Visualisation and manipulation tools for Modal logic.
In this thesis, an investigation into how visualisation and manipulation tools can provide better
support for learners of Modal logic is described. Problems associated with learning Modal logic are
Seven areas topics in Modal logic are investigated, as is the influence of domainindependent
factors (e. g. motivation) on learning. Studies show that students find concepts
such as Modal proofs and systems difficult to learn, whilst possible worlds and Modes are
fairly straightforward. Areas such as reference, belief and accessibility relations fall between these
Two roles for representations in reasoning are identified: providing a concrete domain for
students to reason about, and supporting the process of reasoning. Systems which make use
of these complementary representations were found to be more effective for learners than
either the syntactic or the diagrammatic representations traditionally used to teach
A review of software used to support students learning logic highlights two important
features: the use of examples, and automation of routine tasks. A learning environment for
Modal logic was designed which incorporated these. The environment was developed using
an adapted version of Smalltalk's Model-View-Controller mechanism, and incorporates
complementary representations, enhance by direct manipulation.
A further study investigates the added benefits of using this tool, as opposed to using the
same representation but working with pen and paper. This confirms the importance of using
'concrete' content representations and minimising learners' cognitive load. Performance
measures show that software users learnt more, had a deeper style of learning, and found
the topics less abstract than their counterparts working with pen & paper.
This research shows that complementary representations are an effective way of
supporting students studying Modal logic, and that visualisation and manipulation tools
which incorporate these systems will provide additional benefits for learners.