are not sufficiently-adequately trained and do not have the necessary diagnostic tools and have not adopted appropriate strategies to support students with Specific Learning Difficulties.

... European Journal of Education Studies -Volume 10 │ Issue 7 │ 2023 218 includes the ability of individuals to understand, solve and apply mathematical issues, is becoming more and more essential for all individuals today. Especially 21st century technology jobs and many other daily activities require a mathematical ability (Mazzocco & Thompson, 2005). Curriculum and assessment standards for school mathematics in the United States [NCTM, 1989] and the National paper on mathematics for Australian schools [AEC, 1991] identify the development of "number sense" as an important core output of school mathematics. ...

In this research, the cartoon "Yade Yade" broadcasted on TRT Çocuk, Turkey's national channel where programs for children's education are broadcast, was examined in terms of number sense components. In this context, 52 episodes of the cartoon "Yade Yade", which has been broadcast on TRT Çocuk since 2020, were used as data sources. Document analysis method was used in data analysis. The 52 episodes of the cartoon "Yade Yade" were examined in terms of number sense components (counting aloud, measuring concepts, nonverbal calculation, number identification, and quantity discrimination) used by Lago and DiPerna (2010). When the number components were analyzed for each section, it was seen that the measuring concepts component was mostly emphasized. This number sense component was followed by number determination, recognizing quantity, counting aloud and nonverbal calculation components. Various suggestions were developed in line with the results of the study. "Yade Yade" cartoon can be used for educational purposes in mathematics lessons in schools to emphasize the number sense, especially the component of measuring concepts. This and similar cartoons can be analyzed in terms of content and concept teaching can be realized in lessons.
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... More specifically, participants were only included in the high-achieving group if they showed persistent high achievement in mathematics (i.e., above the 90th percentile across multiple time points). This multiple assessment criterion has been applied in literature on children with dyscalculia with the main aim of lowering the possibility of having false positives in the achievement groups (Mazzocco & Thompson, 2005). ...

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.

... Furthermore, early quantitative weaknesses, such as deficiencies in number relations and basic operations, can create difficulties in mathematics for children later in life (Bull et al., 2020;Mazzocco & Thompson, 2005;Desoete et al., 2012) linked the ability of pre-school children to compare numbers as symbols and writing with 1st and 2nd grade arithmetic and operational skills. Moreover, children with math difficulties who struggle with comparing symbolic and non-symbolic numbers during the pre-school period also tend to experience difficulties with numerical operations later in their schooling. ...

Early identification of children with learning disabilities (LD) is extremely important. In order for early identification to be made, it is necessary to determine the characteristics of these children in early life. The present study aimed to examine the developmental characteristics of children with LD in the age intervals of 0–2, 2–4, and 4–6, based on parental observations. For this purpose, interviews were conducted with the parents of 35 children identified with LD. The data were collected through a semi-structured interview form and they were analyzed using content analysis. The data were interpreted and classified using an inductive approach. The results indicated that children with LD have different characteristics in terms of speech and language proficiency, social, psychomotor, cognitive, and sensory skills compared to children without LD. Moreover, the participants’ responses indicated that the majority of the children had their LD identified after the first year of primary school. After a thorough discussion of the study findings, recommendations are made for future research and practice in this area.

... The mathematical skills of children entering kindergarten vary widely: Some children are unable to recognize Arabic numerals or recite the count list, whereas others can already do simple arithmetic (Jordan et al., 2009;Mazzocco & Thompson, 2005;Zill & West, 2001). This variability has implications for later development and academic achievement, as individual differences in mathematical skills demonstrate remarkable rank-order stability throughout elementary school grades and beyond (Duncan et al., 2007;Jordan et al., 2009). ...

We explore whether training parents' math skills or playing number games improves children's mathematical skills. Participants were 162 parent–child dyads; 88.3% were white and children (79 female) were 4 years (M = 46.88 months). Dyads were assigned to a number game, shape game, parent‐only approximate number system training, parent‐only general trivia, or a no‐training control condition and asked to play twice weekly for 8 weeks. Children in the number game condition gained over 15% SD on an assessment of mathematical skill than did those in the no‐training control. After 8 additional weeks without training, effects diminished; however, children of parents in the ANS condition underperformed those in the no‐treatment control, which was partially explained by changes in the home numeracy environment.

... Andernorts erbrachten breitere Variablen Sets (Zählfertigkeiten, Zahlwissen, Vorgänger, Nachfol ger, Vergleiche, nonverbales Rechnen, Addition und Subtraktion, Zahlzerlegung) die beste Prognoseleistung (Jordan, Kaplan, Locuniak und Ramieni, 2007;Jordan, Kaplan, Ramineni & Lokuniak, 2009). Mazzocco & Thompson (2005) wiesen auf eine überlegene Bedeu tung numerischer Basiskompetenzen gegenüber allge meinkognitiven Variablen hin. Sie entwickelten darüber hinaus auf der Grundlage von Einzelitems Prognosemo delle (Invarianz, Mengenbeurteilung, Rückwärts zählen, einfache Addition, Zahlenlesen) mit einer noch größeren Gesamttrefferquote als die Modellierung auf Grundlage der UntertestSummenwerte. Dabei erhielten unter schiedlich schwierige Items derselben Skala Zählfähig keit auch unterschiedliche Gewichte: Während das Rück wärtszählen den größten Beitrag zur Steigerung der Prognosegüte leistete, konnte das Abzählen von Mengen kleiner fünf die Gruppe der rechenschwachen und nicht rechenschwachen Kinder nicht trennen. ...

Zusammenfassung. Hintergrund: Einen wichtigen Baustein im Rahmen der Prävention von Rechenschwierigkeiten stellen Screening-Verfahren dar, die ein individuelles Entwicklungsrisiko zuverlässig und frühzeitig aufzeigen. Die meisten Instrumente zur Prognose solcher Schwächen im Grundschulalter sind überwiegend als vergleichsweise zeitaufwändige Einzelverfahren konzipiert. Das Ziel der vorliegenden Studie ist die Entwicklung und Evaluation eines gruppenbasierten Screening-Verfahrens für den Einsatz am Schulanfang. Methode: Im vorliegenden Beitrag werden die Entwicklung und Evaluation eines Filter-Screenings an einer Stichprobe von insgesamt 174 Erstklässlern beschrieben. Ein breites Variablen-Set aus domänenspezifischen und domänenunspezifischen Prädiktoren der mathematischen Leistung wurde in die Analyse einbezogen. Resultate: Auf der Basis der logistischen Regressionsanalyse konnte ein durch eine Kreuzvalidierung abgesichertes Vier-Variablen- Prognosemodell (Mengenschätzen, Vorgänger benennen, Zahlen lesen, Matrizen-Test) identifiziert werden, das sehr gute AUC-Werte (bis zu >> .90) aufweist. Diskussion: Die Ergebnisse liefern wertvolle Erkenntnisse hinsichtlich der Implementation eines validen und Schuleingangsscreenings als Gruppenverfahren.

... Much of the research on the development of math skills focuses on early numerical predictors of later math achievement (e.g., Jordan et al., 2009;Mazzocco & Thompson, 2005) and the pathways through which these predictors operate. Yet non-numerical skills, such as language, may also be important for learning math. ...

Relational language is thought to influence mathematical skills. This study examines the association between relational language and number relation skills—knowledge of cardinal, ordinal, and spatial principles—among 104 U.S. kindergartners (5.9 years; 44% boys; 37% White, 25% Black, 14% Asian, 24% other) in the 2017–2018 academic year. Controlling for general verbal knowledge, executive function, and counting and number identification skills, relational language predicted later number relation skills, specifically number line estimation, β = .30. Relational language did not differentially predict number line estimation performance in children with low or high number relation skills, likely due to the restricted ranges of data within subgroups. Number relation skills, specifically number line estimation and number ordering, may be a pathway between relational language and mathematical skills.

... On the other hand, approximate knowledge of count+unit syntax, though limited, may nonetheless benefit performance in tasks that require explicit knowledge. Approximate tasks have been widely used in studies showing that early number skills of children in preschool, kindergarten, first grade, and second grade predict later mathematics achievement (Bodovski & Farkas, 2007;Bugden & Ansari, 2011;Duncan et al., 2007;Gersten et al., 2005;Holloway & Ansari, 2009;Jordan et al., 2009;Krajewski & Schneider, 2009a, 2009bMazzocco & Thompson, 2005;Mazzocco et al., 2003;Morgan et al., 2009). For example, first graders' arithmetic skills predicted their later mathematical achievement on a standardized assessment in fourth grade (Krajewski & Schneider, 2009a). ...

Place value concepts were measured longitudinally from kindergarten (2017) to first grade (2018) in a diverse sample (n = 279; Mage = 5.76 years, SD = 0.55; 135 females; 41% Black, 38% White, 8% Asian, 12% Latino). Children completed three syntactic tasks that required an explicit understanding of base-10 symbols and three approximate tasks that could be completed without this explicit understanding. Approximate performance was significantly better in both age groups. A factor analysis confirmed that syntactic and approximate tasks tapped separate latent variables in kindergarten, but not in first grade. Path analyses indicated that only kindergarten approximate performance predicted overall first-grade place value understanding. These findings suggest that explicit understanding of base-10 principles develops from implicit, partial knowledge of multidigit numbers.

