AGILMAT  Automatic Generation of Interactive Drills for
Mathematics Learning
Project POSI/CHS/48565/2002, funded by
Fundação para a Ciência e Tecnologia
, POSI and FEDER.
A 3year project (starting date: December, 2003)
Ana Paula Tomás, José Carlos Santos, José Paulo Leal, Marcos
Domingues, Miguel Filgueiras, Nelma Moreira, Nuno Pereira.
AGILMAT  a Web Application for Math Education (demo story board).
Presented at EPIA 2005, during the Intelligent Systems Demonstrations
Event, Covilhã, Portugal, 2005
Team Members
Senior Researchers
Ana Paula Tomás (IP)
José Paulo Leal
Nelma Moreira
Miguel Filgueiras
José Carlos Santos
Assistant Researchers
Nuno Filipe Pereira (BI grant,
September 2004  March 2006 )
Marcos Aurélio Domingues (BI grant,
May 2005  May 2006)
Ângela Reis (BI grant,
April 2006  December 2006 )
Cláudia Carvalho (BIC undergraduate student grant,
October 2006  March 2007)
Patrício 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 nonnegligible
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 Tomás, José Paulo Leal, Marcos Aurélio Domingues.
A Web Application for Mathematics Education. In Proceedings of
the 6th International Conference on
Webbased Learning (ICWL 2007)
(To appear)
 José Paulo Leal, Marcos Aurélio 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,
SpringerVerlag, 2007, 716725.

Ana Paula Tomás, 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,
SpringerVerlag, 2006, 433441.
 Marcos Aurélio Domingues, José Paulo Leal. Configuring Web
Wizards in XML. In Proceedings of XATA 2006. XML: Aplicações e
Tecnologias Associadas., Portugal, 2006, 315324.

Ana Paula Tomás, 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 Tomás, 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. Geração automática de exercícios de
Matemática . MSc thesis (in Math Education), Departamento de Matemática
Pura. Faculdade de Ciências da Universidade do Porto, Maio 2004. (in Portuguese)
 Ana Paula Tomás, José Paulo Leal. A CLPBased 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, 223240, SpringerVerlag, 2003.
© SpringerVerlag
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.
©DCCFC & LIACC,
Universidade do Porto, 20032007