Mathematics is the science of patterns. Identifying, analysing, and predicting patterns is the source of the power of mathematics – whether it’s a sequence of numbers, the structure of shapes, the change in the climate, the spread of a virus. But finding patterns in a few cases is not enough for mathematicians: the trick is to express the pattern so that it’s true for all cases – to generalise it.
This concept at the heart of mathematics is very difficult to learn and teach. The MiGen project is unlocking the mystery of generalisation to unlock the wonders of maths for 11-14 year olds with an intelligent microworld that presents algebra in a new visual format.
About the project
MiGen has funding of £1.25m (2009– 2011). The 13 members of the team are based at London Knowledge Lab, (IOE and Birkbeck, University of London).
The eXpresser: students can construct patterns, express the structure within thepatterns and the relationships that underpin them.
The eGeneraliser: gives intelligent support to students as they use the eXpresser, giving hints and clues to what to do next.
The eCollaborator: allows students to reflect, share and discuss their patterns with others, compare approaches and refine their work.
The Teacher Assistance tools: provide info on students progress, aiding the facilitation of students’ interaction with the eXpresser.
The team found that nearly all secondary students struggle to see general patterns emerging from specific cases, and to link variables so that one depends on another. Early evidence shows that the system helps students with this difficulty.
The eXpresser allows students to ‘keep an eye on the general’ and this leads to enhanced understanding of what the general case is, why it is important, and how to express it.
In order to support students and assist teachers, the team elaborated on the relationship between exploration, instruction and epistemology. Through the lens of constructionism the MiGen features offer support to students and teachers, while allowing appropriate student autonomy and exploration.
The team conceptualised, designed and implemented an architecture and related tools for intelligent support in microworlds and exploratory learning environments in general.
Test drive MiGen
Publications, demos and tutorials of the MiGen software, will be available from this website soon.