Outline of the talk

1. The Conceptual and Architectural Design of a System Supporting Exploratory Learning of Mathematics Generalisation Darren Pearce, Alex Poulovassilis http://www.migen.org

2. http://www.migen.org

3. Outline of the talk • Project aims and challenges • MiGen context and tools • Conceptual model • System architecture • Architectural proof-of-concept • Conclusions and future work http://www.migen.org

4. Aims • to co-design, build and evaluate • with teachers and teacher educators • a pedagogical and technical environment for improving 11-14-year-old students’ learning of mathematical generalisation • seeing “the general through the particular” is a powerful way to introduce generalisation, and forms the basis of our research • we are adopting a constructionist approach http://www.migen.org

5. Aims • MiGen’s eXpresser tool allows students to create and manipulate patterns and algebraicexpressions, and explore the relationships between them • students are asked to construct “generalised patterns”, to derive corresponding expressions, to test out their patterns and expressions on new problem instances, to compare their constructions with other students’ ones • our aim is to support students’ exploratory construction while also fostering progressive knowledge building http://www.migen.org

6. Challenges • little work so far in supporting students in a constructionist context • conversely, considerable guidance is required to ensure learning in such contexts • feedback needs to be provided to students during their construction process, not just at the end • since students will be undertaking exploratory rather than structured tasks, teachers need to be assisted in monitoring students’ activities and progress by appropriate visualisation and notification tools http://www.migen.org

7. Interdisciplinarity • research challenges are both pedagogical and technological e.g. • modelling the domain, tasks, learners • identifying information necessary for provision of effective feedback to learners and to the teacher • designing learner feedback, developing and trialling appropriate intelligent technologies • designing, developing trialling appropriate visualisation techniques for teacher feedback • designing and developing an appropriate system architecture http://www.migen.org

8. Interdisciplinarity • MiGen research team is diverse: maths education, AI in education, computer science • this paper focuses on a subset of the above challenges, primarily: • designing and developing an appropriate system architecture: extensible, scalable, client-server, multiple concurrent users (learners & teachers) and also aspects of: • modelling the domain, tasks, learners • designing, developing trialling appropriate visualisation techniques for teacher feedback http://www.migen.org

9. MiGen Context • Deployed in classrooms in schools • Students working individually, in pairs, or in groups • Real-time provision of feedback to students and teachers: • aiming to assist the teacher in focusing her attention across the class and informing her interventions (not to replace the teacher) • Provision also of historical information about students’ activities and progress to teachers http://www.migen.org

10. MiGen Tools • MiGen system comprises a number of tools: • eXpresser – a mathematical microworld • Discussion tool • Task design tool • eGeneraliser • Teacher assistance tools: currently Classroom Dynamics (CD) and Student Tracking (ST) • Activity Design and Management tool (possibly) http://www.migen.org

11. Iterative Research Methodology • Pedagogical and technical research • Requirements elicitation within domains of maths generalisation and intelligent support • Requirements analysis, in collaborationwith students, teachers and teacher educators • Development of activity sequences and tasks • Technical design and implementation • Technical&pedagogical environment evaluation • Analysis of evaluation results; elicitation of pedagogical and technical outcomes; iteration http://www.migen.org

12. Conceptual Model • This work falls under item 3 earlier: • Requirements analysis, in collaborationwith students, teachers and teacher educators • The CM currently comprises 4 overlapping subsections; we present three in the paper and refer to a recent project deliverable for the fourth • Further iterative development of the CM is occurring as we move towards V1 of the full MiGen system, and will continue http://www.migen.org

13. (i) Users and Learner Models http://www.migen.org

14. (ii) Students’ Constructions http://www.migen.org

15. (iii) Tasks, Activities, Learning Objectives and Landmarks http://www.migen.org

16. MiGen System Architecture http://www.migen.org

17. Architectural Proof-of-Concept • forms basis for implementation of full architecture (now almost completed) • MiGen schools context  lightweight approach • Lightweight  RPC/SOAP or REST • Many advantages to REST: • More scalable • More cacheable • Easier to performance-tune • we have used Restlet, a lightweight Java REST framework http://www.migen.org

18. Architectural Proof-of-Concept • aim of the proof-of-concept implementation was to develop sufficient server and client infrastructure to demonstrate fulfilment of the system’s architectural requirements • the server side manages the data resources, registration of new clients, handling of messages posted by clients, notifying clients of updated data resources • the client side provides access to server-side data resources, determines any changes made to these, provides presentation functionality http://www.migen.org

19. MiGen Sequence Diagram http://www.migen.org

20. Two functional prototype visualisations for the CD & ST tools http://www.migen.org

21. Conclusions and Future Work • Conceptual model: • derived after extensive requirements elicitation • significant step towards development of a common vocabulary across the disciplines • Architecture: simple, modular, scalable • Proof-of-concept implementation: significant step towards first full version of the system • Continuing iterative development, aiming for full system ready to be tested with students and teachers in November 2009 http://www.migen.org