Language does arithmetic: linguistic differences in children's place-value processing

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 those children putting less emphasis on the tens digit when solving multiplication problems, than Italian-speaking children.

Children's spatial language skills predict their verbal number skills: A longitudinal study

The process of number symbolization is assumed to be critically influenced by the acquisition of so-called verbal number skills (e.g., verbally reciting the number chain and naming Arabic numerals). For the acquisition of these verbal number skills, verbal and visuospatial skills are discussed as contributing factors. In this context, children’s verbal number skills have been found to be associated with their concurrent spatial language skills such as mastery of verbal descriptions of spatial position (e.g., in front of, behind). In a longitudinal study with three measurement times (T1, T2, T3) at an interval of about 6 months, we evaluated the predictive role of preschool children’s (mean age at T1: 3 years and 10 months) spatial language skills for the acquisition of verbal number skills. Children’s spatial language skills at T2 significantly predicted their verbal number skills at T3, when controlling for influences of important covariates such as vocabulary knowledge. In addition, further analyses replicated previous results indicating that children’s spatial language skills at T2 were associated with their verbal number skills at T2. Exploratory analyses further revealed that children’s verbal number skills at T1 predict their spatial language at T2. Results suggests that better spatial language skills at the age of 4 years facilitate the future acquisition of verbal number skills.

Quality of cochlear implant rehabilitation under COVID-19 conditions

Background

The rehabilitation process following cochlear implant (CI) surgery is carried out in a multimodal therapy according to German national guidelines and includes technical and medical aftercare. In times of the corona pandemic surgery and rehabilitation appointments were cancelled or delayed leading to a more difficult access to auditory rehabilitation. Newly implemented hygiene modalities due to the SARS-CoV‑2 pandemic have changed medical aftercare and the rehabilitation process. The aim of this study was to evaluate the quality of rehabilitation under corona conditions.

Material and methods

An anonymous survey of adult cochlear implant patients was carried out by a non-standardized questionnaire. Demographics were analyzed and the quality of medical aftercare, speech therapy, technical aftercare, psychological support and the hygiene modalities were compared to previous rehabilitation stays.

Results

In total 109 patients completed the questionnaire. The quality of rehabilitation and individual therapy were rated as qualitatively similar or improved. The threat of the pandemic and fear of corona were rated unexpectedly high with 68% and 50%, respectively. The hygiene measures during the rehabilitation stay eased subjective fears at the same time. The majority of patients were annoyed by wearing face masks but visors, protection shields and social distancing were more tolerated.

Conclusion

The implementation of the new hygiene modalities within the therapeutic rehabilitation setting was well-accepted by patients allowing access to auditory rehabilitation. A successful rehabilitation should ensure a fear-free environment by adhering to the necessary hygiene modalities.

Electronic supplementary material

The online version of this article (10.1007/s00106-020-00923-z) includes the study questionnaire. Article and supplementary material are available at www.springermedizin.de. Please enter the title of the article in the search field, the supplementary material can be found under “Ergänzende Inhalte”.

[Quality of cochlear implant rehabilitation under COVID-19 conditions. German version]

Hintergrund

Die Rehabilitation nach CI(Cochleaimplantat)-Operation erfolgt leitliniengerecht durch eine multimodale Therapie, technische Anpassungen des Sprachprozessors und medizinische Nachsorge. Zu Zeiten der Corona-Pandemie wurde für die Patienten der Zugang zur auditorischen Rehabilitation verzögert oder erschwert. Die neuen Hygienemaßnahmen durch die SARS-Cov-2-Pandemie verändern auch die medizinische Nachsorge und Rehabilitation nach CI. Ziel der Untersuchung war es, die Qualität der Rehabilitation unter Corona-Bedingungen zu evaluieren.

Material und Methoden

Wir führten eine anonyme Befragung erwachsener Rehabilitanden mittels nichtstandardisiertem Fragebogen durch. Beurteilt wurden im Vergleich zu den Voraufenthalten die Qualität der ärztlichen Betreuung, der Sprach- und Musiktherapie, der technischen Anpassung und der psychologischen Betreuung sowie der Einsatz der Hygienemaßnahmen.