... Children's achievement in mathematics during their kindergarten period has been found to be the best predictor of not only later mathematics, but also their reading achievement (Claessens, Duncan, & Engel, 2009;Claessens & Engel, 2013). Teaching children the early number competencies will maximize their mathematics achievement (Jordan, International Journal of Instruction, January 2022• Vol.15, No.1 Kaplan, Ramineni, & Locuniak, 2009), otherwise, they may have mathematics learning disabilities (Mazzocco & Thompson, 2005). As a result of their poor number competencies, and hence over relying on rote memorization, children may have weak problem-solving skills (Robinson, Menchetti, & Torgesen, 2002). ...

... The analysis of the data made it possible to highlight various explanatory factors for the learning difficulties relating to mathematical knowledge. As mentioned by Mazzocco and Thompson [45], a misunderstanding of number sense can later lead to difficulties in learning various mathematical concepts promoted within the school curriculum. In this regard, we see that the respondents to the study consider that the explanatory factors of learning difficulties relating to mathematical knowledge are mainly associated with the field of arithmetic as well as problem-solving activity. ...

... There is also evidence that preschool working memory skills predict later math performance in school (Gathercole, Brown, & Pickering, 2003;Mazzocco & Thompson, 2005). It is thus plausible that in individuals with dyscalculia, working memory deficits appear even before the problems in arithmetic development become manifest. ...

Dyscalculia is a neurodevelopmental disorder negatively affecting important aspects of maths learning. It results from a complex interplay of cognitive factors that are domain-specific (directly related to the domain of maths learning) or domain-general (related to different domains of learning). While current research has identified early predictors of general math learning, our knowledge of early development of dyscalculia is as yet limited. This chapter gives an overview of research on potential domain-specific predictors (i.e., different aspects of numerical processing) and domain-general predictors (i.e., working memory/executive functions, verbal abilities, spatial reasoning) of maths learning in general and dyscalculia in particular. We also summarize the current state of research on the neurobiological basis of dyscalculia and identify a number of research gaps that should be addressed in future research.

... As an example, Graham et al. (2017) carried out a meta-analysis that reported that students with LD receive lower scores in writing skills compared with their peers. Similarly, it has also been observed in other studies that students with LD display lower performance in mathematics skill compared to their typically developing peers, which also continues in future school processes (Desoete et al., 2012;Mazzocco & Thompson, 2005). ...

The purpose of this study was to examine the impact of training on learning disabilities (LD) on school counsellor candidates' perceptions related to students with LD. The study group was comprised of 51 students in the Counselling and Psychological Guidance Department. The participants responded to an open-ended question: 'Students with learning disabilities are like ....... Because ....... '. A content analysis technique was used in the analysis of the data. Based on the study results, it was determined that before being trained on LD, the majority of the participants considered students with LD as problematic or never progressing. Following the training, a majority of the participants started using metaphors indicating that students with LD may progress and learn.

... De hecho, el rol del sentido numérico en las DAM también ha sido apoyado por múltiples investigaciones donde se ha demostrado que las DAM resultan primariamente de déficits en procesamiento numérico (Mazzocco y Thompson, 2005). Asimismo, Gersten, Jordan, y Flojo (2005) demostraron que la presencia de dificultades a la hora de recuperar de forma rápida hechos numéricos estaba vinculada con el desarrollo del sentido numérico, siendo un rasgo consistente en los estudiantes con DAM. ...

This study analyses the factorial structure of Mathematics Progress Indicators (IPAM), by using Confirmatory Factorial Analysis (CFA) techniques. For this purpose, a longitudinal study was carried out with a sample of 176 first-grade students from the Canary Islands, IPAM was administered to the study sample three times throughout the scholar year. The IPAM is a Curriculum-Based Measurement (CBM) instrument composed of three alternative or parallel measures (A, B and C) that try to measure the same latent structure (i.e., number sense). The IPAM measures were administered three times per year (i.e., fall, winter, spring). Its main objective is the universal screening and evaluation of students' mathematics learning progress in the elementary grades through the evaluation of fluency for different tasks (i.e., magnitude comparison, one-digit operations, two-digit operations, missing number, and position value). Fluency is measured by counting the number of correct answers given by the student at a given time. The results of the CFA confirm a good fit of the proposed model for the different moments of measurement.

... Berg, 2008;Hubbard et al., 2005;Krajewski & Schneider, 2009;Simmons et al., 2012;van der Ven et al., 2013) and visual perception (Kurdek & Sinclair, 2001;Sigmundsson et al., 2010) influence the mathematics achievement because of their links with number sense. It is also stated that students with poor number sense have difficulties in calculation (Gersten et al., 2005;Mazzocco & Thompson, 2005). On the other hand, research has revealed that there are positive and significant relationships between reading comprehension and mathematics achievement (Lin et al., 2013;Harlaar et al., 2012;Kyttala & Björn, 2014) and number sense (Geary et al., 2013). ...

The purpose of this study was to investigate the bibliometric analysis of number sense studies over the past 30 years and monitor the trend regarding the nomological network accordingly. All the published articles in Web of Science database, containing the term number sense between 1990 and 2019, constituted the focus of the study. In the analysis of 448 articles, the distance-based bibliometric maps and the clusters were created by VOSviewer so that they provide information about the existence of nomological networks and the occurrence of the number sense-related concepts. The results of the study indicated that the terms of number sense-related studies were clustered in four groups depending on the degree of the relationships among them. The groups were identified as recognition of number sense to define clearly (recognition), evaluating the number sense to support (evaluation), associating the number sense with other skills and abilities to increase the success (association) and promoting number sense to improve instruction (promotion). This study put forth evidence to list the interrelated terms, to show the close relationship among the terms, to emphasize the diversity, to reveal the intertwining and to show the richness of number sense.

... al 1996;Badian, 1983;Lewis, 1994;Hein, 1999;Rekha, 2008). However, it is estimated in the literature that 5%-10% of school children have learning disabilities in different levels and characteristics, which affect the learning in math(Mazzocco &Thompson, 2005). According to Professor Brian Butterworth proposes that the best estimates indicate a ...

... al 1996;Badian, 1983;Lewis, 1994;Hein, 1999;Rekha, 2008). However, it is estimated in the literature that 5%-10% of school children have learning disabilities in different levels and characteristics, which affect the learning in math(Mazzocco &Thompson, 2005). According to Professor Brian Butterworth proposes that the best estimates indicate a ...

... believe mathematics achievement should be given serious Mathematics is considered a form of art and beauty as attention as the issue of students who have difficulties in well as an effective communication tool. In the era of mathematics are also more serious [3,4,5,6,7,8,9]. At the globalization, the world is dominated by science and same time the issue of the factors that contribute to the technology with a strong focus on the mastery of achievement and the difficulty of mathematics is no less mathematics. ...

This paper reports the use of a systematic review to explore the impact of gender on children's achievement and their skills in mathematics. The review process identified 6 key papers within the lastest five years (2010-2015). An in-depth analysis of these indicated that there was some evidence that there is a significant difference in children's mathematical achievements due to gender. The analysis also found that boys have better math skills compare to girls. These findings very important because have led to some improvement in children's confidence and competence in mathematics. However, the analysis also highlighted some future searches to be studied.

... Early mathematics, or informal math skills, occurs over three stages during which children progress from non-numeric quantity discrimination (e.g., comparing piles of jelly beans), quantity to number-word linkage (e.g., counting the number of jelly beans in a pile), and then to symbolic and nonsymbolic quantity relations (e.g., adding or subtracting jelly beans across piles; Krajewski & Schneider, 2009;Siegler & Lortie-Forgues, 2014) beginning prior to school entry and continuing until from around first grade to third grade where more formal math skills begin to develop (e.g., Sarama & Clements, 2009). Formal math knowledge involves the mastery of number competencies, which include number recognition, number comparisons, and understanding number magnitudes (e.g., Mazzocco & Thompson, 2005;Jordan, Kaplan, Ramineni, & Locuniak, 2009;Merkley & Ansari, 2016). As these comparisons and magnitudes extend to increasingly larger numbers and number arrays, and nonsymbolic concepts are mapped onto increasingly more complex symbolic systems, mastery of formal math knowledge progresses (e.g., Lyons & Ansari, 2015;Siegler & Lortie-Forgues, 2014). ...

This study investigated developmental trajectories of reading and math using latent-growth-curve analyses across multiple academic skills, measures, and multiple time periods within a single sample. Reading-related growth was marked by significant individual differences during the early elementary-school period and non-significant individual differences during the late elementary-school period. For math-related skills, non-significant individual differences were present for early math growth and significant individual differences were present in late elementary-school. No clear pattern of cumulative, compensatory, or stable development emerged for either reading-related or math skills. These differing growth patterns highlight developmental complexities and suggest domain-specific differences in achievement growth that are potentially associated with contextual factors.

... 3. Highlighting text animation significantly improves the AOI fixation ratio of students with MLD. 4. Highlighting text animation leads to an overall shift of the attention distribution of students with MLD. ...

... Children at risk of SLD may exhibit preliminary symptoms in mathematics skills in early childhood. These can include number recognition, number counting, and numerical problems (Mazzocco & Thompson, 2005). These difficulties in mathematics can be a sign of the difficulties children may face in their future learning. ...

... In early primary school (first and second grade), numbers and operations, also referred to as early numeracy (Aunio and Niemivirta, 2010) or symbolic number sense (Jordan et al., 2010), encompasses the skills of number knowledge, verbal counting, basic calculations, and quantity comparison. Early numeracy has been found to be the area of early mathematics most predictive for later success in mathematics (Mazzocco and Thompson, 2005). In this paper the terms numeracy and arithmetic are used interchangeably. ...

