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      Encoding “10ness” Improves First-Graders’ Estimation of Numerical Magnitudes


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          Understanding numerical magnitudes is a foundational skill that significantly impacts later learning of mathematics concepts. The current study tested the idea that encoding of “10ness” is crucial to improving children’s estimation of two-digit number magnitudes. We used commercially available base-10 blocks for this purpose. The children in the experimental condition were asked to construct two-digit numbers by laying down the precise combinations of 10- and 1-blocks horizontally (e.g., three 10-blocks and seven 1-blocks for 37). Two control conditions were also included. In one control condition, children used 1-blocks only. In another control condition, children used one 10-block and as many 1-blocks as necessary. After working with the experimenter for only 15 minutes twice, the children in the experimental condition were significantly more accurate on the estimation task than those in the control conditions. The findings confirmed the importance of encoding 10ness as a unit in making accurate estimates of two-digit number magnitudes. The importance of encoding other units in the base-10 system is discussed.

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          Numerical magnitude representations influence arithmetic learning.

          This study examined whether the quality of first graders' (mean age = 7.2 years) numerical magnitude representations is correlated with, predictive of, and causally related to their arithmetic learning. The children's pretest numerical magnitude representations were found to be correlated with their pretest arithmetic knowledge and to be predictive of their learning of answers to unfamiliar arithmetic problems. The relation to learning of unfamiliar problems remained after controlling for prior arithmetic knowledge, short-term memory for numbers, and math achievement test scores. Moreover, presenting randomly chosen children with accurate visual representations of the magnitudes of addends and sums improved their learning of the answers to the problems. Thus, representations of numerical magnitude are both correlationally and causally related to arithmetic learning.
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            Relations of different types of numerical magnitude representations to each other and to mathematics achievement.

            We examined relations between symbolic and non-symbolic numerical magnitude representations, between whole number and fraction representations, and between these representations and overall mathematics achievement in fifth graders. Fraction and whole number symbolic and non-symbolic numerical magnitude understandings were measured using both magnitude comparison and number line estimation tasks. After controlling for non-mathematical cognitive proficiency, both symbolic and non-symbolic numerical magnitude understandings were uniquely related to mathematics achievement, but the relation was much stronger for symbolic numbers. A meta-analysis of 19 published studies indicated that relations between non-symbolic numerical magnitude knowledge and mathematics achievement are present but tend to be weak, especially beyond 6 years of age. Copyright © 2014 Elsevier Inc. All rights reserved.
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              Enhancing young children’s mathematical knowledge through a pre-kindergarten mathematics intervention


                Author and article information

                J Numer Cogn
                Journal of Numerical Cognition
                J. Numer. Cogn.
                10 February 2017
                : 2
                : 3
                : 190-201
                [a ]Department of Education, University of California Santa Barbara, Santa Barbara, CA, USA
                Author notes
                [* ]Department of Education, University of California Santa Barbara, CA 93106, USA. yukari@ 123456education.ucsb.edu

                This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                : 06 July 2016
                : 01 November 2016
                Self URI (journal-page): https://journals.psychopen.eu/
                Research Reports

                base-10,place value,numerical cognition,numerical board games,numerical estimation,numerical language,numerical magnitudes


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