An investigation on how learners may use multiple representations in a social interaction to promote learning of percentages and fractions: a case study

Abstract

The study examined the use of multiple representations such as the real world, written symbols, spoken symbols, diagrams and manipulatives by learners to promote the learning of percentages and fractions through social interaction. This investigation was carried out through a teaching and learning programme which was developed and implemented by me, the researcher. The effect of the implemented programme was the main focus of the research. The qualitative study was oriented in the interpretive paradigm – a paradigm that seeks to understand the meaning attached to human actions. Twenty learners participated in the implementation of the programme and 9 learners were selected for focus group interviews. The purpose of the interviews was to explore learners' understanding and feelings about the use of multiple representations in the learning of percentages and fractions through social interactions. The other tools employed in this study were pre-and-post diagnostic tests, observations, learners' work and a journal. The pre-test was used to determine learners' prior knowledge for the program design and implementation, while the post-test and learners' work were used to analyze the effect of the programme. Observations were used to investigate how multiple representations promoted or did not promote the learning of percentages and fractions. The teacher's journal was to record and reflect on any relevant information gathered on each lesson observed. The data shows that the effective use of multiple representations helped learners learn the concept of percentages and fractions better. Learners were able to look at representations in useful ways; multiple representations made some aspects of the concept clear; and multiple representations enabled learners to correct errors. Through the interaction between the teacher and learners, the following was found: all the learners changed words to change focus; learners made links between multiple representations; the learners deepened their concepts of percentages and fractions; learners could convert between fractions using multiple representations; learners could work out percentages of a quantity; and learners could express one quantity as a percentage of another. Furthermore, through the interaction between learners and learners all learners could identify more equivalent fractions of an initial fraction which was given to them; and they could increase and decrease a quantity by a given percentage. On the basis of this research, it can be concluded that the programme promoted the learning of percentages and fractions through three effective methodologies. The first methodology consisted of the effective use of multiple representations; the second methodology concerned the interaction between the teacher and learner during the learning process and the last methodology related to the interaction between the learners - interactions that were not strongly mediated by the teacher. I would recommend that teachers use these three effective approaches when teaching percentages and fractions to promote the learning of the concepts