Early numeracy has been found to be one of the strongest predictors for later success in learning. Equipping children with a sound conceptual numerical understanding should therefore be a focus of early primary school mathematics. Assessments that are aligned to empirically validated learning progressions can support teachers to understand their students learning better and target instruction accordingly. This study examines numeracy learning of 101 first grade students over the course of one school year using progression-based assessments. Findings show that the students' performance increased significantly over time and that the initial conceptual numerical understanding had a positive effect on the students' learning progress as well as their end of school year performance. Analyzing the performance data based on the levels of the underlying developmental model uncovered an increasing elaboration of conceptual numerical understanding over time, but also individual differences within this process that need to be addressed through targeted intervention.

... These are often shown with measures of "number sense." For example, kindergartners who cannot complete number comparison, number conservation, and numeral reading tasks are likely to show persistent difficulties in the primary grades (Mazzocco & Thompson, 2005). Understanding specific areas of need can help design programs for individual children. ...

Research Findings: Educators declare their commitment to high-quality education for all children. Science, Technology, Engineering, and Mathematics (STEM) has been increasingly included as critical topics, even for young children. However, there are exceptions, especially the provision of developmentally appropriate STEM experiences to children with disabilities (CWD). In this article, we review evidence concerning this equity gap, including the importance of STEM education to CWD. We find that the early years provide an exceptional opportunity to introduce STEM, but that this potential is often left unrealized, especially for young vulnerable children, who live in poverty, are members of linguistic and ethnic minority groups, or are CWD (some with particular disabilities in STEM domains). Research also indicates the success of some educational approaches. Practice or Policy: Research and development in each of the STEM domains, as well as interdisciplinary approaches provides directions for both policy and practice. For example, both need to change to reflect importance of STEM for all young children, especially CWD, the need to change harmful beliefs, and the positive effects of approaches based on learning trajectories. We conclude with an introduction of a new center to support inclusive innovation in early education in STEM.

... La mayoría de investigaciones se han centrado en la recuperación directa de los hechos de la memoria a largo plazo ya que proporciona la automatización que es necesaria para resolver de forma eficaz tareas aritméticas más complejas (Geary, Hamson, Hoard, 2000;Mazzocco y Thompson, 2005). Sorprendentemente, se localizan pocas investigaciones referidas a la utilización de estrategias de hechos derivados en niños con dificultades aritméticas. ...

Este estudio analizó las estrategias aritméticas manejadas por un total de 138 alumnos de 4º, 5º, y 6º de Educación Primaria, clasificados en tres grupos de competencia aritmética: dificultades de aprendizaje en matemáticas (DAM; n = 51), competencia normal (CN; n = 60) y alto rendimiento (AR; n = 27). Se evaluaron las estrategias utilizadas para resolver las tareas de suma, resta, multiplicación y división a través de la batería BANEVHAR, en una sesión individual para cada participante. Los resultados señalaron efectos principales del nivel educativo en la utilización de la estrategia de recuperación de hechos en las tareas de suma (p < .01), resta (p < .001) y división (p < .001) y en el manejo de las estrategias individualizadas con restas (p < .05) y divisiones (p < .05). También se localizaron efectos significativos del grupo de competencia que señalan que los niños con DAM acudieron menos veces a la estrategia de recuperación que los de AR en tareas de suma (p = .001) y resta (p = .001). Los análisis de seguimiento mostraron como los grupos con DAM y CN consolidan entre 4º y 6º curso la estrategia de recuperación de hechos de la suma, la resta y la multiplicación. Parece que en estos niveles educativos todavía se produce en los grupos con DAM y CN un progreso desde estrategias inmaduras hacia la recuperación directa de los hechos, mientras los niños del grupo con AR parecen dominar esta estrategia al acceder al 4º curso.

Geometric knowledge is one of the important mathematical skills acquired by children at a young age and is a major area of future mathematical learning; however, there is no direct research on the factors influencing kindergarteners' early geometric knowledge. The pathways model to mathematics was modified to examine the cognitive mechanisms underlying geometric knowledge in Chinese kindergarten children aged 5-7 (n = 99). Quantitative knowledge, visual-spatial processing, and linguistic abilities were stepped into hierarchical multiple regression models. The results revealed that after age, sex, and nonverbal intelligence were statistically controlled, visual perception, phonological awareness, and rapid automatized naming in linguistic abilities significantly predicted the variation in geometric knowledge. For quantitative knowledge, neither dot comparison nor number comparison test could be a significant precursor of geometry skills. The findings indicate that visual perception and linguistic abilities, not quantitative knowledge, account for the geometric knowledge of kindergarten children.

Some psychological factors related to preschool teachers significantly impact mathematics teaching in early childhood classrooms. Thus, examining teachers' views on preschool mathematics will guide teachers in understanding which concepts were included in early childhood mathematics and preparing an educational environment and program appropriate for children's developmental levels. This research was a descriptive-study, and was implemented using general-survey model with 107 preschool teachers. Data were collected by teacher views form on early childhood mathematics. Data were evaluated with descriptive and non-parametric statistical methods. Results showed that the teachers used math activities with games, art, drama activities and used limited methods to assess whether children have learned mathematics concepts. In addition, most teachers stated that data analysis, proof, and probability cannot be taught in preschool. Finally, most teachers considered preschool mathematics moderately important and that there was no significant difference among ages, professional service periods, the institution and school types they work in, and the order of importance of mathematics (p > .05).

A educação infantil como a primeira etapa do ensino e agora como uma etapa obrigatória, tem como missão o
desenvolvimento integral da criança. E nessa integralidade incluem-se marcos de desenvolvimento e assim, as
habilidades numéricas. O presente artigo esclarece como os documentos oficiais norteadores se referem a
educação matemática e a intrínseca relação com o brincar. Em seguida descreve como a matemática é erigida na
mente da criança ao longo dos primeiros anos de vida, e por fim demonstra uma lista de brinquedos e uma
sequência didática de como aplicar o uso de um deles no espaço pedagógico.

This study investigates the effectiveness of a number sense instruction program for children at risk of math difficulties in the preschool age. This program was designed based on the fundamental components of number sense and through a developmental approach (e.g. quantity, number, line number, and connection number). First, 426 preschoolers were selected and assessed through two screening questionnaires (teacher form and parent form) and then, after execution of Jordan’s number sense test and number knowledge on these children, 90 children were identified at risk of math difficulties. Using quasi-experimental and random techniques, subjects were classified into two experimental and control groups The experimental group experienced instructional treatments for number sense for 45 minutes for eight weeks. Then, once again both experimental and control groups were evaluated by Jordan’s number understanding test. The results were analyzed using the MANCOVA method, which indicated a meaningful difference between experimental group students’ progression (under the influence of instructional treatment of number sense) in the items of counting, quantity and number relations with the control groups in post-test. The results also indicate that instruction of number sense for improvement of calculation skills in children with math difficulties would play a preventive role in math disabilities in elder ages.

Bu çalışmada kaynaştırma/bütünleştirme uygulamalarının yürütüldüğü okul öncesi sınıflarda eğitim gören özel gereksinimi olan ve olmayan öğrencilerin matematik performanslarının öğretmen görüşüne dayalı olarak belirlenmesi amaçlanmıştır. Bu amaçtan hareketle öncelikle geçerliği ve güvenilirliği ispatlanmış bir ölçme aracının alanyazına kazandırılması, okul öncesi sınıflardaki öğrencilerin matematik performans düzeylerinin belirlenmesi ve matematik performans düzeylerinde farklılık oluşturan değişkenlerin ortaya konulması hedeflenmiştir. Ölçek geliştirme aşamaları dikkate alınarak hazırlanan çalışmada betimsel tarama modeli kullanılmıştır. Çalışma grubu amaçsal örnekleme yöntemi ile belirlenmiştir. Çalışmanın amaçları doğrultusunda öncelikle madde havuzu oluşturulmuş, uzman görüşü alınarak ölçeğin pilot uygulama formu oluşturulmuştur. Daha sonra geçerliğe ve güvenirliğe ilişkin analizlerin yapılması ve ölçme aracının nihai formunun oluşturulması için bağımsız anaokullarında hizmet veren 194 öğretmenden 970 öğrenciye ilişkin veri toplanmıştır. SPSS paket programına aktarılan veriler üzerinde normal dağılıma ilişkin varsayımlar incelenmiş ve uygun istatistiksel işlemler kullanılarak analizler yapılmıştır. Çalışmanın ilk amacı doğrultusunda öncelikle, geliştirilen üç alt formdan oluşan Matematik Performansı Değerlendirme Aracı'nın (MAPEDA 36-72 Ay) kapsam ve yapı geçerliği analizleri ile geçerlik; Cronbach alfa, iki yarı test, alt-üst %27 ve madde toplam korelasyonu analizleri ile güvenirlik analizleri gerçekleştirilmiştir. Yapı geçerliği analizi için yapılan AFA ile ölçeğin faktör yapıları belirlenmiş; 5 faktörlü 27 maddelik MAPEDA (36-48 Ay), 5 faktörlü 34 maddelik MAPEDA (49-60 Ay) ve 5 faktörlü 34 maddelik MAPEDA (61-72 Ay) formları elde edilmiştir. MAPEDA'nın (36-72 Ay) açıklanan toplam varyans değerleri; MAPEDA (36-48 Ay) formu için %66, MAPEDA (49-60 Ay) formu için %71 ve MAPEDA (61-72 Ay) formu için %73'tür. DFA ile test edilen uyum değerlerinin (RCI, CFI, NFI, NNFI, IFI, RF, RMSEA, RMR, SRMR, GFI, AGFI) her bir alt form için mükemmel uyum gösterdiği görülmüştür. MAPEDA (36-72 Ay) için yapılan güvenirlik analizleri sonucunda Cronbach α güvenirlik değerleri; MAPEDA (36-48 Ay) formu için .98, MAPEDA (49-60 Ay) formu için .99 ve MAPEDA (61-72 Ay) formu için .99, iki yarı test güvenirliği r değerleri; MAPEDA (36-48 Ay) formu için .97, MAPEDA (49-60 Ay) formu için .96 ve MAPEDA (61-72 Ay) formu için .96 bulunmuştur. MAPEDA'nın (36-72 Ay) her bir alt formu alt-üst %27 güvenirlik p değeri .05 düzeyinde anlamlı bulunurken madde toplam korelasyon değerlerinin alanyazında belirtilen kriterleri sağladığı tespit edilmiştir. Çalışmanın ikinci amacı doğrultusunda okul öncesi kaynaştırma/bütünleştirme uygulamalarının yürütüldüğü sınıflarda eğitim gören öğrencilerin matematik performans düzeyleri MAPEDA (36-72 Ay) ile değerlendirilmiş ve öğrencilerin çoğunun (%51) çok düşük ve düşük matematik performans düzeyine sahip oldukları belirlenmiştir. Araştırmanın son amacına yönelik kaynaştırma/bütünleştirme uygulamaları yürütülen okul öncesi sınıflarında eğitim gören öğrencilerin matematik performans düzeyleri; aileye (aile gelir düzeyi, anne baba eğitim düzeyi, ailedeki çocuk sayısı), öğrenciye (cinsiyet, eğitim alma süresi, tanı durumu), öğretmene (cinsiyet, yaş, mesleki kıdem) ve sınıfa (sınıf mevcudu, tanılı öğrenci sayısı, yardımcı/gölge öğretmen durumu) yönelik değişkenlere göre değerlendirilmiştir. Analiz sonuçlarına göre; aile gelir durumu, öğrenci cinsiyeti, öğrencinin tanı durumu ve yardımcı/gölge öğretmen durumunun MAPEDA'nın (36-72 Ay) her bir alt formunda öğrencilerin matematik performans düzeyleri üzerinde anlamlı farklılıklara yol açtığı tespit edilmiştir.

