In the literature on numerical cognition, the presence of the capacity to distinguish between numerosities by attending to the number of items, rather than continuous properties of stimuli that correlate with it, is commonly taken as sufficient indication of numerical abilities in cognitive agents. However, this literature does not take into account that there are non-numerical methods of assessing numerosity, which opens up the possibility that cognitive agents lacking numerical abilities may still be able to represent numerosity. In this paper, I distinguish between numerical and non-numerical methods of assessing numerosity and show that the most common models of the internal mechanisms of the so-called number sense rely on non-numerical methods, despite the claims of their proponents to the contrary. I conclude that, even if it is established that agents attend to numerosity, rather than continuous properties of stimuli correlated with it, an answer to the question of the existence of the number sense is still pending the investigation of a further issue, namely, whether the mechanisms the brain uses to assess numerosity qualify as numerical or non-numerical.
{"title":"Non-numerical methods of assessing numerosity and the existence of the number sense","authors":"César Frederico dos Santos","doi":"10.5964/jnc.10215","DOIUrl":"https://doi.org/10.5964/jnc.10215","url":null,"abstract":"In the literature on numerical cognition, the presence of the capacity to distinguish between numerosities by attending to the number of items, rather than continuous properties of stimuli that correlate with it, is commonly taken as sufficient indication of numerical abilities in cognitive agents. However, this literature does not take into account that there are non-numerical methods of assessing numerosity, which opens up the possibility that cognitive agents lacking numerical abilities may still be able to represent numerosity. In this paper, I distinguish between numerical and non-numerical methods of assessing numerosity and show that the most common models of the internal mechanisms of the so-called number sense rely on non-numerical methods, despite the claims of their proponents to the contrary. I conclude that, even if it is established that agents attend to numerosity, rather than continuous properties of stimuli correlated with it, an answer to the question of the existence of the number sense is still pending the investigation of a further issue, namely, whether the mechanisms the brain uses to assess numerosity qualify as numerical or non-numerical.","PeriodicalId":36632,"journal":{"name":"Journal of Numerical Cognition","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41746532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ellen Sammallahti, Jonatan Finell, B. Jonsson, J. Korhonen
The experience of math anxiety can have detrimental effects on students’ math performance, and researchers have in recent years tried to design interventions aiming at reducing math anxiety. This meta-analysis aimed to examine the effectiveness of math anxiety interventions in reducing math anxiety and improving math performance. The meta-analysis comprised 50 studies and included 75 effect sizes. On average, the effect sizes were moderate (g = -0.467) for reducing math anxiety and improving math performance (g = 0.502). Interventions that focused on Cognitive support or regulating Emotions were effective both in reducing math anxiety and improving math performance. In addition, longer interventions and interventions targeting students older than 12 had the biggest decrease in math anxiety. Study quality was not related to intervention outcomes.
{"title":"A meta-analysis of math anxiety interventions","authors":"Ellen Sammallahti, Jonatan Finell, B. Jonsson, J. Korhonen","doi":"10.5964/jnc.8401","DOIUrl":"https://doi.org/10.5964/jnc.8401","url":null,"abstract":"The experience of math anxiety can have detrimental effects on students’ math performance, and researchers have in recent years tried to design interventions aiming at reducing math anxiety. This meta-analysis aimed to examine the effectiveness of math anxiety interventions in reducing math anxiety and improving math performance. The meta-analysis comprised 50 studies and included 75 effect sizes. On average, the effect sizes were moderate (g = -0.467) for reducing math anxiety and improving math performance (g = 0.502). Interventions that focused on Cognitive support or regulating Emotions were effective both in reducing math anxiety and improving math performance. In addition, longer interventions and interventions targeting students older than 12 had the biggest decrease in math anxiety. Study quality was not related to intervention outcomes.","PeriodicalId":36632,"journal":{"name":"Journal of Numerical Cognition","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48997755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mastery of mathematics depends on the people’s ability to manipulate and abstract values such as negative numbers. Knowledge of arithmetic principles does not necessarily generalize from positive number arithmetic to arithmetic involving negative numbers (Prather & Alibali, 2008, https://doi.org/10.1080/03640210701864147). In this study, we evaluate the relationship between participant’s knowledge of the Relation to Operands arithmetic principle in both positive and negative numbers and their spontaneous on numerical relations. Additionally, we tested if the feedback that directs attention to relations affects participants’ attention to relation and their arithmetic principle knowledge. This study contributes to our understanding of the specific skills and cognitive processes that are associated with understanding high-level mathematics.