Ergebnisse

Insgesamt 109 Rehabilitanden beantworteten den Fragebogen. Die Qualität der Rehabilitation und der Therapien wurde als qualitativ unverändert oder besser eingeschätzt. Die Gefährlichkeit der Pandemie, aber auch die Angst in der derzeitigen Situation gaben die Rehabilitanden zu einem unerwartet hohen Prozentsatz mit 68 bzw. 50 % an. Gleichzeitig konnten die getroffenen Hygienemaßnahmen die Patienten subjektiv während des Aufenthalts entlasten. Der Mund-Nasen-Schutz war für die Mehrheit sehr störend, Visiere, Spuckschutz bzw. Abstandsgebot wurden eher toleriert.

Schlussfolgerungen

Die Umsetzung der Hygienemaßnahmen im therapeutischen Setting der CI-Rehabilitation wird von den Rehabilitanden akzeptiert und erlaubt den Zugang zur auditorischen Rehabilitation. Ziel einer erfolgreichen CI-Rehabilitation sollte eine möglichst angstfreie Behandlung unter Wahrung der Hygieneregeln sein.

Zusatzmaterial online

Die Online-Version dieses Beitrags (10.1007/s00106-020-00922-0) enthält den Studienfragebogen. Beitrag und Zusatzmaterial stehen Ihnen auf www.springermedizin.de zur Verfügung. Bitte geben Sie dort den Beitragstitel in die Suche ein, das Zusatzmaterial finden Sie beim Beitrag unter „Ergänzende Inhalte“.

Embodied numerical representations and their association with multi-digit arithmetic performance

There is a well-documented association between fingers and numbers, which was claimed to stem from the use of finger-based strategies for counting and calculating during childhood. Recently, it has been argued that this may lead to a concomitant activation of finger-based alongside other numerical representations when encountering single-digit numbers. Indeed, the occurrence of such a co-activation is supported by observed influences of finger counting habits on different numerical tasks, including single-digit arithmetic problem solving. In this study, we pursued the question whether the influence of finger-based representations on arithmetic generalizes to multi-digit arithmetic by investigating the association between the recognition of canonical and non-canonical finger patterns and multi-digit arithmetic in adults. Results indicated that canonical finger-based numerical representations were significantly associated with addition performance only, whereas non-canonical finger-based representations were associated significantly with all four arithmetic operations. We argue that, because non-canonical patterns do not benefit from the iconicity of canonical patterns, their magnitude may need to be constructed through magnitude manipulation which may in turn increase associations with mental arithmetic. In sum, our findings provide converging evidence for a functional association between finger-based representations and arithmetic performance.

Differential Development of Children's Understanding of the Cardinality of Small Numbers and Zero

Counting and the understanding of cardinality are important steps in children’s numerical development. Recent studies have indicated that language and visuospatial abilities play an important role in the development of children’s cardinal knowledge of small numbers. However, predictors for the knowledge about zero were usually not considered in these studies. Therefore, the present study investigated whether the acquisition of cardinality knowledge on small numbers and the concept of zero share cross-domain and domain-specific numerical predictors. Particular interest was paid to the question whether visuospatial abilities – in addition to language abilities – were associated with children’s understanding of small numbers and zero. Accordingly, we assessed kindergarteners aged 4 to 5 years in terms of their understanding of small numbers and zero as well as their visuospatial, general language, counting, Arabic number identification abilities, and their finger number knowledge. We observed significant zero-order correlations of vocabulary, number identification, finger knowledge, and counting abilities with children’s knowledge about zero as well as understanding of the cardinality of small numbers. Subsequent regression analyses substantiated the influences of counting abilities on knowledge about zero and the influences of both counting abilities and finger knowledge on children’s understanding of the cardinality of small numbers. No significant influences of cross-domain predictors were observed. In sum, these results indicate that domain-specific numerical precursor skills seem to be more important for children’s development of an understanding of the cardinality of small numbers as well as of the concept of zero than the more proximal cross-domain abilities such as language and visuospatial abilities.

More than simple facts: cross-linguistic differences in place-value processing in arithmetic fact retrieval

Linguistic specificities such as the inversion property of number words (e.g., in German 43 is spoken dreiundvierzig, literally three and  forty) moderate Arabic number processing. So far, cross-linguistic studies have mostly focused on inversion-related effects on simple (e.g., number comparison) and calculation-based (e.g., multi-digit addition) magnitude processing of numerical information. Despite the assumption that multiplication facts are represented in verbal format, not much attention has been paid to inversion-related influences on multiplication fact retrieval. Accordingly, the current study evaluated inversion-related effects on the processing of place-value information in multiplication. In a verification paradigm, the decade consistency effect (i.e., more errors when the decade of a solution probe shares the decade digit with the correct solution) was larger for English- than German-speaking participants for table-related probes. Processing of decade digits might be prioritised in English-speaking participants because the decade digit is named first in English number words, whereas in German number words the unit digit is named first. Our results indicate that (1) the influence of specificities of a verbal number word formation on place-value processing generalise to arithmetic fact retrieval and (2) inversion of number words might even be advantageous in specific cases.