We examine a potential mechanism underlying the relation between executive function (EF) skills and mathematics achievement in early childhood. Across two samples of three- to six-year-olds in preschool and kindergarten, we found that children’s EF skills predict their concurrent skills in set counting, numeral identification, number comparison, and number line estimation. The effects of EF on later numeral identification, number comparison, and number line estimation skills remained significant for these two samples of children, but these effects attenuated when controlling for the respective earlier numeracy skill. Further, aspects of numeracy skills mediated the association between EF and mathematics achievement in both samples. Together, these findings provide evidence on the nuanced relations between EF, numeracy, and mathematics achievement, and suggest attention to each numeracy skill in order to support early mathematical development.

Hay evidencias de que la mayoría de los niños entran en la escuela con conocimientos y recursos fundacionales para su aprendizaje matemático. Sin embargo, esta no es la historia completa. Resultados de investigaciones revelan enormes diferencias entre los niveles de competencia matemática de los niños pequeños, y estas diferencias parecen ser más acusadas en los Estados Unidos que en algunos otros países (por ejemplo, China) (Starkey y Klein, 2008). En este artículo se describen los tipos de diferencias que se dan y se ofrece una revisión sobre lo que se sabe acerca de la naturaleza y las fuentes de las variaciones en el desarrollo entre los niños.

The present study examined whether the number of manipulatives used in arithmetic strategy instruction influences learning. First graders were randomly assigned to one of the following conditions for learning a decomposition strategy to solve arithmetic problems: intervention with a single manipulative, intervention with multiple manipulatives, and a business-as-usual control condition. Both intervention conditions produced a greater increase in the use of decomposition for mental calculation than the control condition. The pattern of results across the intervention conditions varied as a function of the outcome examined. In terms of children’s mastery of strategy execution with the manipulatives, there was no difference between these conditions. In terms of generalization, children whose instruction involved two complementary manipulatives tended to generalize the base-10 strategy to mental calculation to a greater extent than children whose instruction involved a single manipulative. Most noteworthy was that the findings indicated path-dependent transfer: children who mastered decomposition in the multiple-manipulatives condition were more likely to generalize this knowledge to mental calculation than those who achieved mastery via practice with a single manipulative. The implications of these findings for better understanding the conditions under which manipulatives are likely to affect learning for different outcomes is discussed.

Language and Mathematics are cornerstones of all educational programs and are vital to both an individual’s success as well as his or her country’s competitiveness. Despite their importance, there is no consensus on the best order or methods to teach early math and language, or even if these are necessary at all. Contributions from neuroscience are relatively new on the stage of early childhood education, though many can offer insights as to the correct hierarchical introduction of math and language skills. “Neuroconstructivism” is a term used to explain how the brain makes basic connections, then successively more complex ones until neural pathways are formed, permitting observable behavior. A better understanding of the logical building blocks of cognition may permit a more precise and orderly introduction of math and language skills in the early years. This international comparative literature review considered language and mathematical milestones in children 0-6 years old, then the contributions from neuroscience related to the early math and pre- literacy brain to see how current learning trajectories in education coincide or contradict neuroscientific evidence. Only slight changes are recommended about the order of skills introduction. More importantly, however, is that attention is called to the many sub-elements of each skill set which are often missed by parents and teachers, leading to gaps in linguistic or mathematical knowledge in small children and which may contribute to school failure in these areas. Finally, a recommendation to use an observational rubric of children’s math and language skills 0-6 years based on 16 neural networks is made.

In 2017 and 2018, the Research Laboratory in Educational Opportunities (LaPOpE) at the Federal University of Rio de Janeiro conducted a study with public school children attending the beginning of compulsory schooling – kindergarten (children of age 4). Only 59.1% of the 4-year-old children were able to count four fixed objects. Therefore, a new counting test was developed and applied to some children. In this test, several aspects were considered: (i) quantity (perceptual, elementary, and complex numbers), (ii) arrangement of the objects (canonical form, randomly arranged, and in a circle), and (iii) categories of counting (loose, fixed objects, and object selection). The results showed that the way in which the objects were arranged influences the way children count as well as the quantities offered to them. This test can be used by teachers as a tool to assess the students’ counting skills and, then, to propose relevant interventions in the classroom.

Increased rates of atypical handedness are observed in neurotypical individuals who are low-performing in mathematical tasks as well as in individuals with special educational needs, such as dyslexia. This is the first investigation of handedness in individuals with Mathematical Learning Difficulties (MLD). We report three new studies (N = 134; N = 1,893; N = 153) and two sets of meta-analyses (22 studies; N = 3,667). No difference in atypical hand preference between MLD and Typically Achieving (TA) individuals was found when handedness was assessed with self-report questionnaires, but weak evidence of a difference was found when writing hand was the handedness criterion in Study 1 (p = .049). Similarly, when combining data meta-analytically, no hand preference differences were detected. We suggest that: (i) potential handedness effects require larger samples, (ii) direction of hand preference is not a sensitive enough measure of handedness in this context, or that (iii) increased rates of atypical hand preference are not associated with MLD. The latter scenario would suggest that handedness is specifically linked to language-related conditions rather than conditions related to cognitive abilities at large. Future studies need to consider hand skill and degree of hand preference in MLD.

Developmental dyscalculia (DD) is a mathematical learning disability that occurs in around 5%–7% of the population. At present, there are only a handful of screening tools to identify children that might be at risk of developing DD. The present study evaluated the classification accuracy of one such tool: The Numeracy Screener, a 2‐min test of symbolic (Arabic numerals) and nonsymbolic (dot arrays) discrimination ability. A sample of 222 children who demonstrated persistent deficits (n = 55), inconsistent deficits (n = 51), or typical performance (n = 116) on standardized tests of math achievement over multiple observations was tested. The Numeracy Screener correctly classified children in all three groups. Notably, the symbolic condition has greater sensitivity in discriminating children with persistent DD from the other two groups. Screening tools that assess early numeracy skills may be promising for identifying children at risk for developing severe mathematical difficulties.

This study examined spring literacy scores among at‐risk prekindergarten students exposed to supplemental support solely in literacy or a combination of literacy and math. Propensity scores were used to match students receiving combined support (n = 39) with an equivalent number of students receiving only literacy tutoring. Students were matched using fall math scores and fall literacy scores. After confirming baseline equivalence, we used a multilevel model to evaluate the association between support type and spring literacy scores, controlling for fall literacy scores, fall numeracy scores, and the total number of intervention sessions completed. In addition to a significant and positive association between fall and spring scores, students who received support in both literacy and math scored significantly better on the spring literacy assessment. More specifically, participating in both literacy and math support was associated with a 23.81 increase in spring literacy scores relative to participating in literacy support alone, explaining 5% of the student‐level variance.

Children’s spontaneous focus on numerosity (SFON) is described as an unprompted tendency that is stable across contexts. The attention to number task (AtN), an experimental forced-choice picture-matching task designed to evaluate select aspects of children’s focus on numerosity, may reveal whether task materials can implicitly prompt children to focus on numerosity. In two studies, we replicate earlier findings showing an effect of task context on children’s performance on the AtN: When asked to identify one or more matches to a target picture from an array of four options, the frequency with which preschoolers and adults identify a numerosity-based match varies as a function of the features on which the remaining match options are based. We addressed a limitation of the original AtN study by including novel combinations of features as additional trials, with which we continued to demonstrate contextual effects. We also showed that adults seemed more susceptible than children to be primed to attend to numerosity on subsequent trials. Children’s focus on numerosity under these experimental conditions was remarkably low. We discuss the implications of these findings for better understanding the SFON construct.

