Numeral order and the operationalization of the numerical system

Múñez, David; Orrantia, Josetxu; Matilla, Laura; Sánchez, Rosario

doi:10.1177/17470218211041953

Cited by 4 publications

(4 citation statements)

References 63 publications

(99 reference statements)

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“…On all other sequences, people may need to perform sequential comparisons to make order decisions, resulting in canonical distance effects (Lyons & Ansari, 2015;Lyons & Beilock, 2013). Together, the canonical and reverse distance effects observed in the order judgment task support the view that cardinal and ordinal processing of symbolic numerals are both involved, depending on the task demands and the extent to which adjacent sequences are present in the stimulus set (Dubinkina et al, 2021;Muñez et al, 2022;Vogel et al, 2021;Vos et al, 2017).…”

Section: Patterns Of Responses In Order Processing Tasksmentioning

confidence: 66%

“…If the sequence is shown for a brief time, they may also need to retain the sequence of digits in working memory. In summary, the literature suggests that order judgment performance is related to familiarity with previously learned sequences, knowledge of relative magnitude, and working memory (Devlin et al, 2022;Dubinkina et al, 2021;Finke et al, 2021;Muñez et al, 2022;Vogel et al, 2021;Vos et al, 2021).…”

Section: The Development Of Order Processingmentioning

confidence: 99%

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A direct comparison of two measures of ordinal knowledge among 8-year-olds

Xu,

LeFevre,

Di Lonardo Burr

et al. 2023

J. Numer. Cogn.

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Children’s knowledge of the ordinal relations among number symbols is related to their mathematical learning. Ordinal knowledge has been measured using judgment (i.e., decide whether a sequence of three digits is in order) and ordering tasks (i.e., order three digits from smallest to largest). However, the question remains whether performance on these two ordinal tasks tap into similar cognitive processes. Canadian children (N = 87; Age M = 8.7 years, Grade 3) completed symbolic number tasks (i.e., number comparison, ordering, and order judgment) and measures of arithmetic fluency (i.e., addition and subtraction) and working memory (i.e., digit span backward). For both ordinal tasks, there was a reverse distance effect for ordered sequences such that children responded faster to adjacent than to non-adjacent sequences (e.g., 2 3 4 vs. 4 7 9) and a canonical distance effect for unordered sequences such that children responded faster to non-adjacent than to adjacent sequences (e.g., 4 2 3 vs. 4 9 7). Working memory and number comparison each predicted unique variance in the ordinal measures (ordering, order judgment, and a latent ordinal factor based on the two measures). Furthermore, ordinal skills superseded the role of number comparison as the key predictor of arithmetic, controlling for children’s gender and working memory skills. In summary, although both ordering and order judgment tasks index ordinal knowledge, a latent factor that excludes task-specific error may be a better index than either task separately.

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Section: Patterns Of Responses In Order Processing Tasksmentioning

confidence: 66%

Section: The Development Of Order Processingmentioning

confidence: 99%

A direct comparison of two measures of ordinal knowledge among 8-year-olds

Xu,

LeFevre,

Di Lonardo Burr

et al. 2023

J. Numer. Cogn.

View full text Add to dashboard Cite

show abstract

“…In contrast, Orrantia et al (2019) highlight the extensive overlap between cardinal (number comparisons) and ordinal processing (order judgements) in adults’ arithmetic, suggesting that both processes draw on underlying symbolic magnitude associations. Other researchers have suggested that both familiarity and magnitude associations may influence performance on the order judgement task, depending on the task demands (e.g., stimulus characteristics; Vos et al, 2021) and individuals’ strategy use (Dubinkina et al, 2021; Muñez et al, 2021; Vogel et al, 2021; Vos et al, 2021). Extending the latter views, strong correlations between order judgements and arithmetic may reflect the extent to which individuals have developed an integrated knowledge system (Xu et al, 2019).…”

Section: Fundamental Numeracymentioning

confidence: 99%

The hierarchical relations among mathematical competencies: From fundamental numeracy to complex mathematical skills.

Burr

LeFevre

2023

Canadian Journal of Experimental Psychology / Revue canadienne

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Mathematical competencies can be conceptualized as layers of knowledge, with numeracy skills as the foundational core and more complex mathematical skills as the additional layers over the core. In this study, we tested an expanded hierarchical symbol integration (HSI) model by examining the hierarchical relations among mathematical skills. Undergraduate students (N = 236) completed order judgement, simple arithmetic, fraction arithmetic, algebra, and verbal working memory tasks. In a series of hierarchical multiple regressions, we found support for the hierarchical model: Additive skills (i.e., addition and subtraction) predicted unique variance in multiplicative skills (i.e., multiplication and division); multiplicative skills predicted unique variance in fraction arithmetic; and fraction skills predicted unique variance in algebra. These results support the framework of the HSI model in which mathematical competencies are related hierarchically, capturing the increasing complexity of symbolic mathematical skills.

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“…Currently, the primary method of investigating the mechanisms underlying order processing involves using order judgement tasks in which participants have to Concepts of order: Why is ordinality processed slower and less accurately for non-consecutive sequences? classify sequences of digits (e.g., 1-2-3) as either correctly or incorrectly ordered (Dubinkina et al, 2023;Finke et al, 2021;Muñez et al, 2022;Wong et al, 2022). A noteworthy feature of these tasks is that they often produce a reverse distance effect whereby consecutive sequences (e.g., 1-2-3) are processed faster than non-consecutive sequences (e.g., 1-3-5; see Goffin & Ansari, 2016;Vogel et al, 2017Vogel et al, , 2021.…”

Section: Introductionmentioning

confidence: 99%

Concepts of order: Why is ordinality processed slower and less accurately for non-consecutive sequences?

Devlin,

Moeller,

Xenidou-Dervou

et al. 2024

Quarterly Journal of Experimental Psychology

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Both adults and children are slower at judging the ordinality of non-consecutive sequences (e.g., 1-3-5) than consecutive sequences (e.g., 1-2-3). It has been suggested that the processing of non-consecutive sequences is slower because it conflicts with the intuition that only count-list sequences are correctly ordered. An alternative explanation, however, may be that people simply find it difficult to switch between consecutive and non-consecutive concepts of order during order judgement tasks. Therefore, in adult participants, we tested whether presenting consecutive and non-consecutive sequences separately would eliminate this switching demand and thus improve performance. In contrast with this prediction, however, we observed similar patterns of response times independent of whether sequences were presented separately or together (Experiment 1). Furthermore, this pattern of results remained even when we doubled the number of trials and made participants explicitly aware when consecutive and non-consecutive sequences were presented separately (Experiment 2). Overall, these results suggest slower response times for non-consecutive sequences do not result from a cognitive demand of switching between consecutive and non-consecutive concepts of order, at least not in adults.

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Numeral order and the operationalization of the numerical system

Cited by 4 publications

References 63 publications

A direct comparison of two measures of ordinal knowledge among 8-year-olds

A direct comparison of two measures of ordinal knowledge among 8-year-olds

The hierarchical relations among mathematical competencies: From fundamental numeracy to complex mathematical skills.

Concepts of order: Why is ordinality processed slower and less accurately for non-consecutive sequences?

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