Longitudinal development of subtraction performance in elementary school

A major goal of education in elementary mathematics is the mastery of arithmetic operations. However, research on subtraction is rather scarce, probably because subtraction is often implicitly assumed to be cognitively similar to addition, its mathematical inverse. To evaluate this assumption, we examined the relation between the borrow effect in subtraction and the carry effect in addition, and the developmental trajectory of the borrow effect in children using a choice reaction paradigm in a longitudinal study. In contrast to the carry effect in adults, carry and borrow effects in children were found to be categorical rather than continuous. From grades 3 to 4, children became more proficient in two-digit subtraction in general, but not in performing the borrow operation in particular. Thus, we observed no specific developmental progress in place-value computation, but a general improvement in subtraction procedures. Statement of contribution What is already known on this subject? The borrow operation increases difficulty in two-digit subtraction in adults. The carry effect in addition, as the inverse operation of borrowing, comprises categorical and continuous processing characteristics. What does this study add? In contrast to the carry effect in adults, the borrow and carry effects are categorical in elementary school children. Children generally improve in subtraction performance from grades 3 to 4 but do not progress in place-value computation in particular.

A Systematic Investigation of Accuracy and Response Time Based Measures Used to Index ANS Acuity

The approximate number system (ANS) was proposed to be a building block for later mathematical abilities. Several measures have been used interchangeably to assess ANS acuity. Some of these measures were based on accuracy data, whereas others relied on response time (RT) data or combined accuracy and RT data. Previous studies challenged the view that all these measures can be used interchangeably, because low correlations between some of the measures had been observed. These low correlations might be due to poor reliability of some of the measures, since the majority of these measures are mathematically related. Here we systematically investigated the relationship between common ANS measures while avoiding the potential confound of poor reliability. Our first experiment revealed high correlations between all accuracy based measures supporting the assumption that all of them can be used interchangeably. In contrast, not all RT based measures were highly correlated. Additionally, our results revealed a speed-accuracy trade-off. Thus, accuracy and RT based measures provided conflicting conclusions regarding ANS acuity. Therefore, we investigated in two further experiments which type of measure (accuracy or RT) is more informative about the underlying ANS acuity, depending on participants’ preferences for accuracy or speed. To this end, we manipulated participants’ preferences for accuracy or speed both explicitly using different task instructions and implicitly varying presentation duration. Accuracy based measures were more informative about the underlying ANS acuity than RT based measures. Moreover, the influence of the underlying representations on accuracy data was more pronounced when participants preferred accuracy over speed after the accuracy instruction as well as for long or unlimited presentation durations. Implications regarding the diffusion model as a theoretical framework of dot comparison as well as regarding the relationship between ANS acuity and math performance are discussed.

Contribution of working memory in multiplication fact network in children may shift from verbal to visuo-spatial: a longitudinal investigation

Number facts are commonly assumed to be verbally stored in an associative multiplication fact retrieval network. Prominent evidence for this assumption comes from so-called operand-related errors (e.g., 4 × 6 = 28). However, little is known about the development of this network in children and its relation to verbal and non-verbal memories. In a longitudinal design, we explored elementary school children from grades 3 and 4 in a multiplication verification task with the operand-related and -unrelated distractors. We examined the contribution of multiplicative fact retrieval by verbal and visuo-spatial short-term and working memory (WM). Children in grade 4 showed smaller reaction times in all conditions. However, there was no significant difference in errors between grades. Contribution of verbal and visuo-spatial WM also changed with grade. Multiplication correlated with verbal WM and performance in grade 3 but with visuo-spatial WM and performance in grade 4. We suggest that the relation to verbal WM in grade 3 indicates primary linguistic learning of and access to multiplication in grade 3 which is probably based on verbal repetition of the multiplication table heavily practiced in grades 2 and 3. However, the relation to visuo-spatial semantic WM in grade 4 suggests that there is a shift from verbal to visual and semantic learning in grade 4. This shifting may be induced because later in elementary school, multiplication problems are rather carried out via more written, i.e., visual tasks, which also involve executive functions. More generally, the current data indicates that mathematical development is not generally characterized by a steady progress in performance; rather verbal and non-verbal memory contributions of performance shift over time, probably due to different learning contents.

