The representation and retrieval of multiplication facts is dependent on linguistic specificities... more The representation and retrieval of multiplication facts is dependent on linguistic specificities such as number word inversion (i.e., 23 is spoken dreiundzwanzig in German which translates to three and twenty). Previous research has evaluated these language influences in adults. Now this study aims to follow-up on earlier findings and takes a closer look at inversion-related effects on place-value processing during multiplication in children. In a task of choice 46 children, either German- or Italian-speaking, had to pick the right answer out of two options for a given multiplication problem. Already established effects in adult participants such as decade-consistency and table-relatedness were also present in elementary school children, but different between the language groups. For decade-consistent items the effect of table-relatedness was larger for Italian-speaking students than for German-speaking. This indicates that the inversion property in the German language leads to tho...
International Journal of Bilingual Education and Bilingualism
ABSTRACT The importance of language in mathematics education becomes increasingly obvious, as mul... more ABSTRACT The importance of language in mathematics education becomes increasingly obvious, as multilingual learners are not an exception nowadays. But how can language dominance and the language of first or later instruction affect arithmetic training in adults? 101 bilingual adults whose first and dominant language was German (LM+ and L1) and who spoke English as their second language (L2) were tested. Participants were assigned to three different training groups and either practiced basic multiplications in German, English or both languages. In a verification paradigm, reaction times on solving multiplication problems in German and English respectively were recorded before and after the training. Results showed a strong influence of the language adult bilinguals initially acquired arithmetic knowledge in (German). German items were overall solved more quickly than English counterparts, irrespective of the language items were specifically trained in. English were affected by differing training conditions with respect to training effects. This leads to the consideration of various factors including language proficiency levels, the language of first mathematics instruction in early school years as well as the language of mathematics instruction in later learning contexts, in understanding bilingual arithmetic learning.
Die Dyskalkulie, als Storung der Rechenfertigkeiten ohne Intelligenzminderung definiert, geht mit... more Die Dyskalkulie, als Storung der Rechenfertigkeiten ohne Intelligenzminderung definiert, geht mit massiven Schwierigkeiten im Erwerb basaler numerischer und arithmetischer Kompetenzen einher. Dabei konnen unterschiedliche mathematische Teilfertigkeiten unabhangig voneinander gestort oder mangelhaft ausgepragt sein konnen. Als effektivste Interventionen haben sich nicht curricular orientierte, neuropsychologische Therapien mit symptomspezifischer Forderung, d. h. bezogen auf mathematische, arithmetische oder basisnumerische Inhalte, erwiesen. Dabei ist es von groser Bedeutung, die Forderung individuell an jenem Punkt zu starten, an welchem das Kind die ersten Probleme gezeigt hat, unabhangig von aktueller Schulstufe und chronologischem Alter. Implikationen fur die Praxis anhand konkreter Forderansatze mit wichtigen, aufeinander aufbauenden Bausteinen werden gegeben, inkl. Beispielen fur die Integration der Forderung in den Alltag des Kindes.
International Handbook of Mathematical Learning Difficulties, 2019
Studies on the predictors of mathematical learning and learning difficulties have been receiving ... more Studies on the predictors of mathematical learning and learning difficulties have been receiving growing attention. It is well established in the literature that IQ is a powerful predictor of several psychosocial outcomes, including school achievement. Other well-consolidated literature shows that cognitive–motivational effects exist but are rather small. There seems to be a big interaction between interest and specific knowledge in a domain (expertise). Variance is confounded. In this chapter, motivation and math anxiety are described within the opportunity–propensity (O-P) model including antecedent, opportunity, and propensity indicators to predict mathematical accuracy and fluency. Analyses on secondary data using this O-P model revealed that motivation as a propensity factor accounted for 10% of unique variance in addition to other predictors. Motivation and engagement were stronger predictors from kindergarten till second grade than from third till sixth grade. In addition, math anxiety might be considered a moderator of the relationship between mathematical achievement and motivation. Aside from acute effects, math anxiety might cause long-term negative impairments in mathematical performance that are kept up by a negative approach to mathematics and resulting avoidance behavior.
