The effect on learners strategies of varying computer-based representations: evidence from gazes, actions, utterances and sketches

Abstract

Computer-based Multiple External Representations (MERs) have been found in some cases to help and in others to hinder the learning process. This thesis examines how varying the external representations that are presented in a computer environment influences the strategies that learners choose when tackling mathematics tasks. It has been noted (Ainsworth, 2006) that learners fail to transfer insights from one representation to another. Previous work analysing video data of learners' problem-solving with computer-based MERs emphasises the need to identify which representation is being considered by a learner as utterances are made, and to examine more closely learners' movement between representations. This research focuses on the relationship between strategy and representation during learners' problem solving. A set of analytical techniques was developed to characterise learner strategies, to identify how different computer-based MERs influence strategy choices, and to explore how these choices change over the course of task completion. Rich data were collected using a variety of technologies: learners' shifts in attention were recorded using an unobtrusive eye-tracking device and screen capture software; keyboard and mouse actions were logged automatically; utterances and gestures were video recorded; notes and sketches were recorded in real-time using a Tablet PC. This research suggests how integrated analysis of learners' gazes, actions, writing, sketches and utterances can better illuminate subtle cognitive strategies. The study involved completion of three tasks by eighteen participants using multiple mathematical representations (numbers, graphs and algebra) presented in different computer-based 'instantiations': Static (non-moving, non-changing, non-Interactive); Dynamic (capable of animation following keyboard inputs); Interactive (directly manipulable using a mouse). Having computer-based MERs available to learners provides an opportunity to use representations with which they are comfortable. A detailed analysis showed that both representation and instantiation have an impact on strategy choice. It identified differences in expression of inferences, construction of visual images, and attention to representations between different types of instantiation. One of the important findings of the research is that learners are less likely to use imagining strategies when representational instantiation is Interactive. These results may provide some explanation of how interactivity helps or hinders learners' understanding of multiple representations.