Processing the order of symbolic numbers: A reliable and unique predictor of arithmetic fluency

A small but growing body of evidence suggests a link between individual differences in processing the order of numerical symbols (e.g., deciding whether a set of digits is arranged in ascending/descending order or not) and arithmetic achievement. However, the reliability of behavioral correlates measuring symbolic and non-symbolic numerical order processing and their relationship to arithmetic abilities remain poorly understood. The present study aims to fill this knowledge gap by examining the behavioral correlates of numerical and non-numerical order processing and their unique associations with arithmetic fluency at two different time points within the same sample of individuals. Thirty-two right-handed adults performed three order judgment tasks consisting of symbolic numbers (i.e., digits), non-symbolic numbers (i.e., dots), and letters of the alphabet. Specifically, participants had to judge as accurately and as quickly as possible whether stimuli were ordered correctly (in ascending/descending order, e.g., 2-3-4; ●●●●-●●●-●●; B-C-D) or not (e.g., 4-5-3; ●●●●-●●●●●-●●●; D-E-C). Results of this study demonstrate that numerical order judgments are reliable measurements (i.e., high test-retest reliability), and that the observed relationship between symbolic number processing and arithmetic fluency accounts for a unique and reliable portion of variance over and above the non-symbolic number and the letter conditions. The differential association of symbolic and non-symbolic numbers with arithmetic support the view that processing the order of symbolic and non-symbolic numbers engages different cognitive mechanisms, and that the ability to process ordinal relationships of symbolic numbers is a reliable and unique predictor of arithmetic fluency.

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EXPRESS: Order Processing of Number Symbols is Influenced by Direction, but not Format

Quarterly Journal of Experimental Psychology ◽

10.1177/17470218211026800 ◽

2021 ◽

pp. 174702182110268

Author(s):

Becky Wong ◽

Rebecca Bull ◽

Daniel Ansari ◽

David M. Watson ◽

Gregory Arief D. Liem

Keyword(s):

Processing Speed ◽

Theoretical Perspective ◽

Mathematical Achievement ◽

Number Sequence ◽

Cognitive Mechanisms ◽

Order Processing ◽

Number Words ◽

Number Sequences ◽

Numerical Order ◽

The Relationship

This study probed the cognitive mechanisms that underlie order processing for number symbols, specifically the extent to which the direction and format in which number symbols are presented influence the processing of numerical order, as well as the extent to which the relationship between order processing and mathematical achievement is specific to Arabic numerals or generalisable to other notational formats. Seventy adults who were bilingual in English and Chinese completed a Numerical Ordinality Task, using number sequences of various directional conditions (i.e., ascending, descending, mixed) and notational formats (i.e., Arabic numerals, English number words, and Chinese number words). Order processing was found to occur for ascending and descending number sequences (i.e., ordered but not non-ordered trials), with the overall pattern of data supporting the theoretical perspective that the strength and closeness of associations between items in the number sequence could underlie numerical order processing. However, order processing was found to be independent of the notational format in which the stimuli were presented, suggesting that the psychological representations and processes associated with numerical order are abstract across different formats of number symbols. In addition, a relationship between the processing speed for numerical order and mathematical achievement was observed for Arabic numerals and Chinese number words, and to a weaker extent, English number words. Together, our findings have started to uncover the cognitive mechanisms that could underlie order processing for different formats of number symbols, and raise new questions about the generalisability of these findings to other notational formats.

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Common and distinct predictors of non-symbolic and symbolic ordinal number processing across the early primary school years

PLoS ONE ◽

10.1371/journal.pone.0258847 ◽

2021 ◽

Vol 16 (10) ◽

pp. e0258847

Author(s):

Sabrina Finke ◽

Chiara Banfi ◽

H. Harald Freudenthaler ◽

Anna F. Steiner ◽

Stephan E. Vogel ◽

...

Keyword(s):

