Assessing Young Children's Number Magnitude Representation: A Comparison Between Novel and Conventional Tasks

Reid, Erin; Baroody, Arthur J.; Purpura, David J.

doi:10.1080/15248372.2014.920844

Cited by 9 publications

(5 citation statements)

References 34 publications

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“…Reid and colleagues [18] investigated estimation strategies that children used when placing numbers 1-9 on a 0-10 number line. They found that children tended to count from 0 (left anchor) for the first six numbers; in contrast, when estimating the position of numbers 7-9 on a number line, the children often used backward counting, using the right anchor point.…”

Section: Discussionmentioning

confidence: 99%

“…Studies investigating developmental differences according to the proportion judgment model within the 0-100 number range [11,[17][18][19][20] showed that children tend to overestimate number positions between the left edge (0) and the midpoint (50) and underestimate the number positions between the midpoint (50) and the right edge (100). In addition, studies have shown that the use of the midpoint as an anchor point is established at the beginning of third grade, thus yielding a more accurate number position within the given range [19,21,22].…”

Section: Introductionmentioning

confidence: 99%

“…In fact, because the ability to place numbers on the number line is based on spatial numerical association (SNA) and numerical cardinalities [26,27], researchers have found a significant correlation between performance in number-line estimation tasks and arithmetic achievements [18,[28][29][30][31][32][33][34][35][36][37]. All the above-mentioned studies examining the relationship between performance in the number line task and mathematical competence have shown evidence of a correlation between a child's percentage of absolute accuracy on the number line estimation task and different arithmetic tasks.…”

Section: Introductionmentioning

confidence: 99%

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Development of the Mental Number Line Representation of Numbers 0–10 and Its Relationship to Mental Arithmetic

Feldman

Berger

2022

Brain Sciences

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The internal representation of numbers on the mental number line (MNL) was demonstrated by performing the computerized version of the number-to-position (CNP) task on a touchscreen while restricting response time. We found that the estimation pattern is best fit by a sigmoid function, further denoted as the “sigmoidal model”. Two developmental leaps occurring during elementary school were recognized: (1) the division of the number line into two segments and (2) consistent use of different anchor points on the number line—the left endpoint in first grade, the right endpoint in second grade, and finally the midpoint in third grade. Additionally, when examining the differences between the breakpoints, we found that first graders demonstrated a breakpoint close to 6, which linearly decreased over the years until stabilizing close to 5. The relation between the ability to place individual numbers on a number line and performance of mental arithmetic showed that the consistent use of anchor points correlated significantly with faster responses in mental arithmetic.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Development of the Mental Number Line Representation of Numbers 0–10 and Its Relationship to Mental Arithmetic

Feldman

Berger

2022

Brain Sciences

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“…Children completed a modified version of the NLE task with paper and pencil designed to be a non-verbal number line task where, rather than being presented with numbers, children were presented with sets of dots (1-10). The task also included modifications according to Reid et al (2015). For example, the set to be represented was presented on a flashcard instead of above the middle of the number line, the number line had a marker at 0, 1, and 10, and used the example of a rabbit hopping was provided to ensure that children understood the task.…”

Section: Number Line Estimation Taskmentioning

confidence: 99%

Conceptual replication and extension of the relation between the number line estimation task and mathematical competence across seven studies

et al. 2021

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A recent meta-analysis demonstrated the overall correlation between the number line estimation (NLE) task and children’s mathematical competence was r = .44 (positively recoded), and this relation increased with age. The goal of the current study was to conceptually replicate and extend these results by further synthesizing this correlation utilizing studies not present in the meta-analysis. Across seven studies, 954 participants, ranging from 3 to 11 years old (Age M = 6.02 years, SD = 1.57), the overall estimation-competence correlations were similar to those of the meta-analysis and ranged from r = −.40 to −.35. The current conceptual replication demonstrated that the meta-analysis captured a stable overall relation between performance on the NLE task and mathematical competence. However, the current study failed to replicate the same moderation of age group presented in the meta-analysis. Furthermore, the current study extended results by assessing the stability and predictive validity of the NLE task while controlling for covariates. Results suggested that the NLE task demonstrated poor stability and predictive validity in the seven samples present in this study. Thus, although concurrent relations replicated, the differential age moderation, lack of stability, and lack of predictive validity in these studies require a more nuanced approach to understanding the utility of the NLE task. Future research should focus on understanding the connection between children’s developmental progression and NLE measurement before further investigating the predictive and diagnostic importance of the task for broader mathematical competence.

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“…Other accounts of number line task performance include proportional reasoning skill and measurement skill (e.g., Cohen & Sarnecka, 2014;Reid, Baroody, & Purpura, 2015). Evidence for the influence of proportional reasoning comes from findings suggesting that models using power functions fit account for more variance in children's estimates than models using logarithmic functions (Barth & Paladino, 2011).…”

Section: What Explains Children's Performance On the Number Line Task?mentioning

confidence: 99%

Neural coding partially accounts for the relation between children’s number line estimation and numerical comparison performance

Prather¹

2018

Preprint

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Numerical comparison is a primary measure of the acuity of children's approximate number system (ANS). ANS acuity is associated with key developmental outcomes such as symbolic number skill, standardized test scores and even employment outcomes (Halberda, Mazzocco, & Feigenson, 2008;Parsons & Bynner, 1997a). We examine the relation between children's performance on the numerical comparison task and the number line estimation task. It is important to characterize the relation between tasks in order to develop mathematics interventions that lead to transfer across tasks. We find that number line performance is significantly predicted by non--symbolic comparison performance for participants ranging in age from 5 to 8 years. We also evaluate, using a computational model, if the relation between the two tasks can be adequately explained based on known neural correlates of number perception. Data from humans and non--human primates characterizes neural activity corresponding to the perception of numerosities. Results of behavioral experimentation and computational modeling suggest that though neural coding of number predicts a correlation in participants' performance on the two tasks, it cannot account for all of the variability in the human data. This is interpreted as consistent with accounts of number line estimation in which number line estimation does not rely solely on participants' numerical perception. Introduction Children in school face the daunting task of learning a complex number system. Children must learn to manipulate numbers in increasingly sophisticated ways to stay on track in the formal education system. Understanding how different aspects of numerical cognition are related to one another within learners is an important goal for improving educational outcomes. Numerical cognition research has focused on performance on a few model tasks, such as number comparison and number line estimation. Numerical comparison is used to measure number sense, learners' fluency with numbers. The number line estimation task measures number to space mapping ability, which has been shown to be important in numerical development (Gunderson, Ramirez, Beilock, & Levine, 2012). It is unclear the degree to which performance on these two tasks relies on the same mechanisms. A central question is whether individual differences in performance across these tasks is primarily due to a shared cognitive mechanism. Study MotivationThe current study addresses the questions, (1) does children's non--symbolic comparison skill predict performance on the symbolic number line task when accounting for age, (2) if so can a computational model of the neural coding of number account for the relation. Several cognitive representations have been used to characterize participants' behavior, such as the mental number

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Assessing Young Children's Number Magnitude Representation: A Comparison Between Novel and Conventional Tasks

Cited by 9 publications

References 34 publications

Development of the Mental Number Line Representation of Numbers 0–10 and Its Relationship to Mental Arithmetic

Development of the Mental Number Line Representation of Numbers 0–10 and Its Relationship to Mental Arithmetic

Conceptual replication and extension of the relation between the number line estimation task and mathematical competence across seven studies

Neural coding partially accounts for the relation between children’s number line estimation and numerical comparison performance

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