Finger Representation and Finger-Based Strategies in the Acquisition of Number Meaning and Arithmetic

Berteletti, Ilaria; Booth, James R.

doi:10.1016/b978-0-12-801871-2.00005-8

Cited by 19 publications

(14 citation statements)

References 134 publications

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“…We cannot rule out the possibility that the effects we found in the brain are the consequence of the way subtractions are taught in the United States. Math curriculum in North America emphasizes conceptual understanding over fact mastery (Geary et al, 1996b), with subtractions usually being taught by using counting strategies or inverse addition (Geary et al, 1993;LeFevre et al, 2006), and engaging brain regions involved in finger representations (Berteletti and Booth, 2015a). According to Siegler's distribution of associations model (Siegler and Jenkins, 1989), with experience, certain problems become associated with certain strategies, as do problems with answers.…”

Section: Educational Relevance and Conclusionmentioning

confidence: 99%

Early Engagement of Parietal Cortex for Subtraction Solving Predicts Longitudinal Gains in Behavioral Fluency in Children

Suárez‐Pellicioni

Berteletti

Booth

2020

Front. Hum. Neurosci.

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There is debate in the literature regarding how single-digit arithmetic fluency is achieved over development. While the Fact-retrieval hypothesis suggests that with practice, children shift from quantity-based procedures to verbally retrieving arithmetic problems from long-term memory, the Schema-based hypothesis claims that problems are solved through quantity-based procedures and that practice leads to these procedures becoming more automatic. To test these hypotheses, a sample of 46 typically developing children underwent functional magnetic resonance imaging (fMRI) when they were 11 years old (time 1), and 2 years later (time 2). We independently defined regions of interest (ROIs) involved in verbal and quantity processing using rhyming and numerosity judgment localizer tasks, respectively. The verbal ROIs consisted of left middle/superior temporal gyri (MTG/STG) and left inferior frontal gyrus (IFG), whereas the quantity ROIs consisted of bilateral inferior/superior parietal lobules (IPL/SPL) and bilateral middle frontal gyri (MFG)/right IFG. Participants also solved a single-digit subtraction task in the scanner. We defined the extent to which children relied on verbal vs. quantity mechanisms by selecting the 100 voxels showing maximal activation at time 1 from each ROI, separately for small and large subtractions. We studied the brain mechanisms at time 1 that predicted gains in subtraction fluency and how these mechanisms changed over time with improvement. When looking at brain activation at time 1, we found that improvers showed a larger neural problem size effect in bilateral parietal cortex, whereas no effects were found in verbal regions. Results also revealed that children who showed improvement in behavioral fluency for large subtraction problems showed decreased activation over time for large subtractions in both parietal and frontal regions implicated in quantity, whereas non-improvers maintained similar levels of activation. All children, regardless of improvement, showed decreased activation over time for large subtraction problems in verbal regions. The greater parietal problem size effect at time 1 and the reduction in activation over time for the improvers in parietal and frontal regions implicated in quantity processing is consistent with the Schema-based hypothesis arguing for more automatic procedures with increasing skill. The lack of a problem size effect at time 1 and the overall decrease in verbal regions, regardless of improvement, is inconsistent with the Fact-retrieval hypothesis.

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Section: Educational Relevance and Conclusionmentioning

confidence: 99%

Early Engagement of Parietal Cortex for Subtraction Solving Predicts Longitudinal Gains in Behavioral Fluency in Children

Suárez‐Pellicioni

Berteletti

Booth

2020

Front. Hum. Neurosci.

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“…Therefore the observed negative correlation is due to better finger sense leading to an earlier symbolic representation of numerosities via canonical finger patterns and a more efficient network for these visuo-spatial and motor representations of number in the service of arithmetic. This explanation is more likely given the accumulating evidence for participation of finger-based representations in mental arithmetic (see Andres & Pesenti, 2015;Berteletti & Booth, 2016;Soylu, Lester, & Newman, in press, for reviews). Addition and subtraction, in particular, rely on finger representations, due to early finger counting experiences.…”

Section: Overlapping Regions Correlating With Finger Gnosismentioning

confidence: 99%

The differential relationship between finger gnosis, and addition and subtraction: An fMRI study

et al. 2018

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The impact of fingers on numerical cognition has received a great deal of attention recently. One sub-set of these studies focus on the relation between finger gnosis (also called finger sense or finger gnosia), the ability to identify and individuate fingers, and mathematical development. Studies in this subdomain have reported mixed findings so far. While some studies reported that finger gnosis correlates with or predicts mathematics abilities in younger children, others failed to replicate these results. The current study explores the relationship between finger gnosis and two arithmetic operations—addition and subtraction. Twenty-four second to third graders participated in this fMRI study. Finger sense scores were negatively correlated with brain activation measured during both addition and subtraction. Three clusters, in the left fusiform, and left and right precuneus were found to negatively correlate with finger gnosis both during addition and subtraction. Activation in a cluster in the left inferior parietal lobule (IPL) was found to negatively correlate with finger gnosis only for addition, even though this cluster was active both during addition and subtraction. These results suggest that the arithmetic fact retrieval may be linked to finger gnosis at the neural level, both for addition and subtraction, even when behavioral correlations are not observed. However, the nature of this link may be different for addition compared to subtraction, given that left IPL activation correlated with finger gnosis only for addition. Together the results reported appear to support the hypothesis that fingers provide a scaffold for arithmetic competency for both arithmetic operations.

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“…Butterworth (1999) put forward a hypothesis that the development of arithmetic skills, and mathematical capabilities in general, are closely related to the use of fingers. Much neuroscientific evidence has been presented in favor of this hypothesis (see for instance Berteletti and Booth 2016;Butterworth et al 2011). In particular, it has been demonstrated that when engaged in mathematics, the region in the brain connected to the use of fingers exhibits considerably heightened activity, even when fingers are not used at all.…”

Section: Introductionmentioning

confidence: 99%

Structuring versus counting: critical ways of using fingers in subtraction

Björklund

Kullberg

Kempe

2018

ZDM Mathematics Education

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The idea of using fingers as a key component in arithmetic development has received a great deal of support, much of which is based on neuroscientific evidence. However, this body of work pays limited attention to how fingers are used and possible different outcomes in arithmetic problem solving. The aim of our paper, based on an analysis of 126 observations of 4-5-yearolds solving a simple subtraction task, is to discuss different ways of using fingers, with some of the ways appearing more, and others less, powerful. The analysis suggests there is much more complexity to children's finger-related strategies than prior research has indicated. Empirical findings in our study point to the decisive effects of different ways of using fingers, and in particular for either keeping track of counted units or for presenting a structured awareness of number. Three ways of using fingers emerge in the analysis, which are discussed in relation to their rate of success in solving the subtraction task and with attention to why the differences matter for the success rate. Through this discussion we suggest that the complexity of how fingers are used must be considered.

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Finger Representation and Finger-Based Strategies in the Acquisition of Number Meaning and Arithmetic

Cited by 19 publications

References 134 publications

Early Engagement of Parietal Cortex for Subtraction Solving Predicts Longitudinal Gains in Behavioral Fluency in Children

Early Engagement of Parietal Cortex for Subtraction Solving Predicts Longitudinal Gains in Behavioral Fluency in Children

The differential relationship between finger gnosis, and addition and subtraction: An fMRI study

Structuring versus counting: critical ways of using fingers in subtraction

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