ABSTRACT

Learning to solve subtraction problems that require borrowing (e.g., 83–57=) is challenging, and these problems often cause ‘bridging’ errors, such as the smaller-from-larger error. This study explores how bridging errors in subtraction are related to students’ mathematical ability. The study involved 694 third-grade students and 35 teachers from 25 Dutch schools. Multilevel regression analyses showed that the number of bridging errors was positively related to the students’ mathematical ability, after controlling for the total number of errors in subtraction. Thus, the students who had a high proportion of bridging errors within the total number of errors had a relatively higher mathematical ability compared to the students who had a low proportion of bridging errors. This result implies that diagnosing bridging errors may help to identify where students’ stand within their mathematical development. The practical implications of this result for the design of diagnostic instruments are addressed in the discussion section.

摘要

学习解决需要借用的减法问题（例如83–57 =）具有挑战性，并且这些问题通常会导致“桥接”错误，例如从小到大的错误。本研究探讨了减法中的桥接错误与学生的数学能力之间的关系。该研究涉及来自25所荷兰学校的694名三年级学生和35名老师。多级回归分析表明，在控制了减法错误的总数之后，桥接错误的数量与学生的数学能力呈正相关。因此，与桥接错误比例较低的学生相比，在桥接错误总数中具有较高比例的桥接错误的学生具有相对较高的数学能力。该结果表明，诊断桥接错误可能有助于确定学生在数学发展中的地位。讨论部分将讨论此结果对诊断仪器设计的实际影响。