Number processing and arithmetic skills in children with cochlear implants

Though previous findings report that hearing impaired children exhibit impaired language and arithmetic skills, our current understanding of how hearing and the associated language impairments may influence the development of arithmetic skills is still limited. In the current study numerical/arithmetic performance of 45 children with a cochlea implant were compared to that of controls matched for hearing age, intelligence and sex. Our main results were twofold disclosing that children with CI show general as well as specific numerical/arithmetic impairments. On the one hand, we found an increased percentage of children with CI with an indication of dyscalculia symptoms, a general slowing in multiplication and subtraction as well as less accurate number line estimations. On the other hand, however, children with CI exhibited very circumscribed difficulties associated with place-value processing. Performance declined specifically when subtraction required a borrow procedure and number line estimation required the integration of units, tens, and hundreds instead of only units and tens. Thus, it seems that despite initially atypical language development, children with CI are able to acquire arithmetic skills in a qualitatively similar fashion as their normal hearing peers. Nonetheless, when demands on place-value understanding, which has only recently been proposed to be language mediated, hearing impaired children experience specific difficulties.

Language influences on numerical development-Inversion effects on multi-digit number processing

In early numerical development, children have to become familiar with the Arabic number system and its place-value structure. The present review summarizes and discusses evidence for language influences on the acquisition of the highly transparent structuring principles of digital-Arabic digits by means of its moderation through the transparency of the respective language's number word system. In particular, the so-called inversion property (i.e., 24 named as “four and twenty” instead of “twenty four”) was found to influence number processing in children not only in verbal but also in non-verbal numerical tasks. Additionally, there is first evidence suggesting that inversion-related difficulties may influence numerical processing longitudinally. Generally, language-specific influences in children's numerical development are most pronounced for multi-digit numbers. Yet, there is currently only one study on three-digit number processing for German-speaking children. A direct comparison of additional new data from Italian-speaking children further corroborates the assumption that language impacts on cognitive (number) processing as inversion-related interference was found most pronounced for German-speaking children. In sum, we conclude that numerical development may not be language-specific but seems to be moderated by language.

Prüfungsangst, Schulleistung und Lebensqualität bei Schülern

Das Hauptziel der vorliegenden Studie ist die systematische Untersuchung des Zusammenhangs zwischen schulbezogenen Ängsten (Prüfungsangst, manifeste Angst, Schulunlust) und Schulleistung (Lesen, Rechtschreiben, Rechnen) in einer großen Stichprobe von Schülern der dritten und sechsten Schulstufe (n = 345 und n = 378, respektive). Weitere Ziele der Studie sind die Erhebung der Vorkommenshäufigkeit von schulbezogenen Ängsten und die Beantwortung der Frage, ob das Ausmaß der subjektiv erlebten Prüfungsangst die subjektive Lebensqualität (bezogen auf Familie, Selbstwert, Freunde, psychisches und körperliches Wohlbefinden) prädizieren kann. Die Ergebnisse zeigen über beide Klassenstufen einen signifikanten Zusammenhang zwischen der Prüfungsangst und den rechnerischen Fertigkeiten, während die Lese- und Rechtschreibkompetenzen nur in der Grundstufe signifikant mit der Prüfungsangst korrelierten. Bemerkenswert ist die relativ hohe Vorkommenshäufigkeit von schulbezogenen Ängsten in unserer Stichprobe. So sind 8 bis 16 % der Schüler von einer ausgeprägten Prüfungsangst betroffen, wobei doppelt so viele Schüler der sechsten Schulstufe als jene der dritten Schulstufe subjektive Prüfungsängste berichten. Demgegenüber sind die manifeste Angst und die Schulunlust über die Klassenstufen hinweg vergleichbar (manifeste Angst liegt zwischen 18 – 20 % und Schulunlust zwischen 20 – 25 %). In unserer Stichprobe der Sechstklässler konnte die Prüfungsangst – neben anderen Faktoren – auch als wichtiger Prädiktor für die subjektive Lebensqualität der Schüler identifiziert werden. Die Implikationen dieser Ergebnisse für die schulische und klinische Praxis werden im Diskussionsteil erörtert.

