A general model framework for multisymbol number comparison.

Huber, Stefan; Nuerk, Hans‐Christoph; Willmes, Klaus; Moeller, Korbinian

doi:10.1037/rev0000040

Cited by 48 publications

(104 citation statements)

References 124 publications

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“…The existence of advantages for componential processing for fractions would be consistent with evidence that other types of multi‐digit numbers (e.g., multi‐digit integers) are typically processed in a componential fashion (e.g., Huber, Moeller, Nuerk, & Willmes, ; Huber, Nuerk, Willmes, & Moeller, ). In this study, we explored the potential benefits of componential fraction processing, focusing on a task that requires arithmetic computations (rather than comparison of numbers to perceptual displays, as in DeWolf et al., 2015a).…”

Section: Introductionsupporting

confidence: 70%

Relational Priming Based on a Multiplicative Schema for Whole Numbers and Fractions

et al. 2017

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Why might it be (at least sometimes) beneficial for adults to process fractions componentially? Recent research has shown that college-educated adults can capitalize on the bipartite structure of the fraction notation, performing more successfully with fractions than with decimals in relational tasks, notably analogical reasoning. This study examined patterns of relational priming for problems with fractions in a task that required arithmetic computations. College students were asked to judge whether or not multiplication equations involving fractions were correct. Some equations served as structurally inverse primes for the equation that immediately followed it (e.g., 4 × 3/4 = 3 followed by 3 × 8/6 = 4). Students with relatively high math ability showed relational priming (speeded solution times to the second of two successive relationally related fraction equations) both with and without high perceptual similarity (Experiment 2). Students with relatively low math ability also showed priming, but only when the structurally inverse equation pairs were supported by high perceptual similarity between numbers (e.g., 4 × 3/4 = 3 followed by 3 × 4/3 = 4). Several additional experiments established boundary conditions on relational priming with fractions. These findings are interpreted in terms of componential processing of fractions in a relational multiplication context that takes advantage of their inherent connections to a multiplicative schema for whole numbers.

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Section: Introductionsupporting

confidence: 70%

Relational Priming Based on a Multiplicative Schema for Whole Numbers and Fractions

et al. 2017

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“…One proposed explanation for that effect is that under certain conditions, the holistic analog magnitude that is encoded when we convert from number symbols becomes anchored on the leftmost digit (Thomas & Morwitz, , ). Alternatively, models of number representation that assume decomposed rather than holistic processing can also explain the LDE (Huber, Nuerk, Willmes, & Moeller, ). Support for decomposed processing of multidigit numbers, rather than analog magnitude representations that encompass the holistic magnitudes of single‐digit and multi‐digit numbers, comes from tasks like two‐digit number comparisons using pairs of numbers that are either unit‐decade compatible (e.g., 42 and 57) or unit‐decade incompatible (e.g., 47 and 62), while overall absolute distance for each pair is held constant.…”

Section: Discussionmentioning

confidence: 99%

Digit identity influences numerical estimation in children and adults

Lai

Zax

Barth

2018

Developmental Science

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Learning the meanings of Arabic numerals involves mapping the number symbols to mental representations of their corresponding, approximate numerical quantities. It is often assumed that performance on numerical tasks, such as number line estimation (NLE), is primarily driven by translating from a presented numeral to a mental representation of its overall magnitude. Part of this assumption is that the overall numerical magnitude of the presented numeral, not the specific digits that comprise it, is what matters for task performance. Here we ask whether the magnitudes of the presented target numerals drive symbolic number line performance, or whether specific digits influence estimates. If the former is true, estimates of numerals with very similar magnitudes but different hundreds digits (such as 399 and 402) should be placed in similar locations. However, if the latter is true, these placements will differ significantly. In two studies (N = 262), children aged 7-11 and adults completed 0-1000 NLE tasks with target values drawn from a set of paired numerals that fell on either side of "Hundreds" boundaries (e.g., 698 and 701) and "Fifties" boundaries (e.g., 749 and 752). Study 1 used an atypical speeded NLE task, while Study 2 used a standard non-speeded NLE task. Under both speeded and non-speeded conditions, specific hundreds digits in the target numerals exerted a strong influence on estimates, with large effect sizes at all ages, showing that the magnitudes of target numerals are not the primary influence shaping children's or adults' placements. We discuss patterns of developmental change and individual difference revealed by planned and exploratory analyses.

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“…In fact, because we observed distractor effects, the current data suggest that the children did not only compute the result, but also processed the distractors. It is possible that estimation occurred for the decomposed processing of units and decades (for reviews, see Nuerk et al ., , ; Nuerk & Willmes, ; for a computational model, see Huber, Nuerk, Willmes, & Moeller, ). In this case, the processing of a distractor differing at the decade position should be slower than the processing of a distractor differing at the unit position.…”

Section: Discussionmentioning

confidence: 99%

Longitudinal development of subtraction performance in elementary school

Artemenko

Pixner²,

Moeller

et al. 2017

British J of Dev Psycho

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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.

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A general model framework for multisymbol number comparison.

Cited by 48 publications

References 124 publications

Relational Priming Based on a Multiplicative Schema for Whole Numbers and Fractions

Relational Priming Based on a Multiplicative Schema for Whole Numbers and Fractions

Digit identity influences numerical estimation in children and adults

Longitudinal development of subtraction performance in elementary school

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