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Fostering Formal Commutativity Knowledge with Approximate Arithmetic.

ABSTRACT: How can we enhance the understanding of abstract mathematical principles in elementary school? Different studies found out that nonsymbolic estimation could foster subsequent exact number processing and simple arithmetic. Taking the commutativity principle as a test case, we investigated if the approximate calculation of symbolic commutative quantities can also alter the access to procedural and conceptual knowledge of a more abstract arithmetic principle. Experiment 1 tested first graders who had not been instructed about commutativity in school yet. Approximate calculation with symbolic quantities positively influenced the use of commutativity-based shortcuts in formal arithmetic. We replicated this finding with older first graders (Experiment 2) and third graders (Experiment 3). Despite the positive effect of approximation on the spontaneous application of commutativity-based shortcuts in arithmetic problems, we found no comparable impact on the application of conceptual knowledge of the commutativity principle. Overall, our results show that the usage of a specific arithmetic principle can benefit from approximation. However, the findings also suggest that the correct use of certain procedures does not always imply conceptual understanding. Rather, the conceptual understanding of commutativity seems to lag behind procedural proficiency during elementary school.

SUBMITTER: Hansen SM

PROVIDER: S-EPMC4652602 | biostudies-literature | 2015

REPOSITORIES: biostudies-literature

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Fostering Formal Commutativity Knowledge with Approximate Arithmetic.

Hansen Sonja Maria SM Haider Hilde H Eichler Alexandra A Godau Claudia C Frensch Peter A PA Gaschler Robert R

PloS one 20151111 11

How can we enhance the understanding of abstract mathematical principles in elementary school? Different studies found out that nonsymbolic estimation could foster subsequent exact number processing and simple arithmetic. Taking the commutativity principle as a test case, we investigated if the approximate calculation of symbolic commutative quantities can also alter the access to procedural and conceptual knowledge of a more abstract arithmetic principle. Experiment 1 tested first graders who h ...[more]

PMID: 26560311

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Project description:Purpose: While the intellectual and scientific rationale for research collaboration has been articulated, a paucity of information is available on a strategic approach to facilitate the collaboration within a research network designed to reduce health disparities. This study aimed to (1) develop a conceptual model to facilitate collaboration among biostatisticians in a research network; (2) describe collaborative engagement performed by the Network's Data Coordinating Center (DCC); and (3) discuss potential challenges and opportunities in engaging the collaboration. Methods: Key components of the strategic approach will be developed through a systematic literature review. The Network's initiatives for the biostatistical collaboration will be described in the areas of infrastructure, expertise and knowledge management and experiential lessons will be discussed. Results: Components of the strategic approach model included three Ps (people, processes and programs) which were integrated into expert management, infrastructure management and knowledge management, respectively. Ongoing initiatives for collaboration with non-DCC biostatisticians included both web-based and face-to-face interaction approaches: Network's biostatistical capacities and needs assessment, webinar statistical seminars, mobile statistical workshop and clinics, adjunct appointment program, one-on-one consulting, and on-site workshop. The outreach program, as a face-to-face interaction approach, especially resulted in a useful tool for expertise management and needs assessment as well as knowledge exchange. Conclusions: Although fostering a partnered research culture, sustaining senior management commitment and ongoing monitoring are a challenge for this collaborative engagement, the proposed strategies centrally performed by the DCC may be useful in accelerating the pace and enhancing the quality of the scientific outcomes within a multidisciplinary clinical and translational research network.

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Dataset Information

Fostering Formal Commutativity Knowledge with Approximate Arithmetic.

Publications

Fostering Formal Commutativity Knowledge with Approximate Arithmetic.

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