Number Knowledge and Error Types of Elementary Portuguese Students: Implications for Instruction

Abstract

In the present study, we examined number knowledge skills of 697 Portuguese elementary students from first to fourth grade. Students completed three number knowledge tasks: 1) translating numbers into words, 2) symbolic magnitude (i.e., number comparison), and 3) decomposing numbers. We evaluated students' answers by means of error analysis using a three-category coding system adopted from specific error types were computed by grade level. Results showed that there were significant differences among grades and that the prerequisite linguistic error type (i.e., pre linguistic rules or principles of the cardinal number system), particularly in the magnitude tasks, significantly contributed to students' performance on number knowledge tasks. This is important for instruction because learning difficulties in mathematics have been associated with weaknesses in intermediate number knowledge competencies (e.g., number comparison). Our qualitative data analyses suggest that instruction, intervention, or remediation need to consider systematic instructing students the prelinguistic rules of the number system, specifically the principles related to larger numbers.