Epistemic errors in students’ four fundamental operations of whole numbers: a radical constructivist grounded theory (RCGT) approach

Abstract

The purpose of this study was to explore four fourth-grade students’ errors in whole number operations and associated causes. Task-based interviews were conducted to explore students' errors and their causes in four operations—addition, subtraction, multiplication, and division of whole numbers. The qualitative data in the form of students’ tasks and interview transcripts were analyzed to examine the nature of errors committed by the students. The findings of the study revealed that students committed epistemic and non-epistemic errors in the operations of whole numbers. Most of the errors in addition, subtraction, multiplication, and division problems were epistemic in nature due to a lack of understanding of the regrouping of numbers with position values and the role of a zero in different operations, a lack of understanding of the minuend and subtrahend in subtraction problems, a lack of understanding the role of zero in position values, and a misalignment of positional places for each numeral in minuend and subtrahend. The students could not comprehend the role of the remainder in the context of division problems and could not relate divisor, dividend, quotient and remainder. The non-epistemic errors seemed to arise from students’ lack of attention and curiosity, forgetting, and de-learning of the concepts in higher order operations and interpretations.