Abstract Word problems are widely used in math instruction to convey arithmetic operations within... more Abstract Word problems are widely used in math instruction to convey arithmetic operations within the context of everyday situations. Although they require solving an arithmetic problem, there is only little research regarding influences of basic numerical processes on the difficulty of arithmetic word problems. Therefore, the present study set out to investigate influences of place-value and magnitude processing as reflected by the carry/borrowing and the problem size effect. Accordingly, we assessed 128 children between 8 and 11 years of age on two-digit addition and subtraction problems presented in both word problem and digital-Arabic formats. Our results indicated that word problems were more difficult to solve. Closer inspection of basic numerical processes indicated that presentation of arithmetic problems in word problem format significantly increased the effects of place-value and magnitude processing, driving a higher level of difficulty. This finding seems to suggest quantitative as well as qualitative differences in arithmetic operations and their underlying basic numerical processes when embedded in word problems.
In the present study, we investigated whether structured quantities like finger or dice patterns ... more In the present study, we investigated whether structured quantities like finger or dice patterns are enumerated better than unstructured quantities because they may not require counting. Moreover, we hypothesized children’s mastery of structured quantities to predict their later arithmetic performance longitudinally. In particular, we expected that children more proficient in enumerating structured quantities early in their numerical development, should develop more effective calculation strategies later because they may rely on counting less. Therefore, we conducted a longitudinal study (including 116 children, 58 girls) over the course of about 7 months from preschool (at about 6 years of age) to the middle of first grade. Results showed that structured quantities were indeed enumerated more accurately and faster than unstructured quantities in preschool. Additionally, we observed significant associations of enumeration of structured and unstructured with children’s addition performance in first grade. However, regression analysis indicated only enumeration of structured but not unstructured quantities to significantly predict later addition performance. In sum, this longitudinal study clearly indicates that mastery of structured quantities seems to be beneficial for children’s development of basic arithmetic abilities.
Recent findings suggest that in addition to severe hypoglycemia, chronic hyperglycemia may also h... more Recent findings suggest that in addition to severe hypoglycemia, chronic hyperglycemia may also hamper the cognitive development of patients with type 1 diabetes. Executive and memory dysfunctions mediated by frontoparietal and temporal brain structures are frequently reported to be associated with type 1 diabetes. However, most studies investigating pediatric patients with diabetes focus on either brain function or brain structure. The current study combines neuropsychological and structural brain imaging methods (i.e., voxel-based-morphometry) to study the neurofunctional integrity of frontoparietal brain areas. We investigated 30 children with type 1 diabetes and 19 healthy controls. Children with diabetes were divided into two groups representing better (HbA1c ≤ 7.9%) and worse (HbA1c ≥ 8.0%) glycemic con- trol. Our findings were threefold: First, results revealed significant group differences with respect to neuropsychological performance (i.e. response accuracies on a marker task tapping frontoparietal brain functions). Second, structural imaging disclosed significant group differences between patients and controls regarding gray matter volume in frontal (anterior cingulate) and occipital (cuneus, bordering precuneus) brain regions and regarding white matter in middle temporal and occipital gyri as well as in the ventromedial temporal lobe (uncus). Third, disease duration, age at diagnosis and white matter volume in a hippocampal region-of-interest (but not HbA1c levels, intelligence, total gray/white matter or other white/gray matter regions-of-interest) explained 56% of neuropsycholo- gical performance variance. Taken together, our findings are among the first to provide evidence of a direct link between brain function and brain structure in pediatric patients with type 1 diabetes.
