M i Gen: Intelligent Support for Mathematical Generalisation

1. MiGen: Intelligent Support for Mathematical Generalisation Richard Noss Alex Poulovassilis George Magoulas Celia Hoyles Niall Winters Ken Kahn Sergio Gutiérrez Manolis Mavrikis Darren Pearce Eirini Geraniou Mihaela Cocea John Mason (consultant) Jose Valente (visiting fellow) Gyta Nicola, Kim Greenhalgh (administrators) 39 months started 1/10/07. Funding EPSRC/ESRC via TLRP

2. Outline • Aims and Objectives of MiGen • Overview of progress since last Advisory Group meeting • Plan for today’s meeting

3. Aims • to co-design, build and evaluate, • with teachers and teacher educators, • a mutually supportive pedagogical and technical environment for improving 11-14 year-old students’ learning of mathematical generalisation.

4. MiGen builds on three clear needs: i. to provide students with appropriate pedagogic support during the modelling process • to support students in the analysis of their models and in generalising from particular cases, and • to support the building and sustaining of a collaborative community in which interaction is effectively focused on specified learning outcomes.

5. We want to.. • develop a pedagogical and technical environment comprising: • sequenced and progressive activities within a prototype microworld – the eXpresser – designed to promote the learning of mathematical generalisation through model-construction; • an intelligent tool, the eGeneraliser, that provides personalised feedback during the process of model analysis and generalisation, adapted to students’ learning development and based on a framework derived from manual and automated analyses of learners' interactions in the eXpresser; • an intelligent tool for learners and teachers, the eCollaborator, that fosters and sustains an effective online learning community by providing assistance to learners based on analyses of their own learning and the activities of the group and advising learners and teachers;

6. Progress since last Advisory Group meeting • We are reaching the end of Phase 1(6 months) • We have established a small team of teachers and teacher educators who are developing with us sequenced activities targeting Year 7 to 9 students around early mainstream algebra. • We have established interdisciplinary teams and research methods pursuing • the design of the MiGen system, focussing initially on the eXpresser, • the design of sequenced activities • Our research methodology during Phase 1 encompasses iterative cycles of requirements analysis, design, implementation, and trialling/revising with teachers and students.

7. System design • A number of “mock-ups” of the eXpresser have been developed, the most sophisticated of which is ShapeBuilder • This has been iteratively trialled and extended in a succession of trials with groups of students, focussing particularly on the Pond Tiling task after some familiarisation tasks • A second mock-up supporting Pond Tiling was also prototyped, based on the MoPiX system • The design team is currently refactoring and extending elements from both ShapeBuilder and MoPiX in order to instantiate a first version of the eXpresser (target April 2008) • We have also refined the overall MiGen architecture, and have identified the need for several models that will need to be co-designed and that will permeate the entire system: • eXpresser model • domain model • task model • learner model

8. Activities co-design • Two Teachers Advisory Group meetings have been held (in November and January) • In January teachers interacted with the latest version of ShapeBuilder and were asked to predict students’ actions and suggest prompts that students might need to support them • The teachers gave us ideas as to how to improve the user interface still further, and suggestions of different types of guidance and prompts that might be needed • Successive versions of ShapeBuilder have been trialled with students and their teachers in two schools, and also small groups of students coming to the LKL • Feedback from both students and teachers has generally been positive, and has enhanced the team’s understanding of the eXpresser model and the eXpresser user interface paradigm • We are also beginning to identify the requirements for the intelligent support of students and teachers to be provided by the eGeneraliser and eCollaborator components

9. Intelligent Support • ShapeBuilder has an automatic logging facility, resulting in detailed interaction data from the student trials to date • screen capture has also been employed during the trials • and also textual note taking of interventions from research team members and students’ responses • We are now in the process of analysing and annotating these multiple information streams, as a first step in informing research and development of the intelligent support • A number of different strategies adopted by students within a task, and possible different categories for classifying learners’ outcomes, are beginning to emerge • Such an identification may ultimately allow the system to be able to predict individual students’ actions and tailor its support to them

10. Intelligent Support cont. • In terms of the pedagogical knowledge incorporated into MiGen, we have identified the need to co-design three models: • domain model • task model • learner model • These models will inform the design of the eGeneraliser, eCollaborator and MiGen repositories • We have also identified the need for three levels of representation and abstraction of learner-related information: • the learner model (one instantiation for each learner) • dynamically derived data (from the interaction logs) • system log data • Refinement of these models and identification of techniques for inferring higher-level learner attributes from lower-level system log and derived data are areas of research in Phase 2

11. Plan for today’s meeting • Prototype development and initial trials with students (EG, MM) • System design (DP) • Intelligent support (SG) • Planning future work

12. APPENDIX • Some useful slides from the first Advisory Group Meeting, if we need to refer to details of the original project plan, MiGen components etc.

