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Examining fifth graders’ conceptual understanding of numbers and operations using an online three-tier test

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Abstract

This study examines the conceptual understanding of numbers and operations among 372 fifth-grade students, based on their responses to an online three-tier test designed to assess their number sense, declarative knowledge, explanatory knowledge, and confidence. The results showed that most students had low performance and low number sense, with only approximately 18% demonstrating profound conceptual understanding of numbers and operations based on their high performance in five number sense components and high confidence in their solutions. In addition, the majority of students struggled with judging the reasonableness of computational results and solving context-based problems. Furthermore, approximately 78% of participants had misconceptions, with many expressing high confidence in their answers and reasoning. The findings of this study can serve as critical references when designing teaching content and materials for elementary students by carefully considering their performance, number sense, misconceptions, and confidence. The report concludes with a discussion of the implications of the results and suggestions for future research to address critical concerns in mathematics teaching and learning.

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Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Notes

  1. The study’s notion of profound understanding is anchored on Ma’s (2010) definition: “By profound understanding, I mean an understanding of the fundamental mathematics terrain that is deep, broad, and thorough. Although 'profound' is typically viewed as signifying intellectual depth, it’s three connotations, deep, vast, and thorough, are interconnected” (p. 120). In this research, we conceive of profound conceptual understanding as the ability to utilize efficient and flexible strategies (as defined in this study) that are derived from a deep, broad, and thorough comprehension of various topics within the numbers and operations domain. This understanding necessitates an in-depth, comprehensive understanding of the fundamental mathematics terrain and mathematical concepts in the numbers and operations domain, consistent with Ma’s (2010) definition.

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Acknowledgements

This work was supported by the Ministry of Science and Technology, Taiwan, with grant no. MOST 105-2511-S-415-003-MY3. The opinions expressed in this paper are those of the authors and do not necessarily reflect the views of the Ministry of Science and Technology.

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Ministry of Science and Technology, Taiwan, MOST 105-2511-S-415-003-MY3, Der-Ching Yang.

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Authors and Affiliations

  1. Department of Curriculum and Instruction, Indiana University, 201 N. Rose Avenue, Bloomington, IN, 47405, USA

    Iwan A. J. Sianturi

  2. School of Education, Faculty of Social Sciences and Humanities, Universiti Teknologi Malaysia, Skudai, Johor Bahru, 81310, Malaysia

    Zaleha Ismail

  3. Department of Education, National Chiayi University, 85, Wen Lung, Ming-Hsiung, Chiayi, 621, Taiwan

    Der-Ching Yang

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  1. Iwan A. J. Sianturi
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Correspondence to Der-Ching Yang.

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Sianturi, I.A.J., Ismail, Z. & Yang, DC. Examining fifth graders’ conceptual understanding of numbers and operations using an online three-tier test. Math Ed Res J (2023). https://doi.org/10.1007/s13394-023-00452-2

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