Spatial Working Memory ◽

Developmental Change ◽

Ordinal Number ◽

Preliminary Evidence ◽

Symbolic Order ◽

Formal Schooling ◽

Cognitive Mechanisms ◽

Magnitude Comparison ◽

Order Processing ◽

Unique Predictor

What are the cognitive mechanisms supporting non-symbolic and symbolic order processing? Preliminary evidence suggests that non-symbolic and symbolic order processing are partly distinct constructs. The precise mechanisms supporting these skills, however, are still unclear. Moreover, predictive patterns may undergo dynamic developmental changes during the first years of formal schooling. This study investigates the contribution of theoretically relevant constructs (non-symbolic and symbolic magnitude comparison, counting and storage and manipulation components of verbal and visuo-spatial working memory) to performance and developmental change in non-symbolic and symbolic numerical order processing. We followed 157 children longitudinally from Grade 1 to 3. In the order judgement tasks, children decided whether or not triplets of dots or digits were arranged in numerically ascending order. Non-symbolic magnitude comparison and visuo-spatial manipulation were significant predictors of initial performance in both non-symbolic and symbolic ordering. In line with our expectations, counting skills contributed additional variance to the prediction of symbolic, but not of non-symbolic ordering. Developmental change in ordering performance from Grade 1 to 2 was predicted by symbolic comparison skills and visuo-spatial manipulation. None of the predictors explained variance in developmental change from Grade 2 to 3. Taken together, the present results provide robust evidence for a general involvement of pair-wise magnitude comparison and visuo-spatial manipulation in numerical ordering, irrespective of the number format. Importantly, counting-based mechanisms appear to be a unique predictor of symbolic ordering. We thus conclude that there is only a partial overlap of the cognitive mechanisms underlying non-symbolic and symbolic order processing.

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Healthy decisions in the cued-attribute food choice paradigm have high test-retest reliability

Scientific Reports ◽

10.1038/s41598-021-91933-6 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Zahra Barakchian ◽

Anjali Raja Beharelle ◽

Todd A. Hare

Keyword(s):

Food Choice ◽

Food Choices ◽

Retest Reliability ◽

Individual Level ◽

Food Items ◽

Intervention Efficacy ◽

The Individual ◽

Test Retest Reliability ◽

Decision Mechanisms ◽

High Test

AbstractFood choice paradigms are commonly used to study decision mechanisms, individual differences, and intervention efficacy. Here, we measured behavior from twenty-three healthy young adults who completed five repetitions of a cued-attribute food choice paradigm over two weeks. This task includes cues prompting participants to explicitly consider the healthiness of the food items before making a selection, or to choose naturally based on whatever freely comes to mind. We found that the average patterns of food choices following both cue types and ratings about the palatability (i.e. taste) and healthiness of the food items were similar across all five repetitions. At the individual level, the test-retest reliability for choices in both conditions and healthiness ratings was excellent. However, test-retest reliability for taste ratings was only fair, suggesting that estimates about palatability may vary more from day to day for the same individual.

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Cardio-ventilatory coupling in young healthy resting subjects

Journal of Applied Physiology ◽

10.1152/japplphysiol.01424.2010 ◽

2012 ◽

Vol 112 (8) ◽

pp. 1248-1257 ◽

Cited By ~ 11

Author(s):

Lee Friedman ◽

Thomas E. Dick ◽

Frank J. Jacono ◽

Kenneth A. Loparo ◽

Amir Yeganeh ◽

...

Keyword(s):

Body Surface ◽

Relative Importance ◽

Statistical Relationship ◽

Sinus Arrhythmia ◽

Retest Reliability ◽

Respiratory Events ◽

Before And After ◽

Test Retest Reliability ◽

Degree Of Coupling ◽

High Test

In this work, cardio-ventilatory coupling (CVC) refers to the statistical relationship between the onset of either inspiration (I) or expiration (E) and the timing of heartbeats (R-waves) before and after these respiratory events. CVC was assessed in healthy, young (<45 yr), resting, supine subjects ( n = 19). Four intervals were analyzed: time from I-onset to both the prior R-wave (R-to-I) and the following R-wave (I-to-R), as well as time from E-onset to both the prior R-wave (R-to-E) and following R-wave (E-to-R). The degree of coupling was quantified in terms of transformed relative Shannon entropy (tRSE), and χ2 tests based on histograms of interval times from 200 breaths. Subjects were studied twice, from 5 to 27 days apart, and the test-retest reliability of CVC measures was computed. Several factors pointed to the relative importance of the R-to-I interval compared with other intervals. Coupling was significantly stronger for the R-to-I interval, coupling reliability was largest for the R-to-I interval, and only tRSE for the R-to-I interval was correlated with height, weight, and body surface area. The high test-retest reliability for CVC in the R-to-I interval provides support for the hypothesis that CVC strength is a subject trait. Across subjects, a peak ∼138 ms prior to I-onset was characteristic of CVC in the R-to-I interval, although individual subjects also had earlier peaks (longer R-to-I intervals). CVC for the R-to-I interval was unrelated to two separate measures of respiratory sinus arrhythmia (RSA), suggesting that these two forms of coupling (CVC and RSA) are independent.

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ShareDisk: A novel visual tool to assess perceptions about who should be responsible for supporting persons with mental health problems

International Journal of Social Psychiatry ◽

10.1177/0020764020913580 ◽

2020 ◽

Vol 66 (4) ◽

pp. 411-418

Author(s):

Srividya N Iyer ◽

Megan A Pope ◽

Gerald Jordan ◽

Greeshma Mohan ◽

Heleen Loohuis ◽

...