{"title":"Does spontaneous attention to relations predict conceptual knowledge of negative numbers?","authors":"R. Prather","doi":"10.5964/jnc.10057","DOIUrl":"https://doi.org/10.5964/jnc.10057","url":null,"abstract":"Mastery of mathematics depends on the people’s ability to manipulate and abstract values such as negative numbers. Knowledge of arithmetic principles does not necessarily generalize from positive number arithmetic to arithmetic involving negative numbers (Prather & Alibali, 2008, https://doi.org/10.1080/03640210701864147). In this study, we evaluate the relationship between participant’s knowledge of the Relation to Operands arithmetic principle in both positive and negative numbers and their spontaneous on numerical relations. Additionally, we tested if the feedback that directs attention to relations affects participants’ attention to relation and their arithmetic principle knowledge. This study contributes to our understanding of the specific skills and cognitive processes that are associated with understanding high-level mathematics.","PeriodicalId":36632,"journal":{"name":"Journal of Numerical Cognition","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44441275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chang Xu, J. LeFevre, Sabrina M. Di Lonardo Burr, Erin A. Maloney, Judith Wylie, Victoria Simms, Sheri-Lynn Skwarchuk, H. Osana
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.
儿童对数字符号序数关系的认识关系到他们的数学学习。序数知识已经通过判断(即，决定三个数字的序列是否有序)和排序任务(即，将三个数字从最小到最大排序)来测量。然而，问题仍然是，这两种顺序任务的表现是否利用了类似的认知过程。加拿大儿童(N = 87;年龄M = 8.7岁，3年级)完成符号数任务(即数字比较、排序和顺序判断)和算术流畅性(即加减法)和工作记忆(即数字向后广度)的测量。对于这两个顺序任务，有序序列存在反向距离效应，使得儿童对相邻序列的反应快于对非相邻序列的反应(例如，2 3 4 vs. 4 7 9)，无序序列存在典型距离效应，使得儿童对非相邻序列的反应快于对相邻序列的反应(例如，4 2 3 vs. 4 9 7)。工作记忆和数字比较各自预测了序数测量(排序，顺序判断，以及一个潜在的序数因素(基于这两个指标)。此外，顺序技能取代了数字比较的作用，成为算术的关键预测因子，控制了儿童的性别和工作记忆技能。综上所述，尽管排序任务和顺序判断任务都索引有序知识，但排除任务特定错误的潜在因素可能比单独使用任何一项任务更好。
{"title":"A direct comparison of two measures of ordinal knowledge among 8-year-olds","authors":"Chang Xu, J. LeFevre, Sabrina M. Di Lonardo Burr, Erin A. Maloney, Judith Wylie, Victoria Simms, Sheri-Lynn Skwarchuk, H. Osana","doi":"10.5964/jnc.10201","DOIUrl":"https://doi.org/10.5964/jnc.10201","url":null,"abstract":"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.","PeriodicalId":36632,"journal":{"name":"Journal of Numerical Cognition","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41810927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Olivia R. Jazbutis, M. Wiseheart, G. Radvansky, Nicole M. McNeil
Arithmetic is commonly taught through timed practice and drill, yet little research exists to guide optimal practice structure. This study investigated the effects of distributed practice and time pressure on the acquisition and retention of arithmetic facts. Following a pretest, adult participants (n = 211) were randomly assigned to learn unfamiliar times tables (17 and 19) in one of ten conditions in a 5 (spacing: daily, every other day, weekly, every 10 days, every other week) x 2 (time pressure: timed or untimed) factorial design. After the learning phase, retention tests were given to measure both accuracy and response time immediately, after a ten-day delay, and at the end of semester. Time pressure during learning elevated participants’ perceived stress. It also led to faster response times during testing when learning was spaced daily and every other day, but slower response times for all other spacings. These patterns were reversed in the absence of time pressure during learning. While timed and untimed practice during learning led to similar forgetting of practiced facts over time, untimed practice allowed participants to gradually improve on unpracticed facts and conceptually related facts across test phases. Ultimately, distributed practice and time pressure may interact in complex ways to affect the learning and retention of arithmetic facts, and the effects shown in previous studies using verbal material (e.g., narrative texts, word lists) may not generalize to arithmetic.
