Development of a three-tier number sense test for fifth-grade students

  • Der-Ching YangEmail author


To assess the strength of conceptual understanding of number sense, a three-tier number sense test (TTNST) for fifth-grade students was developed and validated in this study. The three-tier test includes a content tier that assesses content knowledge of number sense, a reason tier that assesses a reason given for selecting a first-tier response, and a confidence tier that assesses how confident fifth-grade students are in their responses in the first two tiers. A total of 819 fifth-grade students from elementary schools in Taiwan participated in this study. Collected data showed that the test had good reliability and validity. The results revealed that many of the sample students performed poorly on number sense but maintained extremely high confidence; this indicated that many of the students held severe misconceptions and some were lacking in number sense. In addition, this study confirmed that the inclusion of a third tier (with confidence ratings) in the number sense test can mitigate the weaknesses of a previously used two-tier test. The educational implications of the findings are discussed in this paper.


Confidence Fifth-grade student Number sense Three-tier test 



This article was part of a research project supported by the Ministry of Science and Technology, Taiwan (ROC), with grant no. MOST 105-2511-S-415-003-MY3. Any opinions expressed here are those of the author and do not necessarily reflect the views of the Ministry of Science and Technology, Taiwan (ROC).

Compliance with ethical standards

Conflict of interest

The author declares that there is no conflict of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Graduate Institute of Mathematics and Science EducationNational Chiayi UniversityChiayiRepublic of China

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