Dyslexia is characterized by a deficit in language processing which mainly affects word decoding ... more Dyslexia is characterized by a deficit in language processing which mainly affects word decoding and spelling skills. In addition, children with dyslexia also show problems in mathematics. However, for the latter, the underlying structural correlates have not been investigated. Sixteen children with dyslexia (mean age 9.8 years [0.39]) and 24 typically developing children (mean age 9.9 years [0.29]) group matched for age, gender, IQ, and handedness underwent 3 T MR diffusion tensor imaging as well as cognitive testing. Tract-Based Spatial Statistics were performed to correlate behavioral data with diffusion data. Children with dyslexia performed worse than controls in standardized verbal number tasks, such as arithmetic efficiency tests (addition, subtraction, multiplication, division). In contrast, the two groups did not differ in the nonverbal number line task. Arithmetic efficiency, representing the total score of the four arithmetic tasks, multiplication, and division, correlate...
Zusammenfassung. Der vorliegende Artikel soll einen Überblick über die aktuelle Literatur zur Ver... more Zusammenfassung. Der vorliegende Artikel soll einen Überblick über die aktuelle Literatur zur Verarbeitung von zwei- und mehrstelligen Zahlen bei Kindern liefern. Dabei geht es nicht nur um das Lesen und Schreiben von arabischen Ziffern, das zweifelsfrei die erste Hürde auf dem Weg zum Verständnis des arabischen Stellenwertsystems darstellt. Auch der Umgang mit und das Verständnis von mehrstelligen Zahlen werden detailliert diskutiert. So wird zuerst die Metapher des mentalen Zahlenstrahls, auf dem ein- wie mehrstellige Zahlen von links nach rechts aufsteigend angeordnet sind, erläutert. Anschließend wird diskutiert, wie sich dieser bei Kindern entwickelt und welche besonderen Schwierigkeiten die Inversion in deutschen Zahlwörtern (d. h. die Umkehrung der Reihenfolge von Zehnern und Einern, z. B. «einundzwanzig» vs. «21») bedingen kann. Dazu wird u. a. der Frage nachgegangen, inwieweit zwei- und mehrstellige Zahlen als eine Einheit oder getrennt in Einer, Zehner, etc. verarbeitet we...
The representation and retrieval of multiplication facts is dependent on linguistic specificities... more The representation and retrieval of multiplication facts is dependent on linguistic specificities such as number word inversion (i.e., 23 is spoken dreiundzwanzig in German which translates to three and twenty). Previous research has evaluated these language influences in adults. Now this study aims to follow-up on earlier findings and takes a closer look at inversion-related effects on place-value processing during multiplication in children. In a task of choice 46 children, either German- or Italian-speaking, had to pick the right answer out of two options for a given multiplication problem. Already established effects in adult participants such as decade-consistency and table-relatedness were also present in elementary school children, but different between the language groups. For decade-consistent items the effect of table-relatedness was larger for Italian-speaking students than for German-speaking. This indicates that the inversion property in the German language leads to tho...
International Journal of Bilingual Education and Bilingualism
ABSTRACT The importance of language in mathematics education becomes increasingly obvious, as mul... more ABSTRACT The importance of language in mathematics education becomes increasingly obvious, as multilingual learners are not an exception nowadays. But how can language dominance and the language of first or later instruction affect arithmetic training in adults? 101 bilingual adults whose first and dominant language was German (LM+ and L1) and who spoke English as their second language (L2) were tested. Participants were assigned to three different training groups and either practiced basic multiplications in German, English or both languages. In a verification paradigm, reaction times on solving multiplication problems in German and English respectively were recorded before and after the training. Results showed a strong influence of the language adult bilinguals initially acquired arithmetic knowledge in (German). German items were overall solved more quickly than English counterparts, irrespective of the language items were specifically trained in. English were affected by differing training conditions with respect to training effects. This leads to the consideration of various factors including language proficiency levels, the language of first mathematics instruction in early school years as well as the language of mathematics instruction in later learning contexts, in understanding bilingual arithmetic learning.