{"title":"Distributed practice and time pressure interact to affect learning and retention of arithmetic facts","authors":"Olivia R. Jazbutis, M. Wiseheart, G. Radvansky, Nicole M. McNeil","doi":"10.5964/jnc.7721","DOIUrl":"https://doi.org/10.5964/jnc.7721","url":null,"abstract":"Arithmetic is commonly taught through timed practice and drill, yet little research exists to guide optimal practice structure. This study investigated the effects of distributed practice and time pressure on the acquisition and retention of arithmetic facts. Following a pretest, adult participants (n = 211) were randomly assigned to learn unfamiliar times tables (17 and 19) in one of ten conditions in a 5 (spacing: daily, every other day, weekly, every 10 days, every other week) x 2 (time pressure: timed or untimed) factorial design. After the learning phase, retention tests were given to measure both accuracy and response time immediately, after a ten-day delay, and at the end of semester. Time pressure during learning elevated participants’ perceived stress. It also led to faster response times during testing when learning was spaced daily and every other day, but slower response times for all other spacings. These patterns were reversed in the absence of time pressure during learning. While timed and untimed practice during learning led to similar forgetting of practiced facts over time, untimed practice allowed participants to gradually improve on unpracticed facts and conceptually related facts across test phases. Ultimately, distributed practice and time pressure may interact in complex ways to affect the learning and retention of arithmetic facts, and the effects shown in previous studies using verbal material (e.g., narrative texts, word lists) may not generalize to arithmetic.","PeriodicalId":36632,"journal":{"name":"Journal of Numerical Cognition","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47055281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Z. E. Ünal, A. M. Ala, Gamze Kartal, Serkan Özel, D. Geary
Sixty (35 girls) ninth graders were assessed on measures of algebraic reasoning and usage of visual and symbolic representations (with a prompt for visual use) to solve equations and inequalities. The study grouped visual representations into two categories: arithmetic-visual, which entailed the use of real-world objects to represent specific values of variables, and algebraic-visual, which involved formal representations like the number line and the coordinate plane. Symbolic representations, on the other hand, encompassed the use of standard algorithms to solve equations, such as changing the place of terms in an equation. The results reveal that the use of algebraic visuals, as opposed to arithmetic visuals, was associated with enhanced algebraic reasoning. Further, although the students initially relied on standard algorithms to explain equations and inequalities, they could produce accurate algebraic-visual representations when prompted. These findings suggest that students have multiple representations of equations and inequalities but only express visual representations when asked to do so. In keeping with the general relationship between visuospatial abilities and mathematics, self-generated algebraic-visual representations partially mediated the relation between overall mathematics achievement and algebraic reasoning.
{"title":"Visual and symbolic representations as components of algebraic reasoning","authors":"Z. E. Ünal, A. M. Ala, Gamze Kartal, Serkan Özel, D. Geary","doi":"10.5964/jnc.11151","DOIUrl":"https://doi.org/10.5964/jnc.11151","url":null,"abstract":"Sixty (35 girls) ninth graders were assessed on measures of algebraic reasoning and usage of visual and symbolic representations (with a prompt for visual use) to solve equations and inequalities. The study grouped visual representations into two categories: arithmetic-visual, which entailed the use of real-world objects to represent specific values of variables, and algebraic-visual, which involved formal representations like the number line and the coordinate plane. Symbolic representations, on the other hand, encompassed the use of standard algorithms to solve equations, such as changing the place of terms in an equation. The results reveal that the use of algebraic visuals, as opposed to arithmetic visuals, was associated with enhanced algebraic reasoning. Further, although the students initially relied on standard algorithms to explain equations and inequalities, they could produce accurate algebraic-visual representations when prompted. These findings suggest that students have multiple representations of equations and inequalities but only express visual representations when asked to do so. In keeping with the general relationship between visuospatial abilities and mathematics, self-generated algebraic-visual representations partially mediated the relation between overall mathematics achievement and algebraic reasoning.","PeriodicalId":36632,"journal":{"name":"Journal of Numerical Cognition","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42772890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. A. Jeglinski-Mende, M. Fischer, A. Miklashevsky
While some researchers place negative numbers on a so-called extended mental number line to the left of positive numbers, others claim that negative numbers do not have mental representations but are processed through positive numbers combined with transformation rules. We measured spatial associations of negative numbers with a modified implicit association task that avoids spatial confounds present in most previous studies. In two lab-based magnitude classification experiments (each including 24 participants) and two online replications (with 74 and 77 participants, respectively), positive and negative numbers were combined with two spatial contexts: either directional symbols (left- or right-pointing arrows) or rectangles of varying sizes. In all experiments, we found a robust distance effect for negative numbers. However, there were no consistent associations of negative numbers with directional or size contexts. In the context of directional symbols, holistic processing was prevalent only in the small negative number range (-9, -8, -7, -6) when ensured by the stimulus set, supporting an extended mental number line. In the context of rectangles, however, large negative numbers from -4 to -1 were perceived as small, thus supporting rule-based processing. For negative number processing in the context of size, we further suggest the Semantic-Perceptual Size Congruity Cuing model (SPeSiCC model). We show that associations of size with negative numbers underly more complex processing mechanisms than mere recruitment of a transformation rule. In general, we conclude that associations of negative numbers with space and size are situated in the context, as they depend on the presented number range and differ for spatial direction and size.