Resumo O processamento numérico demanda funções que podem apresentar interferência de reações ansiogênicas. A relação entre matemática e situações ameaçadoras é demonstrada pela ansiedade matemática (AM), que é um sentimento de tensão e desorganização mental quando a manipulação de números é necessária. É consequência de preditores genéticos e ambientais, mas, também pode estar associado ao baixo desempenho na memória de trabalho (MT) e controle inibitório (CI). O objetivo deste estudo foi demonstrar o tamanho do efeito da AM sobre o desempenho em tarefas de MT, e investigar a força e significância das correlações entre AM, MT e CI. Para isso, foi realizado um novo teste de hipóteses com dados de artigos que possuem um mesmo padrão de informações estatísticas, comparando grupos com alta e baixa AM. O software utilizado foi o R, na versão 3.6.4, e os pacotes Revmeta, Metafor e Forest. O tamanho do efeito da AM sobre a MT foi uma diferença das médias padronizadas (DMP) = -0,22, IC = 100%, [-0.38; -0.07]; p = 0,01, demonstrando que existe diferença significativa entre as médias da MT para grupos com alta e baixa AM. Porém, foi encontrado um alto índice de heterogeneidade (I2 = 81%), que demonstra pouca robustez em relação à variedade de dados obtidos. Foi demonstrado que os grupos com altos níveis de AM possuem maior taxa de erro e tempo de reação em tarefas de inibição de estímulos irrelevantes, o que verifica dificuldades em resistir a interferências durante a realização de tarefas matemáticas apresentadas por esses indivíduos.

This study examines the interplay of state- and trait-math anxiety (MA) and core executive functions (CEF) on math achievement in children. According to attention control theory, MA affects the CEF by triggering the inhibition function, so that some working memory (WM) is blocked, thus reducing task processing capacity. However, research on the interplay between MA and CEF in children is rare, and the findings in the literature are inconsistent. In this paper, state- and trait-MA, math achievement, CEF (inhibition, cognitive flexibility, working memory capacity, global index of CEF) and self-ratings of ADHD symptoms (attention deficits, hyperactivity,impulsiveness) of 646 fourth and fifth grade students (48.1% girls) are assessed. CEF were evaluated with atablet-based test. The data revealed negative correlations between state-MA and math achievement for all CEF levels and cognitive processes. However, inhibition control functioned as a moderator of the relation between state-MA and math achievement. Children with higher inhibition abilities showed more pronounced negative relations. No moderation effects were identified for working memory capacity and the CEF global index. The findings highlight the importance of distinguishing between these three CEF and raise questions for future research on the interplay between cognitive and affective factors as predictors of math achievement.
ShareLink: https://authors.elsevier.com/a/1b46Z2Hx2jDbb

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.

Numerical Cognition: The Basics provides an understanding of the neural and cognitive mechanisms that enable us to perceive, process, and memorize numerical information. Starting from basic numerical competencies that humans share with other species, the book explores the mental coding of numbers and their neural representation. It explains the strategies of mental calculation, their pitfalls and their development, as well as the developmental steps children make while learning about numbers. The book gradually builds our understanding of the underlying mental processes of numeracy and concludes with an insightful examination of the diagnosis, etiology and treatment of dyscalculia. Written in an accessible manner, the book summarizes and critically evaluates the major psychological explanations for various empirical phenomena in numerical cognition. Containing a wealth of student-friendly features including end of chapter summaries, informative figures, further reading lists, and links to relevant websites, Numerical Cognition: The Basics is an essential starting point for anybody new to the field.

The performance of 210 2nd graders in different areas of mathematical cognition was examined. Children were divided into 4 achievement groups: children with difficulties in mathematics but not in reading (MD-only), children with difficulties in both mathematics and reading (MD/RD), children with difficulties in reading but not in mathematics, and children with normal achievement. Although both MD groups performed worse than normally achieving groups in most areas of mathematical cognition, the MD-only group showed an advantage over the MD/RD group in exact calculation of arithmetic combinations and in problem solving. The 2 groups did not differ in approximate arithmetic and understanding of place value and written computation. Children with MD-only seem to be superior to children with MD/RD in areas that may be mediated by language but not in ones that rely on numerical magnitudes, visuospatial processing, and automaticity. (PsycINFO Database Record (c) 2012 APA, all rights reserved)

[Correction Notice: An erratum for this article was reported in Vol 101(3) of
Psychological Bulletin (see record
2008-10701-001). In this article, it was wrongly stated that that U. Schallberger put forward a hypothesis or hypotheses concerning the magnitude of Swiss IQ gains; in fact, he did not. The erratum includes the author's clarification.] Data from 14 nations reveal IQ gains ranging from 5 to 25 points in a single generation. Some of the largest gains occur on culturally reduced tests and tests of fluid intelligence. The Norwegian data show that a nation can make significant gains on a culturally reduced test while suffering losses on other tests. The Dutch data proved the existence of unknown environmental factors so potent that they account for 15 of the 20 points gained. The hypothesis that best fits the results is that IQ tests do not measure intelligence but rather a correlate with a weak causal link to intelligence. This hypothesis can also explain difficult trends on various mental tests, such as the combination of IQ gains and Scholastic Aptitude Test losses in the United States. (PsycINFO Database Record (c) 2012 APA, all rights reserved)

The authors investigated the etiology of low mathematics performance in 7-year-olds in the context of normal variation. The lowest 15% were selected from a representative U.K. sample of 2,178 same-sex twin pairs rated by their teachers according to National Curriculum criteria in 3 domains of mathematics. Model-fitting analyses of mathematics performance and low performance yielded remarkably similar results. The heritability estimate for the teacher-reported mathematics performance composite is .66, whereas the group heritability estimate for low performance is .65. These results are consistent with the hypothesis that the same genetic and environmental factors are largely responsible for low mathematics performance as for normal variation in mathematics. The limitations of the present study and further directions for research are discussed. (PsycINFO Database Record (c) 2012 APA, all rights reserved)

This paper is a descriptive report of findings from a prospective longitudinal study of math disability (MD). The study was designed to address the incidence of MD during primary school, the utility of different MD definitions, and evidence of MD subtypes. The results illustrate the dynamic properties of psychometrically derived definitions of MD. Different groups of children meet criteria for MD depending on which measure(s) are used for identification. Over time, a given individual may not continue to meet MD criteria, even when using the same assessments. Thus, the findings lead to cautions regarding the single-tool/ one-time assessment for a clinical diagnosis of MD. Twenty-two of 209 participants demonstrated "persistent MD" (MD-p), or MD for more than one school grade. Reading disability was relatively more frequent in this MD-p subgroup than in the remaining participants (25 percent vs. 7 percent). Reading-related skills were correlated with math achievement, as were select visual spatial skills. There was minimal overlap between groups who met either a "poor achievement" criteria or an "IQ-achievement discrepancy," and the latter was far less stable a measure over time than the former. The results highlight the complexities of defining MD and illustrate the need for more research in this area.

Cognitive, neuropsychological, and genetic correlates of mathematical achievement and mathematical disability (MD) are reviewed in an attempt to identify the core deficits underlying MD. Three types of distinct cognitive, neuropsychological, or cognitive and neuropsychological deficits associated with MD are identified. The first deficit is manifested by difficulties in the representation or retrieval of arithmetic facts from semantic memory. The second type of deficit is manifested by problems in the execution of arithmetical procedures. The third type involves problems in the visuospatial representation of numerical information. Potential cognitive, neuropsychological, and genetic factors contributing to these deficits, and the relationship between MD and reading disabilities, are discussed. Finally, suggestions for the subtyping of mathematical disorders are offered.

Although results obtained from recent twin and adoption studies suggest that individual differences in mathematics performance are due in part to heritable influences, no genetic analysis of mathematics disability (MD) has been previously reported. In this article we present data from the first twin sample ascertained for mathematics deficits (40 identical and 23 same-sex fraternal twin pairs in which at least one member had MD). When mathematics performance data from these twin pairs were subjected to a multiple regression analysis, evidence for a significant genetic etiology was obtained. However, tests for the differential etiology of MD as a function of reading performance level were nonsignificant. Results of this first twin study of MD indicate that the condition is significantly heritable, but data from additional twin pairs will be required to test hypotheses of differential etiology more rigorously.

The prevalence of developmental dyscalculia (DC) in the school population ranges from 3-6 %, a frequency similar to that of developmental dyslexia and ADHD. These studies fulfilled the criteria for an adequate prevalence study, i.e., were population based, using standardized measures to evaluate arithmetic function. Although the variation in prevalence is within a narrow range, the differences are probably due to which definition of dyscalculia was used, the age the diagnosis was made and the instrument chosen to test for DC. The relative predominance of girls with DC may reflect a greater vulnerability to environmental influences alone or in addition to a biological predisposition. DC is not only encountered as a specific learning disability but also in diverse neurological disorders, examples of which include ADHD, developmental language disorder, epilepsy, treated phenylketonuria and Fragile X syndrome. Although the long-term prognosis of DC is as yet unknown, current data indicate that DC is a stable learning disability persisting, at least for the short term, in about half of affected children. The long-term consequences of DC and its impact on education, employment and psychological well-being have yet to be determined.