Die Dyskalkulie, als Storung der Rechenfertigkeiten ohne Intelligenzminderung definiert, geht mit... more Die Dyskalkulie, als Storung der Rechenfertigkeiten ohne Intelligenzminderung definiert, geht mit massiven Schwierigkeiten im Erwerb basaler numerischer und arithmetischer Kompetenzen einher. Dabei konnen unterschiedliche mathematische Teilfertigkeiten unabhangig voneinander gestort oder mangelhaft ausgepragt sein konnen. Als effektivste Interventionen haben sich nicht curricular orientierte, neuropsychologische Therapien mit symptomspezifischer Forderung, d. h. bezogen auf mathematische, arithmetische oder basisnumerische Inhalte, erwiesen. Dabei ist es von groser Bedeutung, die Forderung individuell an jenem Punkt zu starten, an welchem das Kind die ersten Probleme gezeigt hat, unabhangig von aktueller Schulstufe und chronologischem Alter. Implikationen fur die Praxis anhand konkreter Forderansatze mit wichtigen, aufeinander aufbauenden Bausteinen werden gegeben, inkl. Beispielen fur die Integration der Forderung in den Alltag des Kindes.
International Handbook of Mathematical Learning Difficulties, 2019
Studies on the predictors of mathematical learning and learning difficulties have been receiving ... more Studies on the predictors of mathematical learning and learning difficulties have been receiving growing attention. It is well established in the literature that IQ is a powerful predictor of several psychosocial outcomes, including school achievement. Other well-consolidated literature shows that cognitive–motivational effects exist but are rather small. There seems to be a big interaction between interest and specific knowledge in a domain (expertise). Variance is confounded. In this chapter, motivation and math anxiety are described within the opportunity–propensity (O-P) model including antecedent, opportunity, and propensity indicators to predict mathematical accuracy and fluency. Analyses on secondary data using this O-P model revealed that motivation as a propensity factor accounted for 10% of unique variance in addition to other predictors. Motivation and engagement were stronger predictors from kindergarten till second grade than from third till sixth grade. In addition, math anxiety might be considered a moderator of the relationship between mathematical achievement and motivation. Aside from acute effects, math anxiety might cause long-term negative impairments in mathematical performance that are kept up by a negative approach to mathematics and resulting avoidance behavior.
Abstract Word problems are widely used in math instruction to convey arithmetic operations within... more Abstract Word problems are widely used in math instruction to convey arithmetic operations within the context of everyday situations. Although they require solving an arithmetic problem, there is only little research regarding influences of basic numerical processes on the difficulty of arithmetic word problems. Therefore, the present study set out to investigate influences of place-value and magnitude processing as reflected by the carry/borrowing and the problem size effect. Accordingly, we assessed 128 children between 8 and 11 years of age on two-digit addition and subtraction problems presented in both word problem and digital-Arabic formats. Our results indicated that word problems were more difficult to solve. Closer inspection of basic numerical processes indicated that presentation of arithmetic problems in word problem format significantly increased the effects of place-value and magnitude processing, driving a higher level of difficulty. This finding seems to suggest quantitative as well as qualitative differences in arithmetic operations and their underlying basic numerical processes when embedded in word problems.
In the present study, we investigated whether structured quantities like finger or dice patterns ... more In the present study, we investigated whether structured quantities like finger or dice patterns are enumerated better than unstructured quantities because they may not require counting. Moreover, we hypothesized children’s mastery of structured quantities to predict their later arithmetic performance longitudinally. In particular, we expected that children more proficient in enumerating structured quantities early in their numerical development, should develop more effective calculation strategies later because they may rely on counting less. Therefore, we conducted a longitudinal study (including 116 children, 58 girls) over the course of about 7 months from preschool (at about 6 years of age) to the middle of first grade. Results showed that structured quantities were indeed enumerated more accurately and faster than unstructured quantities in preschool. Additionally, we observed significant associations of enumeration of structured and unstructured with children’s addition performance in first grade. However, regression analysis indicated only enumeration of structured but not unstructured quantities to significantly predict later addition performance. In sum, this longitudinal study clearly indicates that mastery of structured quantities seems to be beneficial for children’s development of basic arithmetic abilities.