{"title":"Below zero? Universal distance effect and situated space and size associations in negative numbers","authors":"M. A. Jeglinski-Mende, M. Fischer, A. Miklashevsky","doi":"10.5964/jnc.6763","DOIUrl":"https://doi.org/10.5964/jnc.6763","url":null,"abstract":"While some researchers place negative numbers on a so-called extended mental number line to the left of positive numbers, others claim that negative numbers do not have mental representations but are processed through positive numbers combined with transformation rules. We measured spatial associations of negative numbers with a modified implicit association task that avoids spatial confounds present in most previous studies. In two lab-based magnitude classification experiments (each including 24 participants) and two online replications (with 74 and 77 participants, respectively), positive and negative numbers were combined with two spatial contexts: either directional symbols (left- or right-pointing arrows) or rectangles of varying sizes. In all experiments, we found a robust distance effect for negative numbers. However, there were no consistent associations of negative numbers with directional or size contexts. In the context of directional symbols, holistic processing was prevalent only in the small negative number range (-9, -8, -7, -6) when ensured by the stimulus set, supporting an extended mental number line. In the context of rectangles, however, large negative numbers from -4 to -1 were perceived as small, thus supporting rule-based processing. For negative number processing in the context of size, we further suggest the Semantic-Perceptual Size Congruity Cuing model (SPeSiCC model). We show that associations of size with negative numbers underly more complex processing mechanisms than mere recruitment of a transformation rule. In general, we conclude that associations of negative numbers with space and size are situated in the context, as they depend on the presented number range and differ for spatial direction and size.","PeriodicalId":36632,"journal":{"name":"Journal of Numerical Cognition","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49309411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Barbara W. Sarnecka, James Negen, Nicole R. Scalise, Meghan C. Goldman, Jeffrey N. Rouder
The authors assessed a battery of number skills in a sample of over 500 preschoolers, including both monolingual and bilingual/multilingual learners from households at a range of socio-economic levels. Receptive vocabulary was measured in English for all children, and also in Spanish for those who spoke it. The first goal of the study was to describe entailment relations among numeracy skills by analyzing patterns of co-occurrence. Findings indicated that transitive and intransitive counting skills are jointly present when children show understanding of cardinality and that cardinality and knowledge of written number symbols are jointly present when children successfully use number lines. The study’s second goal was to describe relations between symbolic numeracy and language context (i.e., monolingual vs. bilingual contexts), separating these from well-documented socio-economic influences such as household income and parental education: Language context had only a modest effect on numeracy, with no differences detectable on most tasks. However, a difference did appear on the scaffolded number-line task, where bilingual learners performed slightly better than monolinguals. The third goal of the study was to find out whether symbolic number knowledge for one subset of children (Spanish/English bilingual learners from low-income households) differed when tested in their home language (Spanish) vs. their language of preschool instruction (English): Findings indicated that children performed as well or better in English than in Spanish for all measures, even when their receptive vocabulary scores in Spanish were higher than in English.
