Applying constructivist`s learning theory in understanding year four children`s concept of multiplication

Abstract

Multiplication is an important arithmetic topic that need to be mastered by children in primary schools. The lack in understanding of the topic will build a weak prior knowledge and be a barrier for further topics. Consequently, it will affect children’s personalities and motivations in learning mathematics. Hence, the main purpose of this study was to explore year four children basic concept of multiplication by asking three research questions: (a) what is the children’s mental image of multiplication? (b) what is the children’s understanding of multiplication? and (c) how do the children represent multiplication? Thus, three year four children with different learning abilities were selected to be involved in this study via clinical one-to-one interview and answering questions by using concrete material tasks. The data collection and subsequent analysis were guided by qualitative research method based on constructivist theory of learning. This study identified seven mental images captured by the children in multiplication: multiplication as a process of producing bigger digits, multiplication as doubling of digits, multiplication as two digit numbers, multiplication as an array, multiplication as association of addition in multiplication number structure, multiplication as grouping of numbers and multiplication as commutative. The findings also showed that the children’s understanding of multiplication were demonstrated by applications in real life and non-applications in real life. In addition, the children illustrated their representation of multiplication in three forms: operational symbol, arrangement of concrete objects and erratic array representation. This study concluded that understanding basic concept of multiplication is a vital aspect in understanding basic concept of mathematics and need to be emphasised in teaching and learning activities. Meanwhile, the teaching and learning activities must be suited with children’s learning abilities and the use of concrete materials must be considered as fundamental teaching aids.