Recent findings suggest that in addition to severe hypoglycemia, chronic hyperglycemia may also h... more Recent findings suggest that in addition to severe hypoglycemia, chronic hyperglycemia may also hamper the cognitive development of patients with type 1 diabetes. Executive and memory dysfunctions mediated by frontoparietal and temporal brain structures are frequently reported to be associated with type 1 diabetes. However, most studies investigating pediatric patients with diabetes focus on either brain function or brain structure. The current study combines neuropsychological and structural brain imaging methods (i.e., voxel-based-morphometry) to study the neurofunctional integrity of frontoparietal brain areas. We investigated 30 children with type 1 diabetes and 19 healthy controls. Children with diabetes were divided into two groups representing better (HbA1c ≤ 7.9%) and worse (HbA1c ≥ 8.0%) glycemic con- trol. Our findings were threefold: First, results revealed significant group differences with respect to neuropsychological performance (i.e. response accuracies on a marker task tapping frontoparietal brain functions). Second, structural imaging disclosed significant group differences between patients and controls regarding gray matter volume in frontal (anterior cingulate) and occipital (cuneus, bordering precuneus) brain regions and regarding white matter in middle temporal and occipital gyri as well as in the ventromedial temporal lobe (uncus). Third, disease duration, age at diagnosis and white matter volume in a hippocampal region-of-interest (but not HbA1c levels, intelligence, total gray/white matter or other white/gray matter regions-of-interest) explained 56% of neuropsycholo- gical performance variance. Taken together, our findings are among the first to provide evidence of a direct link between brain function and brain structure in pediatric patients with type 1 diabetes.
Dyslexia is characterized by a deficit in language processing which mainly affects word decoding ... more Dyslexia is characterized by a deficit in language processing which mainly affects word decoding and spelling skills. In addition, children with dyslexia also show problems in mathematics. However, for the latter, the underlying structural correlates have not been investigated. Sixteen children with dyslexia (mean age 9.8 years [0.39]) and 24 typically developing children (mean age 9.9 years [0.29]) group matched for age, gender, IQ, and handedness underwent 3 T MR diffusion tensor imaging as well as cognitive testing. Tract-Based Spatial Statistics were performed to correlate behavioral data with diffusion data. Children with dyslexia performed worse than controls in standardized verbal number tasks, such as arithmetic efficiency tests (addition, subtraction, multiplication, division). In contrast, the two groups did not differ in the nonverbal number line task. Arithmetic efficiency, representing the total score of the four arithmetic tasks, multiplication, and division, correlate...
Zusammenfassung. Der vorliegende Artikel soll einen Überblick über die aktuelle Literatur zur Ver... more Zusammenfassung. Der vorliegende Artikel soll einen Überblick über die aktuelle Literatur zur Verarbeitung von zwei- und mehrstelligen Zahlen bei Kindern liefern. Dabei geht es nicht nur um das Lesen und Schreiben von arabischen Ziffern, das zweifelsfrei die erste Hürde auf dem Weg zum Verständnis des arabischen Stellenwertsystems darstellt. Auch der Umgang mit und das Verständnis von mehrstelligen Zahlen werden detailliert diskutiert. So wird zuerst die Metapher des mentalen Zahlenstrahls, auf dem ein- wie mehrstellige Zahlen von links nach rechts aufsteigend angeordnet sind, erläutert. Anschließend wird diskutiert, wie sich dieser bei Kindern entwickelt und welche besonderen Schwierigkeiten die Inversion in deutschen Zahlwörtern (d. h. die Umkehrung der Reihenfolge von Zehnern und Einern, z. B. «einundzwanzig» vs. «21») bedingen kann. Dazu wird u. a. der Frage nachgegangen, inwieweit zwei- und mehrstellige Zahlen als eine Einheit oder getrennt in Einer, Zehner, etc. verarbeitet we...
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