Unbounded number line estimation: A purer measure of numerical estimation?

Kürzlich präsentierten Cohen und Blanc-Goldhammer (2011) eine neue, unbounded Version der Zahlenstrahl-Schätzaufgabe. Die Autoren gehen davon aus, dass diese Aufgabe ein reineres Maß als die traditionelle bounded Zahlenstrahl-Schätzaufgabe darstellt, um die zugrunde liegende Zahlenrepräsentation zu messen. In der vorliegenden Dissertation werden verschiedene Einflussfaktoren auf Schätzstrategien betrachtet, die beim Lösen angewendet werden, mit dem Ziel, deren Validität genauer zu beurteilen. Diese Fragestellung wurde in drei Studien näher überprüft, welche (1) die Ähnlichkeit sowie Unterschiede zwischen symbolischen und nicht-symbolischen Schätzungen mit der bounded wie auch unbounded Zahlenstrahl-Schätzaufgabe systematisch untersuchten, wobei eine stärkere Assoziation zwischen der nicht-symbolischen und unbounded im Vergleich zur bounded Aufgabe bestehen soll, (2) Augenbewegungen in beiden Aufgabenversionen untersuchen und eine Abnahme an Fixationen mit grösser werdenden Targets bei der unbounded Version erwartet wurde und (3) Geschlechterunterschiede in beiden genannten Aufgaben erforschen sowie die jeweils angewandten Lösungsstrategien. Die erste Studie stützte sich auf die konzeptionelle Ähnlichkeit zwischen der unbounded Zahlenstrahl-Schätzaufgabe und der bewährten analogen nicht-symbolischen Numerositäts-Aufgabe, um systematische Verzerrungen von Unter- und Überschätzung (in der Wahrnehmungs- und Produktionsversion der Aufgabe), welche in letzterer beobachtet wurden, auf die unbounded Aufgabe zu verallgemeinern. Dasselbe Muster systematischer Unter- und Überschätzung bei Numerositäts-Schätzungen wurde auch bei der unbounded, jedoch nicht bei der bounded Zahlenstrahl-Schätzaufgabe gefunden. Die zweite Studie wurde durchgeführt, um Lösungsstrategien in der bounded und unbounded Zahlenstrahl-Schätzaufgabe zu erforschen, indem die Schätzleistung der Teilnehmer den dazugehörigen Augenbewegungsmustern gegenübergestellt wurde. Die Ergebnisse untermauern die Verwendung von Referenzpunkten in der bounded Aufgabe und deuten darauf hin, dass diejenige Stelle, welche zuerst auf dem Zahlenstrahl fixiert wurde, ein zuverlässiger Prädiktor der endgültigen Schätzung darstellt. Die dritte Studie befasste sich mit Geschlechterunterschieden bei Zahlenstrahl-Schätzungen, wobei Unterschiede zwischen Männern und Frauen beim Anwenden unkonventioneller Lösungsstrategien im Fokus standen. Da Frauen eher dazu tendieren, Methoden anzuwenden, welche sie (in der Schule) gelernt haben, wurde festgestellt, dass sie bei der unbounded Aufgabe im Nachteil sind, da in dieser keine spezifisch bekannten Strategien anwendbar sind, sondern numerisches Größenschätzen notwendig ist. Insgesamt stützen die Ergebnisse aller drei Experimente die Annahme, dass die unbounded Zahlenstrahl-Schätzaufgabe tatsächlich ein reineres und valideres Maß zur Erfassung der Zahlenrepräsentation darstellt. Diese Schlussfolgerung wurde insbesondere bekräftigt i) durch ähnliche Schätzverzerrungen, wie sie bei der nicht-symbolischen Numerositäts-Aufgabe beobachtet wurden, ii) weniger Fixierungen auf Referenzpunkten und iii) Geschlechterunterschieden bei der Anwendung spezifischer Lösungsstrategien. Allerdings legen die Ergebnisse der vorliegenden Dissertation nahe, dass auch die unbounded Zahlenstrahl-Schätzaufgabe nicht frei von spezifischen Schätzstrategien ist.Recently, a new unbounded version of the number line estimation task has been introduced by Cohen and Blanc-Goldhammer (2011). The authors suggested the task to provide a purer measure of the representation of numerical magnitude than the traditional bounded number line estimation task. The present dissertation considers various factors influencing estimation strategies to solve the unbounded number line estimation task with the aim at evaluating the claims associated with its validity more appropriately. This question was pursued in three studies that (1) systematically evaluate similarities and differences between symbolic and non-symbolic estimation with the bounded and unbounded number line estimation task with a closer association of non-symbolic with unbounded than bounded number line estimation, (2) examine eye-fixation behaviour in these two task versions by an expected decrease of the numbers of fixations with increasing target size on the unbounded number line, and (3) investigate sex differences in the aforementioned tasks with solution strategies applied respectively. The first study drew on the conceptual similarity between unbounded number line estimation and the renowned analogue non-symbolic numerosity estimation task to generalize systematic biases of under- and overestimation (for the perception vs. production version of the task, respectively) observed in the latter to the unbounded number line estimation task. The same pattern of systematic biases of under- and overestimation in numerosity estimation was also found in the unbounded but not in the bounded number line estimation task. The second study was conducted to investigate solution strategies in bounded and unbounded number line estimation by contrasting participants´ estimation performance with their corresponding eye-fixation behaviour. Results substantiated the use of reference points in the bounded version of the task and suggested the location of the very first fixation on the number line to be a reliable predictor of the final estimation. The third study addressed sex differences in number line estimation focussing on differences in solution strategies in terms of differences between males and females in approaching unconventional problems. As women tend more strongly to use (classroom-)learnt procedures as compared to estimation, they were found to be at a disadvantage in unbounded number line estimation as it does not allow to apply leant strategies such as proportion judgement in bounded number line estimation, but requires numerical estimations. In summary, the results of all three experiments support the claim that unbounded number line estimation might indeed provide a more pure and valid measure of number magnitude representation. This conclusion was particularly supported by i) comparable estimation biases as observed in non-symbolical numerosity estimation, ii) fewer fixations on reference points, and iii) sex differences associated with applying specific solution strategies. Nevertheless, the findings of the current dissertation also suggest that unbounded number line estimation task is not independent of specific estimation strategies

