Diagnostic Assessment in Third-Grade Subtraction: The Relation between Bridging Errors, Number of Errors and Mathematical Ability

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.