Numerical Knowledge

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Geetha B Ramani - One of the best experts on this subject based on the ideXlab platform.

  • give yourself a hand the role of gesture and working memory in preschoolers Numerical Knowledge
    2021
    Co-Authors: Raychel Gordon, Nicole R Scalise, Geetha B Ramani
    Abstract:

    Abstract Hand gestures can be beneficial in math contexts to reduce the user’s cognitive load by supporting domain-general abilities such as working memory. Although prior work has shown a strong relation between young children’s early math performance and their general cognitive abilities, it is important to consider how children’s working memory ability may relate to their use of spontaneous gesture as well as their math-specific abilities. The current study examined how preschool-aged children’s gesture use and working memory relate to their performance on an age-appropriate math task. Head Start preschoolers (N = 81) were videotaped while completing a modified version of the Give-N task to measure their cardinality understanding. Children also completed a forward word span task and a computerized Corsi Block task to assess their working memory. The results showed that children’s spontaneous gesture use and working memory were related to their performance on the cardinality task. However, children’s gestures were not significantly related to working memory after controlling for age. Findings suggest that young children from low-income backgrounds use gestures during math contexts in similar ways to preschoolers from higher-income backgrounds.

  • racing dragons and remembering aliens benefits of playing number and working memory games on kindergartners Numerical Knowledge
    2020
    Co-Authors: Geetha B Ramani, Emily N Daubert, Grace C Lin, Snigdha Kamarsu, Alaina Wodzinski, Susanne M Jaeggi
    Abstract:

    Sources that contribute to variation in mathematical achievement include both Numerical Knowledge and general underlying cognitive processing abilities. The current study tested the benefits of tablet-based training games that targeted each of these areas for improving the mathematical Knowledge of kindergarten-age children. We hypothesized that playing a number-based game targeting Numerical magnitude Knowledge would improve children's broader Numerical skills. We also hypothesized that the benefits of playing a working memory (WM) game would transfer to children's Numerical Knowledge given its important underlying role in mathematics achievement. Kindergarteners from diverse backgrounds (n = 148; 52% girls; Mage  = 71.87 months) were randomly assigned to either play a number-based game, a WM game, or a control game on a tablet for 10 sessions. Structural equation modeling was used to model children's learning gains in mathematics and WM across time. Overall, our results suggest that playing the number game improved kindergarten children's Numerical Knowledge at the latent level, and these improvements remained stable as assessed 1 month later. However, children in the WM group did not improve their Numerical Knowledge compared to children in the control condition. Playing both the number game and WM game improved children's WM at the latent level. Importantly, the WM group continued to improve their WM for at least a month after playing the games. The results demonstrate that computerized games that target both domain-specific and domain-general skills can benefit a broad range of kindergarten-aged children.

  • math and memory in bilingual preschoolers the relations between bilingualism working memory and Numerical Knowledge
    2019
    Co-Authors: Emily N Daubert, Geetha B Ramani
    Abstract:

    Bilingual children exhibit enhanced working memory (WM) skill relative to monolingual children, which could have implications for early mathematics development. Competency in mathematics is support...

  • role of play and games in building children s foundational Numerical Knowledge
    2019
    Co-Authors: Geetha B Ramani, Emily N Daubert, Nicole R Scalise
    Abstract:

    Abstract Children learn early foundational mathematical Knowledge during the preschool years. In this chapter, we describe how play and games can provide children with opportunities to practice and build this Knowledge. We first focus on the importance of Numerical magnitude Knowledge and then draw upon theoretical and empirical work to demonstrate that both traditional games and computer games can improve young children's mathematical Knowledge. We close with a discussion of the use of age appropriate, engaging, and motivating numeracy-related games to promote Numerical Knowledge in early childhood classrooms.

  • narrowing the early mathematics gap a play based intervention to promote low income preschoolers number skills
    2018
    Co-Authors: Nicole R Scalise, Emily N Daubert, Geetha B Ramani
    Abstract:

    Preschoolers from low-income households lag behind preschoolers from middle-income households on Numerical skills that underlie later mathematics achievement. However, it is unknown whether these gaps exist on parallel measures of symbolic and non-symbolic Numerical skills. Experiment 1 indicated preschoolers from low-income backgrounds were less accurate than peers from middle-income backgrounds on a measure of symbolic magnitude comparison, but they performed equivalently on a measure of non-symbolic magnitude comparison. This suggests activities linking non-symbolic and symbolic number representations may be used to support children’s Numerical Knowledge. Experiment 2 randomly assigned low-income preschoolers (Mean Age = 4.7 years) to play either a Numerical magnitude comparison or a Numerical matching card game across four 15 min sessions over a 3-week period. The magnitude comparison card game led to significant improvements in participants’ symbolic magnitude comparison skills in an immediate posttest assessment. Following the intervention, low-income participants performed equivalently to an age- and gender-matched sample of middle-income preschoolers in symbolic magnitude comparison. These results suggest a brief intervention that combines non-symbolic and symbolic magnitude representations can support low-income preschoolers’ early Numerical Knowledge.

