Numerical Sequence Recognition: Is Familiarity or Ordinality the Primary Factor in Performance?

Bourassa, Angelle

doi:10.22215/etd/2014-10567

Cited by 10 publications

(38 citation statements)

References 65 publications

(75 reference statements)

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“…That said, it may be that reversed distance effects are not so much indicative of a fundamental property of number symbols but are more just a by‐product of other numerical processes. For instance, one account of reversed distance effects is that they are essentially a consequence of our familiarity with the count sequence (Bourassa, ; Franklin et al, ; LeFevre & Bisanz, ; Lyons & Beilock, ; Turconi et al, ). However, the current data do not support this view.…”

Section: Discussionmentioning

confidence: 99%

“…Perhaps the current leading explanation for the reversed distance effect is that it is a by‐product of familiarity with a recited sequence (e.g., the counting or alphabetical sequence: Bourassa, ; Franklin et al, ; LeFevre & Bisanz, ; Lovelace & Snodgrass, ; Lyons & Beilock, ; Turconi et al, ). That is, one directly retrieves and matches an ordered sequence with a subset of the count list: for instance, 1‐2‐3 and 5‐6‐7 are more familiar and thus more rapidly identified as “in‐order” than 1‐3‐5 or 4‐6‐8.…”

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confidence: 99%

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Numerical Order Processing in Children: From Reversing the Distance‐Effect to Predicting Arithmetic

Lyons

Ansari

2015

Mind Brain and Education

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Recent work has demonstrated that how we process the relative order—ordinality—of numbers may be key to understanding how we represent numbers symbolically, and has proven to be a robust predictor of more sophisticated math skills in both children and adults. However, it remains unclear whether numerical ordinality is primarily a by‐product of other numerical processes, such as familiarity with overlearned count sequence, or is in fact a fundamental property of symbolic number processing. In a sample of nearly 1,500 children, we show that the reversed distance effect—a hallmark of symbolic ordinal processing—obtains in children as young as first grade, and is larger for less familiar sets of numbers. Furthermore, we show that the children's efficiency in evaluating the simplest ordered sequences (e.g., 2‐3‐4, 6‐7‐8) captures more unique variance in mental arithmetic than any other type of numerical sequence, and that this result cannot be accounted for by counting ability. Indeed, performance on just five such trials captured more unique mental arithmetic variance than any of several other numerical tasks assessed here. In sum, our results are consistent with the notion that ordinality is a fundamental property of how children process numerical symbols, that this property helps underpin more complex math processing, and that it shapes numerical processing even at the earliest stages of elementary education.

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Section: Discussionmentioning

confidence: 99%

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confidence: 99%

Numerical Order Processing in Children: From Reversing the Distance‐Effect to Predicting Arithmetic

Lyons

Ansari

2015

Mind Brain and Education

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“…Lyons and Beilock argued that the order judgment task could be very useful for understanding how numerical knowledge was represented, more generally, citing the correlation with working memory ability as potentially linking ordinal processing skill with mathematical proficiency. Bourassa (2014) conducted two experiments exploring the role of familiarity rather than ordinality in sequence judgments. Four types of three single-digit stimuli were used (counting, balanced, arithmetic, neutral) with two conditions (ascending, descending).…”

Section: Ordered Sequencesmentioning

confidence: 99%

“…Accordingly, Bourassa concluded that rather than ordinality, the familiarity of a number sequence was the chief factor in recognizing the sequence. Lyons and Beilock (2011) used the same order judgment task as Lyons and Beilock (2009) and Bourassa (2014) to examine the relationship between non-symbolic number discrimination ability and arithmetic skill. They concluded that number ordering ability fully mediated the relationship between approximate number system ability and mental arithmetic ability.…”

Section: Ordered Sequencesmentioning

confidence: 99%

“…Turconi et al's work suggested that using only two digits in order judgments might not result in clear distinctions between order and magnitude processes, however, whereas three-digit sequences seemed more likely to elicit consistent order judgments. However, Bourassa (2014) showed that participants do use serial search processes to establish order. Thus, in this thesis I used order judgments on three-digit sequences, but I also manipulated the selection of sequences in an attempt to control the processes that participants used across the stimuli.…”

Section: Ordered Sequencesmentioning

confidence: 99%

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Hunting for the SNARC: Spatial-Numerical Associations in an Order Judgment Task are Surprisingly Elusive