Effektive Förderung rechenschwacher Kinder

Kinder und Jugendliche mit schwachen Rechenfertigkeiten sind nicht nur in der Schule, sondern auch im täglichen Leben vielfältig beeinträchtigt. Eine effektive Förderung ist daher dringend notwendig. In der vorliegenden Metaanalyse wurden Studien, in denen die Wirksamkeit von Förderprogrammen bei deutschsprachigen Kindern mit schwachen Rechenleistungen untersucht wurde, systematisch zusammengefasst. Insgesamt zehn Experimental-Kontrollgruppen-Vergleiche aus acht Interventionsstudien mit 328 Kindern konnten in die Auswertung eingeschlossen werden. Die mittlere Effektstärke der Studien war mittelgroß (g’ = 0.50). Eine Subgruppenanalyse zeigte keine Wirksamkeitsunterschiede zwischen curricularen und nicht-curricularen Förderansätzen. Weitere Subgruppenanalysen zeigten, dass der Fördereffekt durch das Setting, den Interventionsleiter, sowie durch Dauer und Umfang der Förderung moderiert wird. Langfristige Effekte konnten nicht metaanalytisch ausgewertet werden. Es gibt jedoch empirische Evidenz für langfristige Transfereffekte bei nicht-curricularen Förderansätzen.

One language, two number-word systems and many problems: numerical cognition in the Czech language

Comparing numerical performance between different languages does not only mean comparing different number-word systems, but also implies a comparison of differences regarding culture or educational systems. The Czech language provides the remarkable opportunity to disentangle this confound as there exist two different number-word systems within the same language: for instance, "25" can be either coded in non-inverted order "dvadsetpät" [twenty-five] or in inverted order "pätadvadset" [five-and-twenty]. To investigate the influence of the number-word system on basic numerical processing within one culture, 7-year-old Czech-speaking children had to perform a transcoding task (i.e., writing Arabic numbers to dictation) in both number-word systems. The observed error pattern clearly indicated that the structure of the number-word system determined transcoding performance reliably: In the inverted number-word system about half of all errors were inversion-related. In contrast, hardly any inversion-related errors occurred in the non-inverted number-word system. We conclude that the development of numerical cognition does not only depend on cultural or educational differences, but is indeed related to the structure and transparency of a given number-word system.

Early place-value understanding as a precursor for later arithmetic performance--a longitudinal study on numerical development

It is assumed that basic numerical competencies are important building blocks for more complex arithmetic skills. The current study aimed at evaluating this interrelation in a longitudinal approach. It was investigated whether first graders' performance in basic numerical tasks in general as well as specific processes involved (e.g., place-value understanding) reliably predicted performance in an addition task in third grade. The results indicated that early place-value understanding was a reliable predictor for specific aspects of arithmetic performance. Implications of the role of basic numerical competencies for the acquisition of complex arithmetic are discussed.

Language Effects on Children’s Nonverbal Number Line Estimations

The mental number line of children is usually assumed to be language-independent; however, this independency has not yet been studied. In this cross-cultural study, we examined the influence of language properties on a nonverbal version of the number line task in Italian- and German-speaking first graders. The essential difference between the two languages concerns the inversion property of most German multi-digit numbers (e.g., 48 → “eight-and-forty”), whereas in Italian number-words no inversion is found. The analyses revealed two language-specific differences in the number line task: (a) Generally, the estimates of Italian children were more accurate than those of Austrian children, even when controlling for general cognitive abilities. (b) Italian children performed particularly better when inversion errors led to large estimation errors. In conclusion, these findings indicate that the organization of children’s mental number line is indeed influenced by language properties even in nonverbal settings.

Attentional Strategies in Place-Value Integration

To process a multi-digit number its constituting digits need to be integrated into the place-value structure of the Arabic number system. For two-digit numbers, processes of unit-decade integration are reflected by the compatibility effect in magnitude comparison. Recent research in adults indicated that the size of the compatibility effect increases when stimuli prevent to focus on the decade digits as achieved by the inclusion of within-decade items (43_47). In the present study within- and between-decade items (47_62) were used to assess the compatibility effect in children. We observed reliable compatibility effects that increased with grade level and that were larger than in a previous study without within-decade stimuli. Furthermore, evaluation of the developmental trajectories showed that two-digit number processing develops to more automatic parallel processing of the constituent digits of tens and units. From these results we conclude that (i) even for children attentional processes can strongly influence multi-digit number processing and (ii) with increasing age and experience more parallel and automated understanding of two-digit numbers develops which seems to remain relatively stable once achieved.