Robert S Siegler - One of the best experts on this subject based on the ideXlab platform.

  • how informal learning activities can promote children s Numerical Knowledge
    2015
    Co-Authors: Geetha B Ramani, Robert S Siegler
    Abstract:

    and Keywords Before children begin school, there is a wide range of individual differences in children's early Numerical Knowledge. Theoretical and empirical work from the sociocultural perspective suggests that children's experiences in the early home environment and with informal number activities can contribute to these differences. This article draws from this work to hypothesize that differences in the home explain, in part, why the Numerical Knowledge of children from low-income backgrounds trails behind that of peers from middle-class backgrounds. By integrating sociocultural perspectives with a theoretical analysis of children's mental number line, the authors created an informal learning activity to serve as an intervention to promote young children's Numerical Knowledge. Our studies have shown that playing a simple number board game can promote the Numerical Knowledge of young children from low-income backgrounds. The authors discuss how informal learning activities can play a critical role in the development of children's early maths skills.

  • reducing the gap in Numerical Knowledge between low and middle income preschoolers
    2011
    Co-Authors: Geetha B Ramani, Robert S Siegler
    Abstract:

    We compared the learning from playing a linear number board game of preschoolers from middle-income backgrounds to the learning of preschoolers from low-income backgrounds. Playing this game produced greater learning by both groups than engaging in other Numerical activities for the same amount of time. The benefits were present on number line estimation, magnitude comparison, numeral identification, and arithmetic learning. Children with less initial Knowledge generally learned more, and children from low-income backgrounds learned at least as much, and on several measures more, than preschoolers from middle-income backgrounds with comparable initial Knowledge. The findings suggest a class of intervention that might be especially effective for reducing the gap between low-income and middle-income children's Knowledge when they enter school.

  • linear Numerical magnitude representations aid children s memory for numbers
    2010
    Co-Authors: Clarissa A Thompson, Robert S Siegler
    Abstract:

    We investigated the relation between children’s Numerical-magnitude representations and their memory for numbers. Results of three experiments indicated that the more linear children’s magnitude representations were, the more closely their memory of the numbers approximated the numbers presented. This relation was present for preschoolers and second graders, for children from low-income and middle-income backgrounds, for the ranges 0 through 20 and 0 through 1,000, and for four different tasks (categorization and number-line, measurement, and numerosity estimation) measuring Numerical-magnitude representations. Other types of Numerical Knowledge—numeral identification and counting—were unrelated to recall of the same Numerical information. The results also indicated that children’s representations vary from trial to trial with the numbers they need to represent and remember and that general strategy-choice mechanisms may operate in selection of Numerical representations, as in other domains.

  • promoting broad and stable improvements in low income children s Numerical Knowledge through playing number board games
    2008
    Co-Authors: Geetha B Ramani, Robert S Siegler
    Abstract:

    Theoretical analyses of the development of Numerical representations suggest that playing linear number board games should enhance young children's Numerical Knowledge. Consistent with this prediction, playing such a game for roughly 1 hr increased low-income preschoolers' (mean age = 5.4 years) proficiency on 4 diverse Numerical tasks: Numerical magnitude comparison, number line estimation, counting, and numeral identification. The gains remained 9 weeks later. Classmates who played an identical game, except for the squares varying in color rather than number, did not improve on any measure. Also as predicted, home experience playing number board games correlated positively with Numerical Knowledge. Thus, playing number board games with children from low-income backgrounds may increase their Numerical Knowledge at the outset of school.

  • special section the development of mathematical cognition playing linear Numerical board games promotes low income children s Numerical development
    2008
    Co-Authors: Robert S Siegler, Geetha B Ramani
    Abstract:

    The Numerical Knowledge of children from low-income backgrounds trails behind that of peers from middle-income backgrounds even before the children enter school. This gap may reflect differing prior experience with informal Numerical activities, such as Numerical board games. Experiment 1 indicated that the Numerical magnitude Knowledge of preschoolers from low-income families lagged behind that of peers from more affluent backgrounds. Experiment 2 indicated that playing a simple Numerical board game for four 15-minute sessions eliminated the differences in Numerical estimation proficiency. Playing games that substituted colors for numbers did not have this effect. Thus, playing Numerical board games offers an inexpensive means for reducing the gap in Numerical Knowledge that separates less and more affluent children when they begin school.

Emily N Daubert - One of the best experts on this subject based on the ideXlab platform.

