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Project Leaders
Richard Noss
Alex Poulovassilis
Project Staff
Celia Hoyles
George Magoulas
Niall Winters
Ken Kahn
Research Officers
Eirini Geraniou (IOE)
Sergio Gutiérrez (BBK)
Manolis Mavrikis (IOE)
Darren Pearce (BBK)
PhD Student
Mihaela Cocea (BBK)
Project Details
ESRC/EPSRC (TLRP) Oct 2007-Dec 2010
Keywords
mathematical generalisation, model construction, intelligent collaborative learning systems, personalised feedback and support
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Project Aims
The MiGen project is tackling a thorny problem that confronts all teachers of mathematics:
What is algebra for?
- How is it useful for expressing generalisations?
- What does it mean to generalise in mathematics?
We are building a pedagogical and technical environment to support 11-14 year-old students' learning of mathematical generalisations. The system comprises a microworld, the eXpresser and two intelligent tools, the eGeneraliser and the eCollaborator. When students are tackling generalisation tasks, the eGeneraliser will be providing personalised feedback adapted to the learning trajectories of each student. Through the eCollaborator, students will be able to view each others' constructions and compare, critique and discuss them. Both intelligent tools will send information to teachers to help them provide appropriate guidance.
Our research team of social, educational and computer scientists, together with teachers and teacher educators are co-designing the system and iteratively testing it with students.
The ShapeBuilder Mockup
We have developed a mockup tool (ShapeBuilder) to allow us to explore with teachers and students the functionalities that we expect to implement as part of the eXpresser.
Currently, we are using ShapeBuilder to tackle a generalisation task typically known in the National Curriculum as "pond-tiling" (see Figure 1). ShapeBuilder aims to encourage structured algebraic reasoning by providing tools for the learner to build general shapes using expressions. A critical feature of the software allows users to define expressions using shapes which are represented iconically (see Figure 2). Three representations, (iconic, symbolic and numeric) are available to the students.
Sam wants to know the number of square tiles needed to surround a rectangular swimming pool with one layer of tiles. Sam took an aerial photograph of the pool but there was a cloud covering part of it. Can you find a rule for the number of tiles needed?
Figure 1: The Pond-Tiling Task
The pond-tiling task, which is just one of many activities that our system will support, is surprisingly rich in that it lends itself to a variety of different solutions. Different learners can produce multiple but valid solutions leading them to discuss the equivalence of different representations. We intend that these sorts of scenarios will provide an incentive for students to develop together some basic rules of algebra.
Figure 2: ShapeBuilder
References
- Download the project proposal.
- Hoyles, C. & Noss, R. (2004) Making rules in collaborative game design. In: Siraj-Blatchford, J. (Ed.) Developing new technologies for young children. Stoke on Trent: Trentham Books. 55-73.
- Kahn, K. (1996) ToonTalk - An animated programming environment for children. Journal of Visual Languages and Computing 7(2): 197-217.
- Noss R. & Hoyles, C. (2006) Exploring mathematics through construction and collaboration. In: Sawyer, K. (Ed.) Cambridge Handbook of the Learning Sciences. Cambridge UK: C.U.P. 389-408.
- Poulovassilis, A. and Hild, S.G. (2001). A Graph-Based System for Database Browsing, Querying, and Update. IEEE Transactions on Knowledge and Data Engineering 13(2): 316-333.
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