AGILMAT - Automatic Generation of Interactive Drills for Mathematics Learning

Project POSI/CHS/48565/2002, funded by Funda��o para a Ci�ncia e Tecnologia , POSI and FEDER.

A 3-year project (starting date: December, 2003)

AGILMAT Prototype

AGILMAT -- a Web Application for Math Education (demo story board).

Team Members

Senior Researchers

Ana Paula Tom�s (IP)
Jos� Paulo Leal
Nelma Moreira
Miguel Filgueiras
Jos� Carlos Santos

Assistant Researchers

Nuno Filipe Pereira (BI grant, September 2004 --- March 2006 )
Marcos Aur�lio Domingues (BI grant, May 2005 --- May 2006)
�ngela Reis (BI grant, April 2006 --- December 2006 )

Cl�udia Carvalho (BIC undergraduate student grant, October 2006 --- March 2007)
Patr�cio Correia (BIC undergraduate student grant, October 2006 --- March 2007)

Project summary

AGILMAT would give oportunity to continue and consolidate research work that has been carried out by the members of the team, independently or in collaboration, on the application of new technologies in education.

AGILMAT aims at the design and implementation of a system to automatically generate exercises of Mathematics, that must be versatile enough to cater for different stages and curricula.

There exist a huge number of courseware applications spread over the Web, namely tools to create and make available homework and assignments. All of them require from the teacher non-negligible effort specially to generate several instances of a given problem, which may not be easily recognized as simple variants of the same basic expression.

Many of the exercises of a certain grade may be actually solved successfully by some algebraic algorithmic procedures. The major idea of this project is therefore to analyse such algorithms in order to abstract and constrain the form of exercises that may be generated automatically. Not only the system shall generate drills of pedagogic interest, but it shall be used to provide illustrative examples, and in assessment.

The project consists of five major tasks:

to collect problem templates for given topics and to describe their solving procedures;
to abstract and obtain a formal representation of the problems that are to be tackled; to design parametric models for their generation with control on the difficulty level and adequacy for a given curriculum and student; to study decidability and complexity questions;
to define the architecture and to implement a prototype using constraint logic programming languages, though other platforms shall also be considered;
to design different interfaces, for students and teachers, and to integrate the system in Web environments;
to evaluate the project's impact and possible reusage of the results to develop similar tools for other subjects.

Related publications

Ana Paula Tom�s, Jos� Paulo Leal, Marcos Aur�lio Domingues. A Web Application for Mathematics Education. In Proceedings of the 6th International Conference on Web-based Learning (ICWL 2007) (To appear)
Jos� Paulo Leal, Marcos Aur�lio Domingues. Rapid Development of Web Interfaces to Heteregeneous Systems. In Proceedings of 33rd Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM'07). Lecture Notes in Computer Science, 4362, Springer-Verlag, 2007, 716-725.
Ana Paula Tom�s, Nelma Moreira, Nuno Pereira. Designing a Solver for Arithmetic Constraints to Support Education in Mathematics. In Proceedings of Artificial Intelligence Applications & Innovations (AIAI 2006)., IFIP Series 204, Springer-Verlag, 2006, 433-441.
Marcos Aur�lio Domingues, Jos� Paulo Leal. Configuring Web Wizards in XML. In Proceedings of XATA 2006. XML: Aplica��es e Tecnologias Associadas., Portugal, 2006, 315-324.
Ana Paula Tom�s, Nelma Moreira, Nuno Pereira. Designing a Symbolic Solver for Arithmetic Constraints to Support Education in Mathematics DCC - FC & LIACC, Universidade do Porto, August 2005. (working paper)
Ana Paula Tom�s, Nuno Pereira, Nelma Moreira. Designing a Symbolic Solver for Arithmetic Constraints for Computer Assisted Learning (extended abstract). DCC - FC & LIACC, Universidade do Porto, 2005. ( progress report , abstract )
Rui Pedro Costa. Gera��o autom�tica de exerc�cios de Matem�tica . MSc thesis (in Math Education), Departamento de Matem�tica Pura. Faculdade de Ci�ncias da Universidade do Porto, Maio 2004. (in Portuguese)
Ana Paula Tom�s, Jos� Paulo Leal. A CLP-Based Tool for Computer Aided Generation and Solving of Maths Exercises. In V. Dahl, P. Wadler (eds.), Proceedings of the Fifth International Symposium on Practical Aspects of Declarative Languages (PADL'2003), Lecture Notes in Computer Science 2562, 223-240, Springer-Verlag, 2003. � Springer-Verlag

Related work at LIACC

AGILMAT is intended to further develop research in the area at LIACC, in particular, Demomath prototype.

Users interaction in AGILMAT will build on the experience gained with Ganesh, an environment for learning computer science that provides a Web platform where teachers can deploy exercises in different learning domains.

The integration of automatic grading systems with pedagogical contents and exploratory environments was also addressed in the EDIC project. It shares with AGILMAT the goal of using exercises and an explanatory environment to consolidate students' knowledge.