The Conceptual and Architectural Design of a System Supporting Exploratory Learning of Mathematics Generalisation

Abstract

Abstract. The MiGen project is designing and developing an intelligent, exploratory environment to support 11-14-year-old students in their learning of mathematical generalisation. Deployed within the classroom, the system will also provide tools to assist teachers in monitoring students' activities and progress. This paper describes the conceptual and architectural design of the system, and gives a detailed technical explanation of a working proof-of-concept prototype of the architecture, motivating in particular the technologies and approaches chosen to implement the necessary functionality given the context of the project. We also discuss how the prototype will be used as a basis for developing the first full version of the MiGen system, in the context of ongoing knowledge acquisition and analysis within the project's iterative, stakeholder-centred design, development and testing methodology.

Scalable Monitoring of Student Interaction Indicators in Exploratory Learning Environments

“…To our knowledge, MiGen's TA tools represent the first work targeted at providing teachers with information about students' progress during exploratory learning activities in the classroom (preliminary results appeared in [18,19]). …”

“…Our case study here is the MiGen system, an intelligent ELE that aims to foster 11-14 year old students' learning of algebraic generalisation [16]. In its initial implementation, all the MiGen system components were implemented in Java and integrated into a lightweight architecture based on REST, with the aim of facilitating iterative prototyping and trialling in schools during the course of the MiGen project [18]. Our stress-testing of this implementation showed that it scales up to a few hundred users (students and teachers) working concurrently, which was sufficient for local installation and usage of the system in individual schools but not sufficient to be run nation-wide in a software-as-a-service fashion.…”

Design of Teacher Assistance Tools in an Exploratory Learning Environment for Algebraic Generalization

“…An extensive requirements analysis for these tools has been undertaken since early 2010 with the teachers involved in the MiGen project, and this has driven the iterative specification and co-design of these tools. The overall MiGen system has a client-server architecture, as discussed in [12], [13]. The client software is executed on each student's computer (without the Teacher Assistance and Task Design tools) and on the teacher's computer (the whole suite of tools), while the server software is executed on one server computer.…”

“…One of the principles in the design of MiGen's teacher tools has been to make them as unobtrusive as possible with respect to current teacher practice in the UK classroom. The tools collect information about students passively in the background [12] and show it to teachers through their computer in the classroom or a mobile terminal (e.g. a tablet).…”

Unified Modelling Language (UML) Model for Compressed Message Exchange

“…It provides machine-to-machine interoperability communication across the web using an XML-based standard to create and consume the services by the provider and the consumer [13], [12]. Pearce and Poulovassilis (2009) [14] developed a clientserver architecture for student-teacher feedback mechanism. The authors used UML to focus on the core functionalities in the implementation of the system.…”