Children's mathematical skills were considered in relation to executive functions. Using multiple measures--including the Wisconsin Card Sorting Task (WCST), dual-task performance, Stroop task, and counting span-it was found that mathematical ability was significantly correlated with all measures of executive functioning, with the exception of dual-task performance. Furthermore, regression analyses revealed that each executive function measure predicted unique variance in mathematics ability. These results are discussed in terms of a central executive with diverse functions (Shallice & Burgess, 1996) and with recent evidence from Miyake, et al. (2000) showing the unity and diversity among executive functions. It is proposed that the particular difficulties for children of lower mathematical ability are lack of inhibition and poor working memory, which result in problems with switching and evaluation of new strategies for dealing with a particular task. The practical and theoretical implications of these results are discussed, along with suggestions for task changes and longitudinal studies that would clarify theoretical and developmental issues related to executive functioning.

This paper describes the procedures adopted by two independent studies in India for identifying and classifying children with dyscalculia in primary schools. For determining the presence of dyscalculia both inclusionary and exclusionary criteria were used. When other possible causes of arithmetic failure had been excluded, figures for dyscalculia came out as 5.98% (15 cases out of 251) in one study and 5.54% (78 out of 1408) in the second. It was found in the latter study that 40 out of the 78 (51.27%) also had reading and writing problems. The findings are discussed in the light of previous studies.

Despite the high incidence of numerical deficits in neurological patients, little attention has been paid to the development of diagnostic tools. In fact, most of the published reports on acquired numerical disorders, whether single case or group studies, do not refer to standardised measures of performance providing little, if any, control data specifically collected for the examination. In this study we present data of 282 healthy controls of different age groups and educational levels in a new battery of Number Processing and Calculation (NPC). The NPC battery includes a total of 35 tasks, assessing different counting abilities, various aspects of number comprehension (such as parity and magnitude judgements), numerical transcoding, calculation, arithmetic reasoning and conceptual knowledge. Special attention is paid to the assessment of different calculation abilities, including simple fact retrieval, rule based processing, mental calculation and written calculation in all four operations. Moreover, text problem solving is assessed as well as the understanding of arithmetic principles. Thus, the NPC battery differs from the EC 301 battery proposed by Deloche et al., 1994 (Dellatolas, Deloche, Basso, & Claros-Salinas, 2001) and allows a more fine grained diagnosis which is relevant for planning targeted interventions. The battery is easy to administer and does not require special materials or equipment.

Thirty-one 8- and 9-year-old children selected for dyscalculia, reading difficulties or both, were compared to controls on a range of basic number processing tasks. Children with dyscalculia only had impaired performance on the tasks despite high-average performance on tests of IQ, vocabulary and working memory tasks. Children with reading disability were mildly impaired only on tasks that involved articulation, while children with both disorders showed a pattern of numerical disability similar to that of the dyscalculic group, with no special features consequent on their reading or language deficits. We conclude that dyscalculia is the result of specific disabilities in basic numerical processing, rather than the consequence of deficits in other cognitive abilities.

Between 5% and 8% of school-age children have some form of memory or cognitive deficit that interferes with their ability to learn concepts or procedures in one or more mathematical domains. A review of the arithmetical competencies of these children is provided, along with discussion of underlying memory and cognitive deficits and potential neural correlates. The deficits are discussed in terms of three subtypes of mathematics learning disability and in terms of a more general framework for linking research in mathematical cognition to research in learning disabilities.

This is a review of the relationship between schooling, IQ, and the cognitive processes presumed to underpin IQ. The data suggest that much of the causal pathway between IQ and schooling points in the direction of the importance of the quantity of schooling one attains (highest grade successfully completed). Schooling fosters the development of cognitive processes that underpin performance on most IQ tests. In western nations, schooling conveys this influence on IQ and cognition through practices that appear unrelated to systematic variation in quality of schools. If correct, this could have implications for the meaning one attaches to IQ in screening and prediction as well as for efforts to influence the development of IQ through changes in schooling practices.

Data from 14 nations reveal IQ gains ranging from 5 to 25 points in a single generation. Some of the largest gains occur on culturally reduced tests and tests of fluid intelligence. The Norwegian data show that a nation can make significant gains on a culturally reduced test while suffering losses on other tests. The Dutch data prove the existence of unknown environmental factors so potent that they account for 15 of the 20 points gained. The hypothesis that best fits the results is that IQ tests do not measure intelligence but rather a correlate with a weak causal link to intelligence. This hypothesis can also explain differential trends on various mental tests, such as the combination of IQ gains and Scholastic Aptitude Test losses in the United States.

Thirty-one 8- and 9-year-old children selected for dyscalculia, reading difficulties or both, were compared to controls on a range of basic number processing tasks. Children with dyscalculia only had impaired performance on the tasks despite high-average performance on tests of IQ, vocabulary and working memory tasks. Children with reading disability were mildly impaired only on tasks that involved articulation, while children with both disorders showed a pattern of numerical disability similar to that of the dyscalculic group, with no special features consequent on their reading or language deficits. We conclude that dyscalculia is the result of specific disabilities in basic numerical processing, rather than the consequence of deficits in other cognitive abilities.

The effectiveness of neuropsychological test performance during early elementary school in predicting subsequent academic achievement through high school was evaluated. Previously (Townes, Trupin, Martin, & Goldstein, 1980), a normal, nonreferred sample of kindergarten (N = 230) and second‐grade children (N = 226) had been tested individually using the Wechsler Intelligence Scale for Children and the Reitan‐Indiana Neuropsychological Test Battery. Predictor variables were derived from these neuropsychological and intelligence tests. Ten years later, permission was obtained to examine the school records of 215 of the original subjects and to review standardized achievement tests that had been administered when the subjects were in Grades 3, 4,6, and 9. Criterion variables were derived from students' standardized achievement test scores in reading, mathematics, spelling, written language, and overall achievement Multivariate and univariate regression analyses were performed to determine the relation between the earlier IQ and neuropsychological predictors and academic achievement in several skill domains over the subsequent 10‐year period. In general, the neuropsychological and IQ variables were comparable predictors and in many cases the neuropsychological variables significantly improved the prediction over IQ alone.

Neighborhoods are increasingly studied as a context where children and youth develop; however, the extent of neighborhoods' impact remains debatable because it is difficult to disentangle this impact from that of the family context, in part because families have some choice as to where they live. Evidence from randomized experiments, studies using advanced statistical models, and longitudinal studies that control for family characteristics indicates that neighborhoods do matter. In nonexperimental studies, small to moderate associations were found, suggesting that children and adolescents living in high-income neighborhoods had higher cognitive ability and school achievement than those living in middle-income neighborhoods, and children and adolescents living in low-income neighborhoods had more mental and physical health problems than those living in middle-income neighborhoods. The home environment has been shown to be partly responsible for the link between neighborhood and children's development. For adolescents, neighborhood effects are partially accounted for by community social control. Experimental studies in which families were randomly assigned to move to low-poverty neighborhoods from housing projects found larger neighborhood effects than nonexperi-mental research, particularly for boys' outcomes. Additional issues reviewed are relevant neighborhood characteristics, theoretical models explaining the pathways underlying neighborhood effects, methods for research assessing neighborhood processes, and policy implications.

Large epidemiological studies of almost an entire population in Scotland have found that intelligence (as measured by an IQ-type test) in childhood predicts substantial differences in adult morbidity and mortality, including deaths from cancers and cardiovascular diseases. These relations remain significant after controlling for socioeconomic variables. One possible, partial explanation of these results is that intelligence enhances individuals' care of their own health because it represents learning, reasoning, and problem-solving skills useful in preventing chronic disease and accidental injury and in adhering to complex treatment regimens.

The aim of the study is to investigate the informal and formal mathematical knowledge of children suffering from "mathematics difficulty" (MD). The research involves comparisons among three groups: fourth-grade children performing poorly in mathematics but normal in intelligence; fourth-grade peers matched for intelligence but experiencing no apparent difficulties in mathematics; and a randomly selected group of third graders. These children were individually presented with a large number of tasks designed to measure key mathematical concepts and skills. The findings suggest that: (1) MD children are not seriously deficient in key informal mathematical concepts and skills; (2) MD children seem to have elementary concepts of base ten notation but experience difficulty in related enumeration skills, particularly when large numbers are involved; (3) MD children's calculational errors often result from common error strategies; (4) MD children display severe difficulty in recalling common addition facts; and (5) in the area of problem solving, MD children are capable of "insightful" solutions and can solve simple forms of word problems, but experience difficulty with complex word problems. MD children are in many respects similar to normal, younger peers; an hypothesis of "essential cognitive normality" is advanced. The only and dramatic exception occurs in the area of number facts. While clinical experience corroborates this finding, its explanation is not evident.