Verger¹

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Spatial-numerical associations (SNA) have been studied in various numerical and nonnumerical tasks. Classically, participants respond faster with their right hand to larger numbers and faster with their left hand to smaller numbers even when number identity is irrelevant. SNAs are often explained as activation of a left-to-right mental number line.Thus, SNAs may reflect magnitude processes, relative order, or both. In the present research, I explored the SNA in an order judgment task. In three experiments, participants judged whether three digit sequences were ordered (e.g., 1 2 3) or unordered (e.g., 2 1 3).People with more efficient calculation skill are faster and more accurate on order judgments than those with less efficient skills. Thus this task is assumed to capture important aspects of the mental representation of numerical sequences. Accordingly, I hypothesized that participants would show a SNA similar to that in other number tasks (e.g., parity, number comparison), that is, faster right hand responses to number sequences that are assumed to activate the right side (e.g., 6 7 8) and faster left hand responses to number sequences that are assumed to activate the left side (e.g., 2 3 4) of the mental number line. In three experiments, ordered but not unordered sequences showed consistent evidence for a typical SNA. In Experiment 1, Asian-educated individuals showed a typical, stable SNA effect on both ascending and descending sequences whereas Arabic-speaking participants showed no significant SNA effects.English-speaking participants showed a typical SNA on descending sequences and a reversed SNA on ascending sequences. In Experiments 2 and 3, only individuals with better arithmetic fluency showed a typical SNA. In Experiments 2 and 3, analyses using a multi-factor ANOVA design did not show evidence for SNARC effects. Instead, SNARC iii iii effects were found only using slope analyses on differences in responses with the right versus the left hand. The results are discussed in relation to the processes involved in sequence judgments and how those might differ from the processes involved in other numerical tasks. In summary, the SNA was surprisingly elusive, even though participants were quite sensitive to number magnitude and the task itself required order judgments, which presumably should have activated the mental number line. iv iv Acknowledgements Some years ago, I set off on a journey. Along the way there were those who provided guidance, when I was willing to look and listen; those whose laughter coloured a grey day; those whose own adventures lent wind to my sails. These, then, are my thanks to all who made the travel through ideas so worthwhile.

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Rules of order: Evidence for a novel influence on ordinal processing of numbers.

Gattas¹,

Bugden²,

Lyons³

2021

Journal of Experimental Psychology: General

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Research on how people process numerical order carries implications for our theoretical understanding of what a number means and our practical understanding of the foundation upon which more sophisticated mathematics is built. Current thinking posits that ordinal processing of numbers is linked to repeated practice with the integer count list, but the mechanisms underlying this link remain unclear. For instance, in standard ordinal verification paradigms, participants more rapidly and accurately verify that count-list sequences (e.g., 3-4-5) are "in-order" than non-count-list sequences (e.g., 2-4-6), although it remains unclear whether this is due to strong count-list processing or poor non-count-list processing. If the count list primarily facilitates ordinal processing of count-list sequences, then forcing participants to classify sequences like 3-4-5 as "not-in-order" should adversely affect ordinal verification performance. We found that it does, but only moderately in single-digit sequences (d = À.26), and not at all in the case of double-digit sequences (d = À.02). Alternatively, the count list may influence ordinal processing in an exclusionary manner, creating a tendency to view anything that does not match the count-list as not-in-order. If so, then allowing participants to classify ordered (but non-count-list) sequences like 2-4-6 as not-in-order should improve ordinal verification performance. It did, with strong effects for both single-digit (d = .74) and double-digit sequences (d = 1.04). Furthermore, we demonstrated that the reverse distance effect found in standard ordinal verification paradigms is driven primarily by poor non-count-list processing. Taken together, our results advance our understanding of the mechanisms by which the count list shapes ordinal processing, even in highly numerate adults.

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Numerical Sequence Recognition: Is Familiarity or Ordinality the Primary Factor in Performance?

Cited by 10 publications

References 65 publications

Numerical Order Processing in Children: From Reversing the Distance‐Effect to Predicting Arithmetic

Numerical Order Processing in Children: From Reversing the Distance‐Effect to Predicting Arithmetic

Hunting for the SNARC: Spatial-Numerical Associations in an Order Judgment Task are Surprisingly Elusive

Rules of order: Evidence for a novel influence on ordinal processing of numbers.

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