13. eGeneraliser • will assist students in model construction, in two ways: • during the construction process, as students are developing models within the eXpresser, by • suggesting possible next actions in the construction of a model, use of appropriate components, alternative construction strategies • this assistance will be based on a learner interaction model initially designed by the research team with teachers, and subsequently refined by information extracted from a log of learners’ actions maintained by the eXpresser, identifying patterns of actions that can be associated with specific types of personalised support • at local endpoints of activity: suggesting alternative representations of solutions, and directing focus on next learning goals • for this, we will employ CI techniques such as neuro-fuzzy systems and case-based planning

14. eCollaborator • will support an online learning community, based on learners sharing and discussing their models • will have access to the eXpresser’s logs, students’ constructions, reports that students publish, and learning activity sequences designed by teachers; will determine similar patterns in the model construction process in order to: • advise students/teachers which constructions and reports of others’ to view, compare, critique and build on • appropriate heuristics to underpin this will be developed with teachers • will provide search facilities for students/teachers over information relating to their learning community and the artefacts it is producing • will provide students/teachers with visual representations of the ongoing modelling, reflection and interaction activities of their community

15. MiGen methodology • design experiment with iterative cycles of preparing, designing, testing and revision of the pedagogical+technical system • working throughout the project with a small group of teacher-educators and teachers

16. Project phases: I • four phases: • Develop sequenced learning activities, with teachers, around early mainstream algebra. Develop the eXpresser. Research techniques for the eGeneraliser and eCollaborator. Identify the types of observation and data collection needed during eXpressor piloting e.g. for developing the learner interaction models and feeding into the eGen & eCollab.

17. Project phases: II & III • Pilot the eXp+LAMS with small team of teachers and students in lab. Refine learner interaction models. Develop eGen and eCollab. Enhance eXp.

18. Project phases: III • Pilot first version of complete system with small group of teachers in their classroms. Track learning trajectories of the students and match against the system’s learner interaction models. Analyse data collected to enhance the learner interaction models, and to evaluate the system and its effects on student engagement and learning. Enhance system and co-design additional learning activity sequences.

19. Project Phases: IV • Piloting of enhanced system, with teachers in their classrooms, at different times in the year. Overall learning progress assessed by reference to learners’ achievement of learning outcomes specified in the activity sequences. Summative evaluation of the system.

20. Phase I Workpackages and Deliverables • WP 1.1 Develop sequenced activities Lead: MM; with EG, teachers Deliverables: V1 Sequenced Activities in LAMS + Report: Dec 07 V2 Sequenced Activities in LAMS + Report: March 08 • WP 1.2 Develop V1 of eXpresser + interfacing with LAMS Lead: KK; with MM, SG, DP, EG Deliverables: The eXpresser. Report on eXpresser design and development. March 08 • WP 1.3 Research Techniques for Personalisation/ Adaptation in eGen and eCollab Lead: SG; with MC Deliverables: Report + pre-prototype software. March 08

21. Phase I Workpackages and Deliverables • WP 1.4 Research Techniques for Search and Visualisation in eCollab Lead: DP; with SG, MC Deliverables: Report + pre-prototype software. March 08 • WP 1.5Develop V1 of overall system architecture: component functionalities, interfaces, technologies Lead: DP; with KK, SG Deliverables: Pre-prototype + report. Dec 07 Prototype + report. March 08 • WP 1.6Design and undertake task-based interviews with teachers Lead: EG (from Jan 08); MM Deliverable: Report. March 08 • WP 1.7Ongoing Liaison with Teachers Lead: EG (from Jan 08); MM. Ongoing.