Keyword(s):

Mental Health ◽

Psychometric Properties ◽

Clinical Utility ◽

Mental Health Problems ◽

Health Problems ◽

Language And Literacy ◽

Retest Reliability ◽

Visual Tool ◽

Test Retest Reliability ◽

High Test

Objectives: Views on who bears how much responsibility for supporting individuals with mental health problems may vary across stakeholders (patients, families, clinicians) and cultures. Perceptions about responsibility may influence the extent to which stakeholders get involved in treatment. Our objective was to report on the development, psychometric properties and usability of a first-ever tool of this construct. Methods: We created a visual weighting disk called ‘ShareDisk’, measuring perceived extent of responsibility for supporting persons with mental health problems. It was administered (twice, 2 weeks apart) to patients, family members and clinicians in Chennai, India ( N = 30, 30 and 15, respectively) and Montreal, Canada ( N = 30, 32 and 15, respectively). Feedback regarding its usability was also collected. Results: The English, French and Tamil versions of the ShareDisk demonstrated high test–retest reliability ( rs = .69–.98) and were deemed easy to understand and use. Conclusion: The ShareDisk is a promising measure of a hitherto unmeasured construct that is easily deployable in settings varying in language and literacy levels. Its clinical utility lies in clarifying stakeholder roles. It can help researchers investigate how stakeholders’ roles are perceived and how these perceptions may be shaped by and shape the organization and experience of healthcare across settings.

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A Reliability Analysis of the Revised Competitiveness Index

Psychological Reports ◽

10.2466/pr0.106.3.870-874 ◽

2010 ◽

Vol 106 (3) ◽

pp. 870-874 ◽

Cited By ~ 35

Author(s):

Paul B. Harris ◽

John M. Houston

Keyword(s):

Reliability Analysis ◽

Factor Structure ◽

Dynamic State ◽

Retest Reliability ◽

Stable Factor ◽

Competitiveness Index ◽

Test Retest Reliability ◽

High Test

This study examined the reliability of the Revised Competitiveness Index by investigating the test-retest reliability, interitem reliability, and factor structure of the measure based on a sample of 280 undergraduates (200 women, 80 men) ranging in age from 18 to 28 years ( M = 20.1, SD = 2.1). The findings indicate that the Revised Competitiveness Index has high test-retest reliability, high interitem reliability, and a stable factor structure. The results support the assertion that the Revised Competitiveness Index assesses competitiveness as a stable trait rather than a dynamic state.

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High test-retest reliability of a neural index of rapid automatic discrimination of unfamiliar individual faces

Journal of Vision ◽

10.1167/19.10.136c ◽

2019 ◽

Vol 19 (10) ◽

pp. 136c

Author(s):

Milena Dzhelyova ◽

Giulia Dormal ◽

Corentin Jacques ◽

Caroline Michel ◽

Christine Schiltz ◽

...

Keyword(s):

Retest Reliability ◽

Test Retest Reliability ◽

High Test

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Imagery, Concreteness, Emotionality, Meaningfulness, and Pleasantness of Words

Perceptual and Motor Skills ◽

10.2466/pms.1995.80.3.867 ◽

1995 ◽

Vol 80 (3) ◽

pp. 867-880 ◽

Cited By ~ 9

Author(s):

Alfredo Campos

Keyword(s):

Gender Differences ◽

Retest Reliability ◽

Test Retest Reliability ◽

High Test

This account of the literature on the relationships among imagery, concreteness, emotionality, meaningfulness, and pleasantness shows high test-retest reliability for all five attributes which are stable for subjects of both genders and of several nationalities. Gender differences and the influence of attributes on other attributes are also examined.

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Assessing linguistic competence: when are children hard to understand?

Journal of Child Language ◽

10.1017/s0305000900002701 ◽

1980 ◽

Vol 7 (2) ◽

pp. 401-412 ◽

Cited By ~ 2

Author(s):

Veronica Fabian-Kraus ◽

Paul Ammon

Keyword(s):

General Problem ◽

Empirical Relation ◽

Linguistic Competence ◽

Target Structure ◽

Retest Reliability ◽

Test Retest Reliability ◽

High Test

ABSTRACTIt is argued that previous assessments of children's knowledge of the hard to see type of construction were confounded by a variety of extra-linguistic factors. Therefore, the relatively delayed age of comprehension previously reported (6½–8 years) may have been due to younger children's deficiencies in extralinguistic skills. In the present study, with these extralinguistic complications eliminated, the passing age was found to be 5 years, and even 4-year-olds evidenced considerable knowledge of the target structure. Other findings were: variation in sentence difficulty as a function of the syntactic and/or aspectual character of the verb; high test–retest reliability at all levels of performance; and a necessary-but-not-sufficient empirical relation between comprehension of the target construction and the passive. Results are discussed in terms of their implications for the acquisition of this particular structure and for the general problem of detecting linguistic competence from performance.

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