The Third International Mathematics and Science Study (TIMSS; Beatty, 1997), a large-scale study that compared the mathematics performance of youngsters in 40 different countries, served as a wake-up call for many of the participating countries. For these countries, including the United States, the results reinforced the long-acknowledged need to question the quality of mathematics education in their respective school systems and to take action to remedy the poor math performance of students. In this special issue, we have attempted to pull together a representative group of TIMSS participants to provide a perspective on the state of mathematics education in the developed world. (PsycINFO Database Record (c) 2012 APA, all rights reserved)

Reviews the relationship between schooling, IQ, and the cognitive processes presumed to underpin IQ. The data suggest that much of the causal pathway between IQ and schooling points in the direction of the importance of the quantity of schooling one attains (highest grade successfully completed). Schooling fosters the development of cognitive processes that underpin performance on most IQ tests. In Western nations, schooling conveys this influence on IQ and cognition through practices that appear unrelated to systematic variation in quality of schools. If correct, this could have implications for the meaning one attaches to IQ screening and prediction as well as for efforts to influence the development of IQ through changes in schooling practices. (PsycINFO Database Record (c) 2012 APA, all rights reserved)

Clinical interpretation of subtest score profiles on intelligence tests is a common practice. The ACID profile found on Wechsler's scales has been widely accepted as a clinical indicator which has both diagnostic and treatment implications. However, this practice has been based on clinical rather than empirical evidence. This study examines the discriminant and predictive validity of the Wechsler Intelligence Scale for Children-Third Edition (WISC-III) ACID profile among 612 students with learning disabilities. Analyses included diagnostic utility statistics (sensitivity, selectivity, etc.) and ROC methods as well as correlational and descriptive statistics. Results indicated that the ACID profile does not efficiently separate children with disabilities from those without disabilities, and further, there is no ACID cutting score which significantly exceeds chance discriminatory power. Likewise, the ACID profile did not robustly predict academic achievement among children with learning disabilities. © 1997 John Wiley & Sons, Inc.

Based on performance on standard achievement tests, first-grade children (mean age 82 months) with IQ scores in the low-average to high-average range were classified as at risk for a learning disability (LD) in mathematics, reading, or both. These at-risk children (n 55) and a control group of academically normal peers (n 35) were administered experimental tasks that assessed number comprehension and production skills, counting knowledge, arithmetic skills, working memory, and ease of retrieving information from long-term memory. Different patterns of intact cognitive functions and deficits were found for children in the different at-risk groups. As a set, perfor-mance on the experimental tasks accounted for roughly 50% and 10% of the group differences in mathematics and reading achievement, respectively, above and beyond the influence of IQ. Performance on the experimental tasks thus provides insights into the cognitive deficits underlying different forms of LD, as well as into the sources of individual differences in academic achievement. Quantitative skills influence employability, wages, and on-the-job produc-tivity above and beyond the influence of reading abilities, IQ, and a host of other factors (Paglin & Rufolo, 1990; Rivera-Batiz, 1992). Despite the economic importance of quantitative abilities, little research has been conducted on the factors that contribute to poor mathematical achieve-ment and to mathematical disabilities (MD), in comparison to the research efforts devoted to understanding poor reading achievement and reading disabilities (, and the faculty and staff of the Columbia Public Schools for their assistance with various aspects of the study. Finally, we thank John Adams, Jeff Bisanz, Robert Siegler, and two anonymous reviewers for comments on an earlier draft.

Cognitive research on the number, counting, and arithmetic competencies of children with a learning disability in arithmetic (AD) is reviewed, and similarities between the associated deficits of AD children and the deficits of individuals afflicted with dyscalculia are highlighted. It is concluded that the defining features of AD and most dyscalculias are difficulties with the procedural features associated with the solving of complex arithmetic problems and difficulties in remembering basic arithmetic facts. The procedural deficits and one form of retrieval deficit appear to be associated with functioning of the prefrontal cortex, while a second form of retrieval deficit appears to be associated with the functioning of the left parieto-occipito-temporal areas and several subcortical structures. The review ends with a discussion of the potential relation between this second form of retrieval deficit and dyslexia.

We seek to analyse the notion of structuring resources and their role in shaping mathematical activity, and more broadly to add to our understanding of mathematical epistemologies in workplace settings. Our analysis is of two nursing activities – drug administration and fluid balance monitoring – based on data collected in an in–depth study of paediatric nurses on the ward. In the first activity, we examine ways in which nurses conceptualise ratio and proportion problems, while in the second, we provide a case study of two nurses discussing conflicting strategies when monitoring the fluid balance of a patient. We discuss the ways in which the available resources give mathematical and professional meanings in these situations and draw out some implications for the design of viable didactical strategies in vocational mathematics teaching.

This paper examines the effects of quantitative literacy on the likelihood of employment among young adults in the United States. The data set used is the 1985 Young Adult Literacy Assessment Survey. This survey of persons 21 to 25 years old makes available scores achieved by individuals sampled on a test measuring proficiency in the application of arithmetic skills to practical problems encountered every day. We use these scores as one of a set of variables in a probit model explaining the probability of a person being fully employed. It is found that quantitative literacy skills are a major factor raising the likelihood of full-time employment. Furthermore, low quantitative literacy appears to be critical in explaining the lower probability of employment of young Black Americans relative to Whites.

In this observational study, influences on research enrollment were examined in the context of an educational research study. Recruitment materials were sent to parents of kindergartners in one of 23 classes across 7 public schools, as an invitation to enroll in a longitudinal study. For the 7 classes from 2 of the schools, the school principal prepared a cover letter as an introduction to the educational study. Inclusion of this cover letter was associated with a significantly swifter pace of recruitment and, to a lesser degree, with an increase in the number of children enrolled. However, when potential confounding variables were controlled, no significant increase in final enrollment count was associated with including the cover letter. Thus, inclusion of a cover letter from the school principal did not appear to dramatically increase the number of parents who elected to enroll their child in the educational study, and it did significantly decrease (by 6 weeks) the number of weeks required to achieve final enrollment counts.

The purpose of this study was to investigate the influence of schooling and general environmental conditions on the development of memory and cognitive skills in young children. The subjects were 824 5- and 6-year-old children living in jungle villages and in slum settlements of Lima, Peru. Half of the children in both the jungle and city were Mestizo, and half were Quechua Indians. Some 6-year-olds of each cultural group and in each location attended school; others did not. Memory tasks were presented in different modes of representation, that is, verbal, pictorial, and enactive; and cognitive tasks in "concrete" and "abstract" versions. A sample of parents in each group was interviewed concerning environmental conditions. In addition, samples of upper-middle-class children in Lima and poor children in Detroit were tested to assess the generality of the findings. Attendance at school was related to improvement in performance on all tasks. Improvement was equivalent for both locations, both cultural groups, and each social class. Attendance at school also was accompanied by reduced within-group variability on some tasks and by greater differentiation of cognitive processes within children. Location and cultural group interacted differentially by task according to a complex pattern of relations. There were no indications that the organization of memory or cognitive processes differed as a function of social class, age, location, or cultural group. The results were interpreted in terms of children's opportunities to acquire specific memory and cognitive skills from schooling and from their general experience in a particular environment.

Performance on tests requiring rapid repetitive naming of pictured objects, colors, letters and numbers differentiates dyslexic children not only from normal controls but also from non-dyslexic, otherwise learning-disabled children. A deficit in automatization of verbal responses to visual stimuli, not restricted to symbols, correlates specifically with dyslexia. That this deficit is not part of a generalized slowing of reaction time is reflected in the higher mean performance I.Q. (WISC) of the dyslexic Ss, who also showed fewer signs of neurological impairment than did the non-dyslexic Ss.

In accordance with major theories of handedness and brain organization, differential predictors for math achievement were found as a function of sex and handedness subgroups among eighth graders. Although there was no difference in absolute levels of performance as a function of either sex or handedness, predictive structures did differ. Regression analyses showed that spatial ability predicts math achievement for: (1) girls with anomalous dominance (non-right-handers and right-handers with non-right-handed relatives), and (2) all boys (independent of handedness group). In contrast, for the standard dominance girls who are right-handed with all right-handed relatives (considered strongly left-hemisphere dominant for language), spatial ability did not predict for math achievement. These findings occurred, even when scholastic aptitude and verbal achievement factors were controlled. It was concluded that further studies of sex differences in math achievement should consider subgroup differences within the sexes, based on handedness patterns.

Working memory has been proposed as an important component of reading and arithmetic skills. The development of working memory was studied in normally achieving and subtypes of learning disabled children. The performance of reading disabled (RD), arithmetic disabled (ARITHD), and attentional deficit disordered (ADD) children, age 7-13, was compared to normal achievers (NA) on 2 working memory tasks, 1 involving sentences and the other involving counting. There was a significant growth of working memory as a function of age. In addition, the RD children had significantly lower scores on both tasks. The ARITHD children had significantly lower scores only on the Working Memory--Counting task, and the ADD group had scores similar to the normally achieving children except at the youngest age level in the Working Memory--Sentences task. Thus, a reading disability appears to involve a generalized deficit in working memory. Children with an arithmetic disability do not have a generalized language deficit but have a specific working memory deficit in relation to processing numerical information. As children with ADD did not have deficits in these tasks, working memory may not have significant attentional components. An important component of the development of reading and computational arithmetic skills appears to be the growth of working memory for language and numerical information.

The purpose of the longitudinal study was to investigate the prediction of children's academic achievement on the basis of cognitive tasks given prior to kindergarten, and academic attitudes on the basis of teachers' and mothers' ratings of the children's general cognitive abilities and actual achievement. Subjects were tested initially before entering kindergarten; from 105 to 154 of the 255 kindergarten children were followed through grades 1, 2, 3, 5, and 10. A subset of cognitive tasks maintained a high relation to high school achievement scores, especially in reading. Tenth-grade self-concept of ability, expectancy for success, value of success, and perception of task difficulty showed effects of sex and academic content area, with boys generally being more favorable toward math and girls more favorable toward reading. Children's attitudes were related both to mothers' earlier ratings of their children's cognitive abilities and actual achievement scores; this was especially the case for girls. There was a negative relation between mothers' ratings and girls' attitudes toward mathematics. Sex differences in all measures throughout the 11-year period are reviewed.

