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1.
Mental rotation is positively related to arithmetic ability; however, the mechanism underlying this relationship remains unclear. The possible roles of working memory, place-value concept, and number line estimation in the correlation between mental rotation and whole-number computation were investigated. One hundred and fifty-five first-grade students were tested to determine their mental rotation ability, arithmetic ability, and non-verbal intelligence. One year later, their working memory, place-value concept, number line estimation, and overall arithmetic ability were assessed. After controlling for age, gender, and prior arithmetic ability, we found that mental rotation uniquely predicted arithmetic ability after one year. Further mediation analyses demonstrated that number line estimation significantly mediated the relationship between mental rotation and arithmetic ability. In contrast, neither working memory nor place-value concept significantly mediated the relationship between mental rotation and arithmetic ability. This study highlights that mental number line estimation is the most important element explaining the influence of a dynamic spatial skill, that is, mental rotation, on arithmetic ability among young Chinese children. 相似文献
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探讨儿童在数字线估计任务中心理长度的发展及其对数量表征模式的影响.选取7~9岁儿童共109名进行数字线估计任务测试,设置了10cm和20cm两种长度条件,要求儿童完成根据位置判断数字任务(position to number,PN任务).结果表明儿童在数字线PN任务中存在心理长度,且7岁儿童心理长度的范围超过10,随着儿童年龄的增长,他们的心理长度范围不断缩小;心理长度范围影响儿童的表征模式,随着心理长度范围的缩小,儿童的数字线表征出现从指数模式到线性模式的变化趋势;与表征模式的发展趋势一致,儿童估计的精确性随年龄增长逐渐提高. 相似文献
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Andrea L. Patalano Katherine Williams Gillian Weeks Kelsey Kayton Hilary Barth 《决策行为杂志》2022,35(1):e2247
A left digit effect has been broadly observed across judgment and decision-making contexts ranging from product evaluation to medical treatment decisions to number line estimation. For example, $3.00 is judged to be a much greater cost than $2.99, and “801” is estimated strikingly too far to the right of “798” on a number line. Although the consequences of the effects for judgment and decision behavior have been documented, the sources of the effects are not well established. The goal of the current work is to extend investigations of the left digit effect to a new complex judgment activity and to assess whether the magnitude of the effect at the individual level can be predicted from performance on a simpler number skills task on which the left digit effect has also recently been observed. In three experiments (N = 434), adults completed a judgment task in which they rated the strength of hypothetical applicants for college admission and a self-paced number line estimation task. In all experiments, a small or medium left digit effect was found in the college admissions task, and a large effect was found in number line estimation. Individual-level variation was observed, but there was no relationship between the magnitudes of the effects in the two tasks. These findings provide evidence of a left digit effect in a novel multiattribute judgment task but offer no evidence that such performance can be predicted from a simple number skills task such as number line estimation. 相似文献
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《British journal of psychology (London, England : 1953)》2017,108(4):668-686
In this study, we used verbal protocols to identify whether adults spontaneously apply quartile‐based strategies or whether they need additional external support to use these strategies when solving a 0–1,000 number line estimation (NLE) task. Participants were assigned to one of three conditions based on the number of external benchmarks provided on the number line. In the bounded condition only the origin and endpoint were indicated, the mid‐point condition included an additional external benchmark at 50%, and in the quartile condition three additional external benchmarks at 25%, 50%, and 75% were specified. Firstly, participants in the bounded condition reported to spontaneously apply quartile‐based strategies to calibrate their estimates. Moreover, participants frequently relied on the external benchmarks for creating internal benchmarks at the mid‐point, quartiles, and even octiles of the number line. Secondly, overall estimation accuracy improved as the number of external benchmarks increased, and target numbers close to external benchmarks were estimated more accurately and with less variability. Thirdly, the use of a larger variety in benchmark‐based strategies was positively related to NLE accuracy. In summary, this study provides evidence that the NLE task induces more sophisticated strategy use in participants than initially anticipated. 相似文献
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Angela Heine Verena Thaler Sascha Tamm Stefan Hawelka Michael Schneider Joke Torbeyns Bert De Smedt Lieven Verschaffel Elsbeth Stern Arthur M. Jacobs 《Infant and child development》2010,19(2):175-186
To date, a number of studies have demonstrated the existence of mismatches between children's implicit and explicit knowledge at certain points in development that become manifest by their gestures and gaze orientation in different problem solving contexts. Stimulated by this research, we used eye movement measurement to investigate the development of basic knowledge about numerical magnitude in primary school children. Sixty‐six children from grades one to three (i.e. 6–9 years) were presented with two parallel versions of a number line estimation task of which one was restricted to behavioural measures, whereas the other included the recording of eye movement data. The results of the eye movement experiment indicate a quantitative increase as well as a qualitative change in children's implicit knowledge about numerical magnitudes in this age group that precedes the overt, that is, behavioural, demonstration of explicit numerical knowledge. The finding that children's eye movements reveal substantially more about the presence of implicit precursors of later explicit knowledge in the numerical domain than classical approaches suggests further exploration of eye movement measurement as a potential early assessment tool of individual achievement levels in numerical processing. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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《British journal of psychology (London, England : 1953)》2017,108(2):334-350