{"title":"The real preschoolers of Orange County: Early number learning in a diverse group of children","authors":"Barbara W. Sarnecka, James Negen, Nicole R. Scalise, Meghan C. Goldman, Jeffrey N. Rouder","doi":"10.5964/jnc.6577","DOIUrl":"https://doi.org/10.5964/jnc.6577","url":null,"abstract":"<p xmlns=\"http://www.ncbi.nlm.nih.gov/JATS1\">The authors assessed a battery of number skills in a sample of over 500 preschoolers, including both monolingual and bilingual/multilingual learners from households at a range of socio-economic levels. Receptive vocabulary was measured in English for all children, and also in Spanish for those who spoke it. The first goal of the study was to describe entailment relations among numeracy skills by analyzing patterns of co-occurrence. Findings indicated that transitive and intransitive counting skills are jointly present when children show understanding of cardinality and that cardinality and knowledge of written number symbols are jointly present when children successfully use number lines. The study’s second goal was to describe relations between symbolic numeracy and language context (i.e., monolingual vs. bilingual contexts), separating these from well-documented socio-economic influences such as household income and parental education: Language context had only a modest effect on numeracy, with no differences detectable on most tasks. However, a difference did appear on the scaffolded number-line task, where bilingual learners performed slightly better than monolinguals. The third goal of the study was to find out whether symbolic number knowledge for one subset of children (Spanish/English bilingual learners from low-income households) differed when tested in their home language (Spanish) vs. their language of preschool instruction (English): Findings indicated that children performed as well or better in English than in Spanish for all measures, even when their receptive vocabulary scores in Spanish were higher than in English.","PeriodicalId":36632,"journal":{"name":"Journal of Numerical Cognition","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135731452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Are there some differences so small that we cannot detect them? Are some quantities so similar (e.g., the number of spots on two speckled hens) that they simply look the same to us? Although modern psychophysical theories such as Signal Detection Theory would predict that, with enough trials, even minute differences would be perceptible at an above-chance rate, this prediction has rarely been empirically tested for any psychological dimension, and never for the domain of number perception. In an experiment with over 400 adults, we find that observers can distinguish which of two collections has more dots from a brief glance. Impressively, observers performed above chance on every numerical comparison tested, even when discriminating a comparison as difficult as 50 versus 51 dots. Thus, we present empirical evidence that numerical discrimination abilities, consistent with SDT, are remarkably fine-grained.
{"title":"Successful discrimination of tiny numerical differences","authors":"Emily M. Sanford, Justin Halberda","doi":"10.5964/jnc.10699","DOIUrl":"https://doi.org/10.5964/jnc.10699","url":null,"abstract":"Are there some differences so small that we cannot detect them? Are some quantities so similar (e.g., the number of spots on two speckled hens) that they simply look the same to us? Although modern psychophysical theories such as Signal Detection Theory would predict that, with enough trials, even minute differences would be perceptible at an above-chance rate, this prediction has rarely been empirically tested for any psychological dimension, and never for the domain of number perception. In an experiment with over 400 adults, we find that observers can distinguish which of two collections has more dots from a brief glance. Impressively, observers performed above chance on every numerical comparison tested, even when discriminating a comparison as difficult as 50 versus 51 dots. Thus, we present empirical evidence that numerical discrimination abilities, consistent with SDT, are remarkably fine-grained.","PeriodicalId":36632,"journal":{"name":"Journal of Numerical Cognition","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46302268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
From a young age, children’s math achievement is influenced by individual factors, such as math anxiety. While math anxiety has been linked to math avoidance, few studies have explored this link in young children, particularly in the context of play. Because play-based instruction is commonly used for math in early childhood classrooms, understanding the impact of math anxiety on children’s engagement in math-related play may have important implications for children’s early math learning. The current study examined the role of children’s math anxiety in their persistence and exploration during a math toy play task. We observed wide variability in children’s play behaviors, finding that children’s actions during play did not relate to their math anxiety, but their talk related to math while playing with the toy did. There are also age and gender differences in math anxiety, school experience, and reasoning about the toy play task. These results suggest that math anxiety may influence certain aspects of children’s engagement in math-related play, and that more research is needed to consider links between math anxiety and math avoidance in young children.
{"title":"The relation between math anxiety and play behaviors in 4- to 6-year-old children","authors":"M. Depascale, L. Butler, Geetha B. Ramani","doi":"10.5964/jnc.9721","DOIUrl":"https://doi.org/10.5964/jnc.9721","url":null,"abstract":"From a young age, children’s math achievement is influenced by individual factors, such as math anxiety. While math anxiety has been linked to math avoidance, few studies have explored this link in young children, particularly in the context of play. Because play-based instruction is commonly used for math in early childhood classrooms, understanding the impact of math anxiety on children’s engagement in math-related play may have important implications for children’s early math learning. The current study examined the role of children’s math anxiety in their persistence and exploration during a math toy play task. We observed wide variability in children’s play behaviors, finding that children’s actions during play did not relate to their math anxiety, but their talk related to math while playing with the toy did. There are also age and gender differences in math anxiety, school experience, and reasoning about the toy play task. These results suggest that math anxiety may influence certain aspects of children’s engagement in math-related play, and that more research is needed to consider links between math anxiety and math avoidance in young children.","PeriodicalId":36632,"journal":{"name":"Journal of Numerical Cognition","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43492519","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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