Young Malaysian Children’s Representations of Addition in Problem-Solving

Abstract

In Malaysia, the National Preschool Curriculum Standard include the Mathematics standard contents that aim to provide children with knowledge and skills that are important for everyday life and future learning. In spite of the curriculum suggestion to integrate various learning approaches to enable children to have enriching, engaging and fun learning experiences, Asian (including Malaysian) teachers’ preferences are still towards emphasizing on symbols and employs traditional learning that put much attention on arriving at the correct answers. While Mathematics curriculum worldwide emphasize deep, conceptual understanding in mathematics as well as problem solving, teaching and learning of mathematics in Malaysian classrooms focuses on obtaining correct answers. This is often obtained through following the steps demonstrated to the children. Hence it is doubtful whether or not the correct answers came with understanding of the concepts.There are numerous studies reporting on children’s early mathematics learning and understanding. However, there is little research on young children’s understanding of addition particularly involving Malaysian context. Thus, this study investigates children’s usage of representations to support effective learning and problem solving of early mathematics. Drawing on theories emphasizing representation-processing in the development of mathematics understanding, this study explores multiple forms of representation usage by young children (aged six years) in a classroom in Malaysia. The study explores how children create and use a variety of representations and how they make translations between different forms of representations to define their understanding of mathematics concepts. The research design employs a qualitative study involving seven children in a public preschool in Malacca, Malaysia. This study incorporated several methods of data collection including interviews, classroom observations, field notes, photographs and reviews of students’ artefact. The data for this study is collected over a period of five weeks. The study comprised of three phases including initial meetings and an observation of the current lesson, a teaching sequence and problem creation as well as problem solution.The findings showed that there are both distinct as well as similarities in the creation and usage of representations across children of diverse mathematical performances. Concrete and semi concrete representations were the predominant representations used by children of low and middle performances of number skills (as assessed at the start of the study). High performers preferred using symbolic representations, though it is not necessarily that they utilized the symbols successfully. Despite utilizing distinct representation forms by distinct children, it was found that the representations are equally powerful in facilitating all children’s solution for the problems. In addition to using different representation forms, it was also found that children utilized representations at different phases; that resulted in using the representations in different ways during their problem attempt, hence revealed the important roles that representations play for problem solution.As a result of exploring the notion of understanding using both the Pirie-Kieren framework and Lesh Translation model, the findings from this data suggest that there are levels of representation through which children progress. It is an individual process that is influenced by factors related to the student, the teacher, and the problem context. This study also presents evidences that children’s deep understanding is dependent on their flexibility in utilizing multiple representations and performing translations between different representation forms. Hence, providing support that there exist a strong connection between the children’s skills in using representations and their growth in understanding.An important implication of this study for mathematics educators is that there should be emphasis on the use of multiple representations when introducing children to a new concept so as to provide learners with a wide variety of ways to learn the concept being introduced; that can be later utilized to solve posed problems. This is especially beneficial for children of diverse mathematical ability. In addition, to help learners grow in their understanding of mathematical concepts, it is suggested that there is an increased emphasis on assisting children to being flexible in using representations as well as making translations within various representation forms.