Sex differences in mathematical performance have frequently been examined over the last decades indicating an advantage for males especially when numerical problems cannot be solved by (classroom‐)learnt strategies and/or estimation. Even in basic numerical tasks such as number line estimation, males were found to outperform females – with sex differences argued to emerge from different solution strategies applied by males and females. We evaluated the latter using two versions of the number line estimation task: a bounded and an unbounded task version. Assuming that women tend more strongly to apply known procedures, we expected them to be at a particular disadvantage in the unbounded number line estimation task, which is less prone to be solved by specific strategies such as proportion judgement but requires numerical estimation. Results confirmed more pronounced sex differences for unbounded number line estimation with males performing significantly more accurately in this task version. This further adds to recent evidence suggesting that estimation performance in the bounded task version may reflect solution strategies rather than numerical estimation. Additionally, it indicates that sex differences regarding the spatial representation of number magnitude may not be universal, but associated with spatial–numerical estimations in particular. 相似文献
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People tend to underestimate subtraction and overestimate addition outcomes and to associate subtraction with the left side and addition with the right side. These two phenomena are collectively labeled 'operational momentum' (OM) and thought to have their origins in the same mechanism of 'moving attention along the mental number line'. OM in arithmetic has never been tested in children at the preschool age, which is critical for numerical development. In this study, 3–5 years old were tested with non‐symbolic addition and subtraction tasks. Their level of understanding of counting principles (CP) was assessed using the give‐a‐number task. When the second operand's cardinality was 5 or 6 (Experiment 1), the child's reaction time was shorter in addition/subtraction tasks after cuing attention appropriately to the right/left. Adding/subtracting one element (Experiment 2) revealed a more complex developmental pattern. Before acquiring CP, the children showed generalized overestimation bias. Underestimation in addition and overestimation in subtraction emerged only after mastering CP. No clear spatial‐directional OM pattern was found, however, the response time to rightward/leftward cues in addition/subtraction again depended on stage of mastering CP. Although the results support the hypothesis about engagement of spatial attention in early numerical processing, they point to at least partial independence of the spatial‐directional and magnitude OM. This undermines the canonical version of the number line‐based hypothesis. Mapping numerical magnitudes to space may be a complex process that undergoes reorganization during the period of acquisition of symbolic representations of numbers. Some hypotheses concerning the role of spatial‐numerical associations in numerical development are proposed. 相似文献
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ABSTRACTMental arithmetic is characterised by a tendency to overestimate addition and to underestimate subtraction results: the operational momentum (OM) effect. Here, motivated by contentious explanations of this effect, we developed and tested an arithmetic heuristics and biases model that predicts reverse OM due to cognitive anchoring effects. Participants produced bi-directional lines with lengths corresponding to the results of arithmetic problems. In two experiments, we found regular OM with zero problems (e.g., 3+0, 3?0) but reverse OM with non-zero problems (e.g., 2+1, 4?1). In a third experiment, we tested the prediction of our model. Our results suggest the presence of at least three competing biases in mental arithmetic: a more-or-less heuristic, a sign-space association and an anchoring bias. We conclude that mental arithmetic exhibits shortcuts for decision-making similar to traditional domains of reasoning and problem-solving. 相似文献
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María Isabel Núez‐Pea ngels Colom David Aguilar‐Lleyda 《British journal of psychology (London, England : 1953)》2019,110(1):40-59
In this study, we aimed to investigate the difficulties highly math‐anxious individuals (HMA) may face when having to estimate a number's position in a number line task. Twenty‐four HMA and 24 low math‐anxiety (LMA) individuals were presented with four lines with endpoints 0–100, 0–1,000, 0–100,000, and 267–367 on a computer monitor on which they had to mark the correct position of target numbers using the mouse. Although no differences were found between groups in the frequency of their best‐fit model, which was linear for all lines, the analysis of slopes and intercepts for the linear model showed that the two groups differed in performance on the less familiar lines (267–367 and 0–100,000). Lower values for the slope and higher values for the intercept were found in the HMA group, suggesting that they tended to overestimate small numbers and underestimate large numbers on these non‐familiar lines. Percentage absolute error analyses confirmed that HMA individuals were less accurate than their LMA counterparts on these lines, although no group differences were found in response time. These results indicate that math anxiety is related to worse performance only in the less familiar and more difficult number line tasks. Therefore, our data challenge the idea that HMA individuals might have less precise numerical representations and support the anxiety–complexity effect posited by Ashcraft and colleagues. 相似文献