A potential dissociation between perception and production version for bounded but not unbounded number line estimation.

BACKGROUND What, exactly, do number line estimation (NLE) tasks measure? Different versions of the task were observed to have different effects on performance. METHOD We investigated associations between the production (indicating the location) and perception version (indicating the number) of the bounded and unbounded NLE task and their relationship to arithmetic. RESULTS A stronger correlation was observed between the production and perception version of the unbounded than the bounded NLE task, indicating that both versions of the unbounded-but not the bounded-NLE task measure the same construct. Moreover, overall low but significant associations between NLE performance and arithmetic were only observed for the production version of the bounded NLE task. CONCLUSION These results substantiate that the production version of bounded NLE seems to rely on proportion judgment strategies, whereas both unbounded versions and the perception version of the bounded NLE task may rely more on magnitude estimation

The new unbounded number line estimation task: A systematic literature review

In 2011, Cohen and Blanc-Goldhammer introduced a new unbounded version of the number line estimation task which they argued to overcome limitations of its ‘traditional’ bounded counterpart. In line with this proposition, there is increasing evidence that the unbounded number line estimation task may indeed reflect a purer measure of the underlying representation of number magnitude. However, only few studies used this task version yet. In the present literature review, we aimed at evaluating all studies employing the unbounded task version so far to provide an overview of the current state of research. To identify all relevant articles and to evaluate the validity of the task, we conducted a systematic literature search in different databases following the PRISMA guidelines in May 2021. Methodological differences and commonalities of the 16 studies that met the inclusion criteria are discussed here. Our evaluation indicated considerable differences between studies with respect to the number range covered or methodological features such as display size. Additionally, five studies observed evidence for estimation biases in the unbounded task as well. Nevertheless, this review also substantiated the claim that the unbounded task version might indeed be a more valid and purer measure of the mental representation of number magnitude as the results of 14 studies confirmed this hypothesis

