Sixth Grade Students’ Performance, Misconceptions, and Confidence When Judging the Reasonableness of Computational Results

Abstract

Judging the reasonableness of computational results is pivotal for students to understand mathematical concepts. This domain is the most sensitive to the presence of misconceptions in mathematics. Confidence ratings can serve as a measure of the strength of students’ conceptual understanding. This study investigated the performance, misconceptions, and confidence ratings of 942 Hong Kong sixth grade students when they were asked to judge the reasonableness of computational results. The results showed that the students performed unsatisfactorily at judging the reasonableness, with an average score of 3.45 (out of 8). Slightly more than half of the students (53.72%) selected the correct computational results, but more than 60% of those students could not judge the reasonableness of the computational results (49.71% had misconceptions and 11.24% simply guessed the answers). In addition, only 20.82% and 18.23% of the students could apply number-sense- and rule-based methods to judge the reasonableness, respectively. Moreover, only 5.73% of the students showed high performance with a high confidence rating, 3.18% exhibited low performance with a low confidence rating, and 35.46% of them showed low performance with a high confidence rating. Furthermore, this study discusses students’ misconceptions, the implications of the study, and suggestions for future research.

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Notes

  1. 1.

    For more details regarding misconceptions on computational results and number sense, see our previous study (Yang, 2017; Yang & Lin, 2015; Yang & Wu, 2010). Judging the reasonableness is a component of number sense.

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Acknowledgments

This article was a part of a research project supported by the Ministry of Science and Technology, Taiwan, with grant no. MOST 105-2511-S-415-003-MY3. Any opinions expressed here are those of the authors and do not necessarily reflect the views of the National Science Council, Taiwan (Republic of China). The authors thank Dr. Ka Luen Cheung (The Education University of Hong Kong) and Cheng-Yi Chuang, M.Ed. (National Chiayi University, Taiwan) for their support in handling the data for the study.

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Correspondence to Iwan Andi J. Sianturi.

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Yang, D., Sianturi, I.A.J. Sixth Grade Students’ Performance, Misconceptions, and Confidence When Judging the Reasonableness of Computational Results. Int J of Sci and Math Educ 17, 1519–1540 (2019). https://doi.org/10.1007/s10763-018-09941-4

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Keywords

  • Confidence
  • Hong Kong
  • Reasonableness
  • Misconceptions
  • Performance