Error patterns in Portuguese students’ addition and subtraction calculation tasks: Implications for teaching

Purpose: The purpose of this descriptive study is to investigate why some elementary children have difficulties mastering addition and subtraction calculation tasks. Design/methodology/approach: The 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. Findings: Data 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/implications: There 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 implications: Students’ 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 implications: Error analysis helps teachers uncover individual students’ difficulties and deliver meaningful instruction to all students. Originality/value: This paper adds to the international literature on error analysis and reinforces its value in diagnosing students’ type and severity of math difficulties.