Error patterns in Portuguese students’ addition and subtraction calculation tasks

Abstract

PurposeThe purpose of this descriptive study is to investigate why some elementary children have difficulties mastering addition and subtraction calculation tasks.Design/methodology/approachThe researchers have examined error types in addition and subtraction calculation made by 697 Portuguese students in elementary grades. Each student completed a written assessment of mathematical knowledge. A system code (e.g. FR = failure to regroup) has been used to grade the tests. A reliability check has been performed on 65 per cent randomly selected exams.FindingsData frequency analyses reveal that the most common type of error was miscalculation for both addition (n= 164; 38.6 per cent) and subtraction (n= 180; 21.7 per cent). The second most common error type was related to failure to regroup in addition (n= 74; 17.5 per cent) and subtraction (n= 139; 16.3 per cent). Frequency of error types by grade level has been provided. Findings from the hierarchical regression analyses indicate that students’ performance differences emerged as a function of error types which indicated students’ types of difficulties.Research limitations/implicationsThere are several limitations of this study: the use of a convenient sample; all schools were located in the northern region of Portugal; the limited number of problems; and the time of the year of assessment.Practical implicationsStudents’ errors suggested that their performance in calculation tasks is related to conceptual and procedural knowledge and skills. Error analysis allows teachers to better understand the individual performance of a diverse group and to tailor instruction to ensure that all students have an opportunity to succeed in mathematics.Social implicationsError analysis helps teachers uncover individual students’ difficulties and deliver meaningful instruction to all students.Originality/valueThis paper adds to the international literature on error analysis and reinforces its value in diagnosing students’ type and severity of math difficulties.