Aims

The MiGen project is tackling some thorny problems that confront all teachers of mathematics: What is algebra for? How is it useful for expressing generalisations? And more fundamental still: What does it mean to generalise in mathematics?

Mathematical Generalisation

Expressing generality, recognising and analysing patterns and articulating structure are at the core of mathematical thinking and scientific enquiry. These ideas are notoriously elusive for students, who routinely find themselves unable to understand what mathematics is about. There have been attempts to foster an appreciation of generality, e.g. by finding ways for students to construct their own mathematical models. Some studies have also attempted to exploit the potential of collaborative learning. However, despite some successes, difficulties remain, and these tend to coalesce around the need for intensive, timely and appropriate pedagogic support.

Our approach

We are building a pedagogical and technical environment to improve 11-14 year-old students’ learning of mathematical generalisations. Our research team of social, educational and computer scientists, together with teachers and teacher educators, are co-designing the system and testing it out with students. Our methodology is characterised by iterative cycles of design, testing and revision of a pedagogical and technical environment consisting of:

  1. sequenced and progressive activities undertaken within a  microworld - called the eXpresser - co-designed with teachers to promote the learning of mathematical generalisation among early secondary school students through model-construction.
  2. an intelligent component, the eGeneraliser, that will provide personalised feedback during the process of model analysis and generalization to students and teachers.
  3. a second intelligent component, the eCollaborator, that will foster cumulative knowledge construction through the sharing and discussion of models, aiming to assist teachers in developing and sustaining an effective online community.

In the latter stages of the project, we will evaluate the environment formatively and summatively, and scale it up from its initial design experiment to a broader group of schools and teachers, so as to form a sustainable learning community.