  • racing dragons and remembering aliens benefits of playing number and working memory games on kindergartners Numerical Knowledge
    2020
    Co-Authors: Geetha B Ramani, Emily N Daubert, Grace C Lin, Snigdha Kamarsu, Alaina Wodzinski, Susanne M Jaeggi
    Abstract:

    Sources that contribute to variation in mathematical achievement include both Numerical Knowledge and general underlying cognitive processing abilities. The current study tested the benefits of tablet-based training games that targeted each of these areas for improving the mathematical Knowledge of kindergarten-age children. We hypothesized that playing a number-based game targeting Numerical magnitude Knowledge would improve children's broader Numerical skills. We also hypothesized that the benefits of playing a working memory (WM) game would transfer to children's Numerical Knowledge given its important underlying role in mathematics achievement. Kindergarteners from diverse backgrounds (n = 148; 52% girls; Mage  = 71.87 months) were randomly assigned to either play a number-based game, a WM game, or a control game on a tablet for 10 sessions. Structural equation modeling was used to model children's learning gains in mathematics and WM across time. Overall, our results suggest that playing the number game improved kindergarten children's Numerical Knowledge at the latent level, and these improvements remained stable as assessed 1 month later. However, children in the WM group did not improve their Numerical Knowledge compared to children in the control condition. Playing both the number game and WM game improved children's WM at the latent level. Importantly, the WM group continued to improve their WM for at least a month after playing the games. The results demonstrate that computerized games that target both domain-specific and domain-general skills can benefit a broad range of kindergarten-aged children.

  • math and memory in bilingual preschoolers the relations between bilingualism working memory and Numerical Knowledge
    2019
    Co-Authors: Emily N Daubert, Geetha B Ramani
    Abstract:

    Bilingual children exhibit enhanced working memory (WM) skill relative to monolingual children, which could have implications for early mathematics development. Competency in mathematics is support...

  • role of play and games in building children s foundational Numerical Knowledge
    2019
    Co-Authors: Geetha B Ramani, Emily N Daubert, Nicole R Scalise
    Abstract:

    Abstract Children learn early foundational mathematical Knowledge during the preschool years. In this chapter, we describe how play and games can provide children with opportunities to practice and build this Knowledge. We first focus on the importance of Numerical magnitude Knowledge and then draw upon theoretical and empirical work to demonstrate that both traditional games and computer games can improve young children's mathematical Knowledge. We close with a discussion of the use of age appropriate, engaging, and motivating numeracy-related games to promote Numerical Knowledge in early childhood classrooms.

  • narrowing the early mathematics gap a play based intervention to promote low income preschoolers number skills
    2018
    Co-Authors: Nicole R Scalise, Emily N Daubert, Geetha B Ramani
    Abstract:

    Preschoolers from low-income households lag behind preschoolers from middle-income households on Numerical skills that underlie later mathematics achievement. However, it is unknown whether these gaps exist on parallel measures of symbolic and non-symbolic Numerical skills. Experiment 1 indicated preschoolers from low-income backgrounds were less accurate than peers from middle-income backgrounds on a measure of symbolic magnitude comparison, but they performed equivalently on a measure of non-symbolic magnitude comparison. This suggests activities linking non-symbolic and symbolic number representations may be used to support children’s Numerical Knowledge. Experiment 2 randomly assigned low-income preschoolers (Mean Age = 4.7 years) to play either a Numerical magnitude comparison or a Numerical matching card game across four 15 min sessions over a 3-week period. The magnitude comparison card game led to significant improvements in participants’ symbolic magnitude comparison skills in an immediate posttest assessment. Following the intervention, low-income participants performed equivalently to an age- and gender-matched sample of middle-income preschoolers in symbolic magnitude comparison. These results suggest a brief intervention that combines non-symbolic and symbolic magnitude representations can support low-income preschoolers’ early Numerical Knowledge.

Pablo Dartnell - One of the best experts on this subject based on the ideXlab platform.

  • promoting preschoolers Numerical Knowledge through spatial analogies numbers spatial alignment influences its learning
    2018
    Co-Authors: Jairo A Navarrete, David M Gomez, Pablo Dartnell
    Abstract:

    Abstract The development of early Numerical representations is a complex cognitive process whereby children acquire Numerical competences. To establish whether analogy making plays a role in this process of learning, we devised a classroom game based on an analysis of a number-line analogy that leverages children' spatial intuitions for helping them understand the numbers. To investigate the role of spatial positioning along the number line, seventy-seven preschoolers were randomly assigned to control tasks (control condition) or to embodied number line tasks in two possible spatial locations: watching numbers increasing either from left to right (space-number alignment condition) or from right to left (space-number misalignment condition). Performing learning activities for roughly two hours promoted children's proficiency in four tasks of Numerical Knowledge, but only children under spatial and Numerical alignment increased their proficiency in a task of number line estimation. This finding shows that the Numerical representations generated by children during training were integrated with spatial information that was implicit in the learning activities, thus revealing that analogical alignments play a key role in the formation of early Numerical representations. Additionally, this study illustrates that interrogating the analogy at the foundation of an instructional activity highlights key instructional decisions that can have a large impact on learning. Future research along this line might provide a framework for using analogy at the foundations of instructional design.