Data from an epidemiological sample (n = 1206) of British schoolchildren were used to estimate the proportions of 9- to 10-year-olds with specific arithmetic difficulties (SAD), combined with arithmetic-and-reading difficulties (ARD), and specific reading difficulties (SRD). Children in the sample contributed scores on separate tests of arithmetic, reading and nonverbal intelligence. Using a cutting-score approach, which took into account performance on all three tests, a small group of children with SAD (1.3%) were distinguished from larger groups with ARD (2.3%) and SRD (3.9%). Contrary to some previous reports, there were equal numbers of males and females within each of the two groups with arithmetic difficulties but a preponderance of males over females amongst the group with specific reading difficulties.

This study examined problem-solving and number-fact skills in two subgroups of third-grade children with mathematics difficulties (MD): MD-specific (n = 12) and MD-general (n = 12). The MD-specific group had difficulties in mathematics but not in reading, and the MD-general group had difficulties in reading as well as in mathematics. A comparison group of nonimpaired children (n = 24) also was included. The findings showed that on both story and number-fact problems, the MD-specific group performed worse than the nonimpaired group in timed conditions but not in untimed conditions. The MD-general group, on the other hand, performed worse than the nonimpaired group, regardless of whether tasks were timed or not. An analysis of children's strategies in untimed conditions showed that both the MD-specific and the MD-general groups relied more on backup strategies than the nonimpaired group. However, children in the MD-specific group executed backup strategies more skillfully than children in the MD-general group, allowing them to achieve parity with children in the nonimpaired group when tasks were not timed. The findings suggest that children with specific MD have circumscribed deficits associated with fact retrieval, whereas children with general MD have more basic delays associated with problem conceptualization and execution of calculation procedures.

In this article, we show that the performances of 5- to 6-year-old children in arithmetic tests can be predicted from their performances in neuro-psychological tests administered a number of months in advance, independently of their level of development.

Working memory impairments in children with difficulties in arithmetic have previously been investigated using questionable selection techniques and control groups, leading to problems concluding where deficits may occur. The present study attempted to overcome these criticisms by assessing 9-year-old children with difficulties specific to arithmetic, as indicated by normal reading, and comparing them with both age-matched and ability-matched controls. A battery of 10 tasks was used to assess different aspects of working memory, including subtypes of executive function. Relative to age-matched controls, children with poor arithmetic had normal phonological working memory but were impaired on spatial working memory and some aspects of executive processing. Compared to ability-matched controls, they were impaired only on one task designed to assess executive processes for holding and manipulating information in long-term memory. These deficits in executive and spatial aspects of working memory seem likely to be important factors in poor arithmetical attainment.

Based on the stability and level of performance on standard achievement tests in first and second grade (mean age in first grade = 82 months), children with IQ scores in the low-average to high-average range were classified as learning disabled (LD) in mathematics (MD), reading (RD), or both (MD/RD). These children (n = 42), a group of children who showed variable achievement test performance across grades (n = 16), and a control group of academically normal peers (n = 35) were administered a series of experimental and psychometric tasks. The tasks assessed number comprehension and production skills, counting knowledge, arithmetic skills, working memory, the ease of activation of phonetic representations of words and numbers, and spatial abilities. The children with variable achievement test performance did not differ from the academically normal children in any cognitive domain, whereas the children in the LD groups showed specific patterns of cognitive deficit, above and beyond the influence of IQ. Discussion focuses on the similarities and differences across the groups of LD children.

The use of cognitive subtest profiles to hypothesize about children's learning strengths and weaknesses implicitly assumes that subtest profiles are predictive of academic performance. To test this assumption, Wechsler Intelligence Scale for Children-Third Edition (WISC-III) subtest profiles were decomposed into elevation, scatter, and shape components and sequentially regressed onto reading and math achievement scores for 1,118 nonexceptional and 538 exceptional students. Profile elevation was statistically and practically significant for both exceptional (R = .36-.61) and nonexceptional (R = .72-.75) students. Profile scatter did not aid in the prediction of achievement. Profile shape accounted for an additional 5%-8% of the variance in achievement measures. It was concluded that using WISC-III subtest scatter and shape to predict academic performance was not supported by the accumulated scientific evidence.

The primary purpose of this longitudinal correlational study was to examine relations between phonological processing abilities and emerging individual differences in math computation skills and also to investigate the source of covariation between reading and math computation skills in a random sample (n = 201). Phonological memory, rate of access to phonological codes in long-term memory, and phonological awareness were uniquely associated with growth in estimated total number of computation procedures mastered (general computation skills) from 92.5 to 134.8 months in age, although the contributions of the first two abilities were developmentally limited. Phonological processing almost completely accounted for the associations between reading and general computation skills. Evidence of bidirectional relations between general computation skills and simple arithmetic problem solving speed was found.

Physicians often elicit ratings from teachers when making diagnostic, treatment, or referral decisions. The purpose of this study was to view the relationship between teachers' ratings and children's academic skills, assess the utility of teacher ratings in detecting academic problems, and thus determine whether physicians can depend on teacher ratings when making decisions about patients' needs. Subjects were a national sample of 80 teachers and 934 children between 6 and 13 years of age participating in a test standardization study. Families were representative of United States demographics in terms of parental level of education, income, and ethnicity, and sites were geographically diverse elementary schools. Children were administered the Comprehensive Inventory of Basic Skills--Revised (CIBS-R), a diagnostic academic achievement test. Teachers rated children's academic performance on a five-point scale ranging from far above average to far below average and were blinded to the results of the CIBS-R. Teacher ratings varied significantly with children's performance for all academic domains. Logistic regression revealed that teacher ratings were best predicted by children's performance in basic reading skills, followed by math skills, and were not influenced by race, parents' level of education, history of retention, or gender. Participation in Title I services, testing in winter or spring, and parents who spoke a language other than English produced significantly lower ratings. Nevertheless, teachers rated as average many students with mild to moderate academic difficulties. School system personnel and health care providers should avoid sole dependence on global teacher ratings when deciding which students need special education referrals or other services. Supplementing teacher ratings with standardized screening test results is needed to ensure accurate decision-making.

Developmental dyscalculia is a specific learning disability affecting the acquisition of arithmetic skills in an otherwise-normal child. Although poor teaching, environmental deprivation, and low intelligence have been implicated in the etiology of developmental dyscalculia, current data indicate that this learning disability is a brain-based disorder with a familial-genetic predisposition. The neurologic substrate of developmental dyscalculia is thought to involve both hemispheres, particularly the left parietotemporal areas. Developmental dyscalculia is a common cognitive handicap; its prevalence in the school population is about 5-6%, a frequency similar to those of developmental dyslexia and attention-deficit-hyperactivity disorder. Unlike these, however, it is as common in females as in males. Developmental dyscalculia frequently is encountered in neurologic disorders, examples of which include attention-deficit-hyperactivity disorder, developmental language disorder, epilepsy, and fragile X syndrome. The long-term prognosis of developmental dyscalculia is unknown; it appears, however, to persist, at least for the short-term, in about half of affected preteen children. The consequences of developmental dyscalculia and its impact on education, employment, and psychologic well-being of affected individuals are unknown.

It has been shown repeatedly that simple mental calculation depends not only on long-term memory (LTM) representations but also on working memory (WM) resources. The study describes the performance of an adolescent, M.O., exhibiting severe developmental dyscalculia, but literacy problems as well. Despite having relatively preserved procedural skills, M.O. exhibited outstanding difficulties in retrieving arithmetic facts which are most pronounced on multiplication and division problems. Interestingly, his performance on non-numerical memory tests was within average (independent of modality), while his attention span was just below average. Testing the different components of WM, the results emphasize the major role of the central executive in solving simple mental calculations.

One form of developmental difficulty with arithmetic affects the storage or retrieval of arithmetical facts, such as tables, which are required to implement arithmetical computations (Temple, 1991, 1994). Such difficulties may arise because of impairment in a specialized system for the storage of arithmetical facts or as a result of causally linked impairment in another cognitive domain. This study explored issues concerning the representation and retrieval of arithmetical facts in children with number fact disorders (NF) and in normal children, in particular the status of hypothesized linked impairments: short-term memory (STM) spans, counting skills, speed of speech, and speed of number fact and lexical retrieval. There was no evidence that NF children had weak STM spans on any span measure or that STM spans related to arithmetical fact skills. There was also no evidence that NF children had weak counting abilities or free counting speeds. The NF children were slower in speeded counting, which also correlated with number fact skill. The significance or not of this is discussed. The NF children were also slower than controls in speed of speech and on some measures of speed of access. However, the absence of correlation with number fact skill, the absence of generality across tasks, and the possibility that delayed speeds in fact retrieval reflect the use of alternative strategies, together suggest that the increased speeds are not causally linked to number fact skill. The results are consistent with modular accounts, in which there is a specialized system for the storage and retrieval of arithmetical facts.

Mathematical competencies of 180 children were examined at 4 points between 2nd and 3rd grades (age range between 7 and 9 years). Children were initially classified into one of 4 groups: math difficulties but normal reading (MD only), math and reading difficulties (MD-RD), reading difficulties but normal math (RD only), and normal achievement in math and reading (NA). The groups did not differ significantly in rate of development. However, at the end of 3rd grade the MD only group performed better than the MD-RD group in problem solving but not in calculation. The NA and RD only groups performed better than the MD-RD group in most areas. Deficiencies in fact mastery and calculation fluency, in particular, are defining features of MD, with or without RD.