| Abstrakt: |
When solving a mathematical problem, students who do not have sufficient conceptual understanding may perform poorly and exhibit misconceptions. This study was aimed to examine students' conceptual understanding and significant misconceptions when solving number sense‐related problems. An online three‐tier diagnostic test was administered to 125 fifth‐grade students with varied socio‐economic backgrounds in Hong Kong. Only 14.40% of the students exhibited high performance with high confidence, indicating that these students had a profound conceptual understanding of number sense. In addition, the majority of the students (66.40%) did not demonstrate number sense; these students exhibited several significant misconceptions and could solve the questions only by using a rule‐based method or guessing. Accordingly, most students performed unsatisfactorily on number sense‐related problems. This study is imperative in identifying early predictors and provides information for further compatible interventions in the teaching and learning of number sense in Hong Kong in particular and worldwide in general. Lay Description: What is already known about this topic: Students must be instilled with conceptual understanding to achieve mastery of mathematical understanding and be able to properly solve complex or novel problems.Students would likely exhibit misconceptions if they do not have sufficient conceptual understanding.Students' conceptual understanding can be examined by evaluating their confidence levels in solving a problem. What this paper adds: A three‐tier diagnostic test (question and answer, reasoning, and confidence) can be used to examine students' conceptual understanding.Students performed unsatisfactorily on number sense because they lack conceptual understanding of topics related to number sense.Students held significant misconceptions on understanding the basic meaning of numbers and operations, recognizing the number size, using multiple representations of numbers and operation, recognizing the relative effect of operations on numbers, and judging the reasonableness of a computational result. Implications for practice and/or policy: Conceptual understanding of related topics reflecting number sense should be prioritized over procedural knowledge and mathematical rules.Lack of conceptual understanding of relevant topics and relying on mathematical rules and formulas are the main root causes of students' unsatisfactory performance.The deliberate use of estimation questions, multiple presentations, and judging the reasonableness of a result can help learners develop their conceptual understanding of number sense. [ABSTRACT FROM AUTHOR] |
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