  • Towards a category theory approach to analogy: Analyzing re-representation and acquisition of Numerical Knowledge.
    2017
    Co-Authors: Jairo A Navarrete, Pablo Dartnell
    Abstract:

    Category Theory, a branch of mathematics, has shown promise as a modeling framework for higher-level cognition. We introduce an algebraic model for analogy that uses the language of category theory to explore analogy-related cognitive phenomena. To illustrate the potential of this approach, we use this model to explore three objects of study in cognitive literature. First, (a) we use commutative diagrams to analyze an effect of playing particular educational board games on the learning of numbers. Second, (b) we employ a notion called coequalizer as a formal model of re-representation that explains a property of computational models of analogy called "flexibility" whereby non-similar representational elements are considered matches and placed in structural correspondence. Finally, (c) we build a formal learning model which shows that re-representation, language processing and analogy making can explain the acquisition of Knowledge of rational numbers. These objects of study provide a picture of acquisition of Numerical Knowledge that is compatible with empirical evidence and offers insights on possible connections between notions such as relational Knowledge, analogy, learning, conceptual Knowledge, re-representation and procedural Knowledge. This suggests that the approach presented here facilitates mathematical modeling of cognition and provides novel ways to think about analogy-related cognitive phenomena

Nicole R Scalise - One of the best experts on this subject based on the ideXlab platform.

  • give yourself a hand the role of gesture and working memory in preschoolers Numerical Knowledge
    2021
    Co-Authors: Raychel Gordon, Nicole R Scalise, Geetha B Ramani
    Abstract:

    Abstract Hand gestures can be beneficial in math contexts to reduce the user’s cognitive load by supporting domain-general abilities such as working memory. Although prior work has shown a strong relation between young children’s early math performance and their general cognitive abilities, it is important to consider how children’s working memory ability may relate to their use of spontaneous gesture as well as their math-specific abilities. The current study examined how preschool-aged children’s gesture use and working memory relate to their performance on an age-appropriate math task. Head Start preschoolers (N = 81) were videotaped while completing a modified version of the Give-N task to measure their cardinality understanding. Children also completed a forward word span task and a computerized Corsi Block task to assess their working memory. The results showed that children’s spontaneous gesture use and working memory were related to their performance on the cardinality task. However, children’s gestures were not significantly related to working memory after controlling for age. Findings suggest that young children from low-income backgrounds use gestures during math contexts in similar ways to preschoolers from higher-income backgrounds.

  • role of play and games in building children s foundational Numerical Knowledge
    2019
    Co-Authors: Geetha B Ramani, Emily N Daubert, Nicole R Scalise
    Abstract:

    Abstract Children learn early foundational mathematical Knowledge during the preschool years. In this chapter, we describe how play and games can provide children with opportunities to practice and build this Knowledge. We first focus on the importance of Numerical magnitude Knowledge and then draw upon theoretical and empirical work to demonstrate that both traditional games and computer games can improve young children's mathematical Knowledge. We close with a discussion of the use of age appropriate, engaging, and motivating numeracy-related games to promote Numerical Knowledge in early childhood classrooms.

  • narrowing the early mathematics gap a play based intervention to promote low income preschoolers number skills
    2018
    Co-Authors: Nicole R Scalise, Emily N Daubert, Geetha B Ramani
    Abstract:

    Preschoolers from low-income households lag behind preschoolers from middle-income households on Numerical skills that underlie later mathematics achievement. However, it is unknown whether these gaps exist on parallel measures of symbolic and non-symbolic Numerical skills. Experiment 1 indicated preschoolers from low-income backgrounds were less accurate than peers from middle-income backgrounds on a measure of symbolic magnitude comparison, but they performed equivalently on a measure of non-symbolic magnitude comparison. This suggests activities linking non-symbolic and symbolic number representations may be used to support children’s Numerical Knowledge. Experiment 2 randomly assigned low-income preschoolers (Mean Age = 4.7 years) to play either a Numerical magnitude comparison or a Numerical matching card game across four 15 min sessions over a 3-week period. The magnitude comparison card game led to significant improvements in participants’ symbolic magnitude comparison skills in an immediate posttest assessment. Following the intervention, low-income participants performed equivalently to an age- and gender-matched sample of middle-income preschoolers in symbolic magnitude comparison. These results suggest a brief intervention that combines non-symbolic and symbolic magnitude representations can support low-income preschoolers’ early Numerical Knowledge.