Learning about abstract concepts can be difficult due to the hidden nature of the phenomena of interest. Developing understanding about abstract concepts is therefore challenging because phenomena, such as the behaviour of electricity, cannot be readily observed; only the outcomes of its behaviour can be observed. Consequently modelling the phenomena of interest becomes a crucial factor in supporting learners in their development of knowledge and understanding. Visualisation skills have been promoted as important when modelling knowledge in different forms, supporting learners in their development of knowledge and understanding by providing both mental and tangible referents to support their thinking.
My research interest has focused on the nature of learning in electronics education, and specifically how visual representation supports thinking (and doing). In this field of education, learning about concepts relies on the ability to interpret and use a range of visual representations. However, research reporting the nature of learners’ actual understanding is uncommon. Instead, research commonly focuses on learners’ misconceptions, or interventions based on theoretical aspects of knowledge. The aim of this research study, therefore, was to explore the use of external visual representations with secondary age students and describe the specific ways those students develop their understanding of abstract concepts.
I adopted a case study approach, focusing on the specific use of representations to problem solve and develop conceptual understanding. The methodology was interpretative and explored students’ understanding across-cases to achieve a synthesised analysis of observations and interview data. The framework of analysis was designed to focus on the translation of and transition between multiple representations, including computer program code, and the representation of phenomena at three levels of representation: observable, symbolic and abstract.
Individual understanding was characterised with the creation of four cognitive profiles representing key learner constructs
Data collection involved the observation of learners engaged with learning activities, documents collected from these activities, individual semi-structured interviews and participant characteristics data collected from course records. The findings show that common processes of learning are accompanied by individual developments in meaning and understanding. Individual understanding was characterised with the creation of four cognitive profiles representing key learner constructs. Understanding about abstract concepts was shown to benefit from representations where concrete referents linked with practical experience and existing knowledge, thereby reducing cognitive load on the learner. Electronics understanding was also shown to benefit from the explanatory use of computer program code as a supporting method with which to model and simulate circuit behaviour. Making a transition from one representation to another was therefore found to be beneficial to learning, as deeper meaning was shown to emerge from an understanding based in the different forms and levels of representation.
The research approach involved the close observation of learners engaged with learning activities, drawing from Siegler’s (2005) microgenetic approach. This strategy involves the intense observation and analysis of data. I found that this provided an in-depth understanding of learners’ approaches to learning in practice, because their actions, decisions and outcomes could be observed in detail. The analysis led to a detailed picture of learners’ understanding of complex phenomena (evidenced in the cognitive profiles) and revealed how their use of visual representations supported learning and problem solving.
This research study offers a glimpse at the learning experiences of one group of students. The close observation of learning during an intense period of time reveals the importance of modelling and simulating strategies as methods with which to think about complex phenomena. Modelling enables phenomena to be worked with in alternative ways, including the use of on-screen simulation tools. These can reveal aspects of the phenomena, through simulations, not apparent in the original representation. The identification of four key cognitive profiles was indicative of the different ways students modelled their own understanding and showed that personal strategy played an important part in the development of their own learning. Understanding these differentiated approaches to learning can benefit teaching because each student develops a conceptual understanding personal to themselves and therefore their point of reference will also be differentiated. Accordingly the presentation of learning materials should take account of this diversity in the development of complex abstract concepts. In particular the synchronous (diagrams and graphics) or sequential (words and sentences) nature of representations was shown to be important to learners in this study. Synchronous representations enabled complex phenomena to be encapsulated within an easily recognisable graphic (e.g., a circuit diagram), thereby reducing cognitive load on the learner. Sequential representations were shown to provide explanatory information, as in the example of computer program code, which is representative of electronic circuit operation.
Implications for teaching and learning are twofold. Firstly students can benefit from opportunities to model and simulate knowledge in practical ways. This was shown to provide a concrete, or unambiguous, referent for learners which could be linked with existing knowledge. Secondly teachers can enhance students’ engagement with phenomena through the careful selection of appropriate modelling and simulating strategies, including opportunities to make transitions from one form of representation to another. Further research is needed to understand how different modelling and simulating strategies can be best employed with learners at different stages of their learning, to enhance their development of understanding about complex abstract phenomena.
Siegler, R. S. (2005) Children’s Learning, American Psychologist, 60, pp. 769-778.