Unbounded number line estimation as a measure of numerical estimation

<div><p>Number magnitude estimation has been investigated over the last decades using different tasks including non-symbolic numerosity but also number line estimation tasks. Recently, a bi-directional mapping process was suggested for numerosity estimation accounting for underestimation in a perception version of the task (i.e., indicating the number of non-symbolic dots in a set) and overestimation in the corresponding production task (i.e., produce the number of dots indicated by a symbolic number). In the present study, we evaluated the generalizability of these estimation biases in perception and production tasks to bounded and unbounded number line estimation. Importantly, target numbers were underestimated/overestimated by participants in the perception/production version of numerosity estimation as well as unbounded number line estimation. However, this pattern was reversed for bounded number line estimation. Thereby, the present data indicate a conceptual similarity of unbounded number line estimation and the established non-symbolic numerosity estimation task as a measure of numerical estimation. Accordingly, this corroborates the notion that unbounded number line estimation may reflect a purer measure of number magnitude representation than the bounded task version. Furthermore, our findings strengthen the bi-directional mapping hypothesis for numerical estimation by providing evidence for its generalizability to unbounded number line estimation for the first time.</p></div

A potential dissociation between perception and production version for bounded but not unbounded number line estimation

Background: What, exactly, do number line estimation (NLE) tasks measure? Different versions of the task were observed to have different effects on performance. Method: We investigated associations between the production (indicating the location) and perception version (indicating the number) of the bounded and unbounded NLE task and their relationship to arithmetic. Results: A stronger correlation was observed between the production and perception version of the unbounded than the bounded NLE task, indicating that both versions of the unbounded—but not the bounded—NLE task measure the same construct. Moreover, overall low but significant associations between NLE performance and arithmetic were only observed for the production version of the bounded NLE task.  Conclusion: These results substantiate that the production version of bounded NLE seems to rely on proportion judgment strategies, whereas both unbounded versions and the perception version of the bounded NLE task may rely more on magnitude estimation.</p

Incidence of severe critical events in paediatric anaesthesia (APRICOT): a prospective multicentre observational study in 261 hospitals in Europe

Background Little is known about the incidence of severe critical events in children undergoing general anaesthesia in Europe. We aimed to identify the incidence, nature, and outcome of severe critical events in children undergoing anaesthesia, and the associated potential risk factors. Methods The APRICOT study was a prospective observational multicentre cohort study of children from birth to 15 years of age undergoing elective or urgent anaesthesia for diagnostic or surgical procedures. Children were eligible for inclusion during a 2-week period determined prospectively by each centre. There were 261 participating centres across 33 European countries. The primary endpoint was the occurence of perioperative severe critical events requiring immediate intervention. A severe critical event was defined as the occurrence of respiratory, cardiac, allergic, or neurological complications requiring immediate intervention and that led (or could have led) to major disability or death. This study is registered with ClinicalTrials.gov, number NCT01878760. Findings Between April 1, 2014, and Jan 31, 2015, 31 127 anaesthetic procedures in 30 874 children with a mean age of 6.35 years (SD 4.50) were included. The incidence of perioperative severe critical events was 5.2% (95% CI 5.0-5.5) with an incidence of respiratory critical events of 3.1% (2.9-3.3). Cardiovascular instability occurred in 1.9% (1.7-2.1), with an immediate poor outcome in 5.4% (3.7-7.5) of these cases. The all-cause 30-day in-hospital mortality rate was 10 in 10 000. This was independent of type of anaesthesia. Age (relative risk 0.88, 95% CI 0.86-0.90; p<0.0001), medical history, and physical condition (1.60, 1.40-1.82; p<0.0001) were the major risk factors for a serious critical event. Multivariate analysis revealed evidence for the beneficial effect of years of experience of the most senior anaesthesia team member (0.99, 0.981-0.997; p<0.0048 for respiratory critical events, and 0.98, 0.97-0.99; p=0.0039 for cardiovascular critical events), rather than the type of health institution or providers. Interpretation This study highlights a relatively high rate of severe critical events during the anaesthesia management of children for surgical or diagnostic procedures in Europe, and a large variability in the practice of paediatric anaesthesia. These findings are substantial enough to warrant attention from national, regional, and specialist societies to target education of anaesthesiologists and their teams and implement strategies for quality improvement in paediatric anaesthesia

Incidence of severe critical events in paediatric anaesthesia (APRICOT): a prospective multicentre observational study in 261 hospitals in Europe

