The enactive equation

Research keywords

representational competence, multiple representations, enactivity, manipulability, embodied cognition, distributed cognition, simulation, oscillation, computer interface

Project description

We designed, developed and tested a fully manipulable simulation interface with interconnected multiple representations (graph, equation and a simple pendulum) of the oscillation phenomenon. The interface was built to help secondary school students improve their representational competence (RC) around the concept of oscillation. RC refers to one’s ability to ‘integrate’ multiple external representations (such as equations, graphs, diagrams, etc.) into a coherent understanding/imagination of scientific entities and phenomena.

Grade VII students interacted with this interface in a semi-guided manner, while we tracked their behaviour using eye and mouse tracking. The students then answered a set of integration/imagination and transfer questions (the former explored if students could integrate the different representations and imagine the dynamic relationships between them in the absence of physical manipulation/dynamics, while the latter explored if the students could extend the oscillation analogy to other real life situations and representations).

We wanted to understand:

(a) if and how the simulation interface supports improvement in student RC,

(b) which types of interaction support/do not support the development of RC, and

(c) what cognitive mechanisms underly RC development

The project follows a design-based research model characterised by multiple cycles of intervention design and testing, where findings from every cycle feed back into the revisions to the intervention design and also add to the knowledge about learning.

All the students did exceptionally well in the transfer questions as opposed to imagination questions where only a few students succeeded. Eye and mouse tracking (interaction analysis) revealed that the successful students employed no single strategy, suggesting that there are multiple ways of being good (or bad) at imagination. Surprisingly, some of the poorly performing students exhibited similar interaction patterns to the successful imaginators, suggesting that interaction does not guarantee imagination. Careful guidance from teachers is necessary as the student interacts with the interface, in order for the interaction to lead to successful imagination.

Link to simulation


Prajakt Pande (PhD thesis), Aditi Kothiyal, Rwitajit Majumdar, Harshit Agrawal (programmer), Sanjay Chandrasekharan (advisor)

Selected Publications
  • Pande, P., & Chandrasekharan, S. (2016): Representational competence: towards a distributed and embodied cognition account, Studies in Science Education, 53 (1), 1-43. UK:Routledge. DOI: 10.1080/03057267.2017.1248627
  • Majumdar, R., Kothiyal, A., Pande, P., Agarwal, H., Ranka, A., Murthy, S., & Chandrasekharan, S. (2014) The enactive equation: exploring how multiple external representations are integrated, using a fully controllable interface and eye-tracking, In Kinshuk & Murthy, S. (Eds.), Proceedings of The 6th IEEE International Conference on Technology for Education, 233-240. IEEE: Kerala.
  • Kothiyal, A., Majumdar, R., Pande, P., Agarwal, H., Ranka, A., & Chandrasekharan, S. (2014) How Does Representational Competence Develop? Explorations Using a Fully Controllable Interface and Eye-tracking, In C.-C. Liu, Y. T. Wu, T. Supnithi, T. Kojiri, H. Ogata, S. C. Kong & A. Kashihara (Eds.). Proceedings of the 22nd International Conference on Computers in Education, 738-743. Japan: Asia-Pacific Society for Computers in Education.

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