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Transcoding Arabic numbers from and into verbal number words is one of the most basic number processing tasks commonly used to index the verbal representation of numbers. The inversion property, which is an important feature of some number word systems (e.g., German einundzwanzig [one and twenty]), might represent a major difficulty in transcoding and a challenge to current transcoding models. The mastery of inversion, and of transcoding in general, might be related to nonnumerical factors such as working memory resources given that different elements and their sequence need to be memorized and manipulated. In this study, transcoding skills and different working memory components in Austrian (German-speaking) 7-year-olds were assessed. We observed that inversion poses a major problem in transcoding for German-speaking children. In addition, different components of working memory skills were differentially correlated with particular transcoding error types. We discuss how current transcoding models could account for these results and how they might need to be adapted to accommodate inversion properties and their relation to different working memory components. 相似文献
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研究主要探讨了整数数量表征和分数数量表征的关系以及年级对两者关系的影响。实验对155名三至六年级儿童进行0~1分数数字线估计任务和0~1000整数数字线估计任务的测量。结果发现:(1)对于整数数字线估计,所有年级儿童均主要采取了线性表征;(2)对于分数数字线估计,五六年级儿童主要采取了线性表征,三四年级儿童没有明显的线性表征或对数表征的倾向;(3)整数数量表征和分数数量表征呈显著正相关,不过年级对两者的关系产生了影响,表现在只有五六年级儿童的整数数字线估计对分数数字线估计有显著预测作用。 相似文献
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McCrink (McCrink, Dehaene, & Dehaene-Lambertz (2007). Moving along the number line: Operational momentum in nonsymbolic arithmetic. Perception and Psychophysics, 69(8), 1324-1333) documented an “Operational Momentum” (OM) effect - overestimation of addition and underestimation of subtraction outcomes in non-symbolic (dot pattern) arithmetic. We investigated whether OM also occurs with Arabic number symbols. Participants pointed to number locations (1-9) on a visually given number line after computing them from addition or subtraction problems. Pointing was biased leftward after subtracting and rightward after adding, especially when the second operand was zero. The findings generalize OM to the spatial domain and to symbolic number processing. Alternative interpretations of our results are discussed. 相似文献
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ABSTRACTThree-to-five-year-old French children were asked to add or remove objects to or from linear displays. The hypothesis of a universal tendency to represent increasing number magnitudes from left to right led to predict a majority of manipulations at the right end of the rows, whatever children's hand laterality. Conversely, if numbers are not inherently associated with space, children were expected to favour laterality-consistent manipulations. The results showed a strong tendency to operate on the right end of the rows in right-handers, but no preference in left-handers. These findings suggest that the task elicited a left-to-right oriented representation of magnitudes that counteracted laterality-related responses in left-handed children. The young age of children and the lack of a developmental trend towards right preference weaken the hypothesis of a cultural origin of this oriented representation. The possibility that our results are due to weaker brain lateralisation in left-handers compared to right-handers is addressed in Discussion section. 相似文献
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In numerical cognition research, the operational momentum (OM) phenomenon (tendency to overestimate the results of addition and/or binding addition to the right side and underestimating subtraction and/or binding it to the left side) can help illuminate the most basic representations and processes of mental arithmetic and their development. This study is the first to demonstrate OM in symbolic arithmetic in preschoolers. It was modeled on Haman and Lipowska's (2021) non-symbolic arithmetic task, using Arabic numerals instead of visual sets. Seventy-seven children (4–7 years old) who know Arabic numerals and counting principles (CP), but without prior school math education, solved addition and subtraction problems presented as videos with one as the second operand. In principle, such problems may be difficult when involving a non-symbolic approximate number processing system, whereas in symbolic format they can be solved based solely on the successor/predecessor functions and knowledge of numerical orders, without reference to representation of numerical magnitudes. Nevertheless, participants made systematic errors, in particular, overestimating results of addition in line with the typical OM tendency. Moreover, subtraction and addition induced longer response times when primed with left- and right-directed movement, respectively, which corresponds to the reversed spatial form of OM. These results largely replicate those of non-symbolic task and show that children at early stages of mastering symbolic arithmetic may rely on numerical magnitude processing and spatial-numerical associations rather than newly-mastered CP and the concept of an exact number. 相似文献
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