Background Little is known about the incidence of severe critical events in children undergoing general anaesthesia in Europe. We aimed to identify the incidence, nature, and outcome of severe critical events in children undergoing anaesthesia, and the associated potential risk factors. Methods The APRICOT study was a prospective observational multicentre cohort study of children from birth to 15 years of age undergoing elective or urgent anaesthesia for diagnostic or surgical procedures. Children were eligible for inclusion during a 2-week period determined prospectively by each centre. There were 261 participating centres across 33 European countries. The primary endpoint was the occurence of perioperative severe critical events requiring immediate intervention. A severe critical event was defined as the occurrence of respiratory, cardiac, allergic, or neurological complications requiring immediate intervention and that led (or could have led) to major disability or death. This study is registered with ClinicalTrials.gov, number NCT01878760. Findings Between April 1, 2014, and Jan 31, 2015, 31â127 anaesthetic procedures in 30â874 children with a mean age of 6·35 years (SD 4·50) were included. The incidence of perioperative severe critical events was 5·2% (95% CI 5·0â5·5) with an incidence of respiratory critical events of 3·1% (2·9â3·3). Cardiovascular instability occurred in 1·9% (1·7â2·1), with an immediate poor outcome in 5·4% (3·7â7·5) of these cases. The all-cause 30-day in-hospital mortality rate was 10 in 10â000. This was independent of type of anaesthesia. Age (relative risk 0·88, 95% CI 0·86â0·90; p<0·0001), medical history, and physical condition (1·60, 1·40â1·82; p<0·0001) were the major risk factors for a serious critical event. Multivariate analysis revealed evidence for the beneficial effect of years of experience of the most senior anaesthesia team member (0·99, 0·981â0·997; p<0·0048 for respiratory critical events, and 0·98, 0·97â0·99; p=0·0039 for cardiovascular critical events), rather than the type of health institution or providers. Interpretation This study highlights a relatively high rate of severe critical events during the anaesthesia management of children for surgical or diagnostic procedures in Europe, and a large variability in the practice of paediatric anaesthesia. These findings are substantial enough to warrant attention from national, regional, and specialist societies to target education of anaesthesiologists and their teams and implement strategies for quality improvement in paediatric anaesthesia. Funding European Society of Anaesthesiology

Incidence of severe critical events in paediatric anaesthesia (APRICOT): a prospective multicentre observational study in 261 hospitals in Europe

Background Little is known about the incidence of severe critical events in children undergoing general anaesthesia in Europe. We aimed to identify the incidence, nature, and outcome of severe critical events in children undergoing anaesthesia, and the associated potential risk factors. Methods The APRICOT study was a prospective observational multicentre cohort study of children from birth to 15 years of age undergoing elective or urgent anaesthesia for diagnostic or surgical procedures. Children were eligible for inclusion during a 2-week period determined prospectively by each centre. There were 261 participating centres across 33 European countries. The primary endpoint was the occurence of perioperative severe critical events requiring immediate intervention. A severe critical event was defined as the occurrence of respiratory, cardiac, allergic, or neurological complications requiring immediate intervention and that led (or could have led) to major disability or death. This study is registered with ClinicalTrials.gov, number NCT01878760. Findings Between April 1, 2014, and Jan 31, 2015, 31 127 anaesthetic procedures in 30 874 children with a mean age of 6.35 years (SD 4.50) were included. The incidence of perioperative severe critical events was 5.2% (95% CI 5.0-5.5) with an incidence of respiratory critical events of 3.1% (2.9-3.3). Cardiovascular instability occurred in 1.9% (1.7-2.1), with an immediate poor outcome in 5.4% (3.7-7.5) of these cases. The all-cause 30-day in-hospital mortality rate was 10 in 10 000. This was independent of type of anaesthesia. Age (relative risk 0.88, 95% CI 0.86-0.90; p<0.0001), medical history, and physical condition (1.60, 1.40-1.82; p<0.0001) were the major risk factors for a serious critical event. Multivariate analysis revealed evidence for the beneficial effect of years of experience of the most senior anaesthesia team member (0.99, 0.981-0.997; p<0.0048 for respiratory critical events, and 0.98, 0.97-0.99; p=0.0039 for cardiovascular critical events), rather than the type of health institution or providers. Interpretation This study highlights a relatively high rate of severe critical events during the anaesthesia management of children for surgical or diagnostic procedures in Europe, and a large variability in the practice of paediatric anaesthesia. These findings are substantial enough to warrant attention from national, regional, and specialist societies to target education of anaesthesiologists and their teams and implement strategies for quality improvement in paediatric anaesthesia