Http:// The Conceptual and Architectural Design of a System Supporting Exploratory Learning of Mathematics Generalisation Darren Pearce, Alex

http://www.migen.org

The Conceptual and Architectural Design of a System Supporting Exploratory

Learning of Mathematics Generalisation

Darren Pearce, Alex Poulovassilis

ECTEL’09, October 09


Richard NossAlex Poulovassilis

George MagoulasCelia HoylesNiall Winters

Ken Kahn

Sergio Gutierrez-Santos Manolis MavrikisDarren PearceEirini Geraniou

Mihaela CoceaBoon Liang Chua

Institute of Education & Birkbeck College


Outline of the talk• Project aims and challenges• MiGen context and tools• Conceptual model• System architecture• Architectural proof-of-concept• Conclusions and future work


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


Aims• MiGen’s eXpresser tool allows students to create

and manipulate patterns and algebraic expressions, 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


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


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


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


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


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)


Iterative Research Methodology1. Pedagogical and technical research

2. Requirements elicitation within domains of maths generalisation and intelligent support

3. Requirements analysis, in collaboration with students, teachers and teacher educators

4. Development of activity sequences and tasks

5. Technical design and implementation

6. Technical&pedagogical environment evaluation

7. Analysis of evaluation results; elicitation of pedagogical and technical outcomes; iteration


Conceptual Model • This work falls under item 3 earlier:

– Requirements analysis, in collaboration with 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


(i) Users and Learner Models


(ii) Students’ Constructions


(iii) Tasks, Activities, Learning Objectives and Landmarks


MiGen System Architecture


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


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


MiGen Sequence Diagram


Two functional prototype visualisations for the CD & ST tools


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

Documents

Http:// The Conceptual and Architectural Design of a System Supporting Exploratory Learning of Mathematics Generalisation Darren Pearce, Alex