[Show abstract][Hide abstract] ABSTRACT: We present a conditional rewrite system for arithmetic and membership univariate constraints over real numbers, designed for computer assisted learning (CAL) in elementary math. Two fundamental principles guided the design of the proposed rewrite rules: cognitive fidelity (emulating steps students should take) and correctness, aiming that step-by-step solutions to problems look like ones carried out by students. In order to gain more flexibility to modify rules, add new ones and customize solvers, the rules are written in a specification language and then compiled to Prolog. The rewrite system is complete for a relevant subset of problems found in high-school math textbooks.
Artificial Intelligence Applications and Innovations, 3rd IFIP Conference on Artificial Intelligence Applications and Innovations (AIAI) 2006, June 7-9, 2006, Athens, Greece; 01/2006
[Show abstract][Hide abstract] ABSTRACT: To understand what people do when they do mathematics and write programs emulating that process is a continuous research topic in artificial intelligence, automated reasoning
and symbolic computation. We present the first release of an web application for athematics education that is being developed within AGILMAT (Automatic Generation of Interactive Drills for Mathematics Learning, POSI/CHS/48565/2002) project.
AGILMAT aims at developing a system to automatically create and solve mathematics exercises that is flexible enough to be easily customizable to different curricula and users. Its major guiding principles are: the abstraction and formal representation of the problems that may be actually solved by algebraic algorithms covered by the curricula; the customization of these models by adding further constraints; and designing flexible solvers that emulate the steps students usually take to solve the generated drills.
Twelfth Portuguese Conference on Artificial Intelligence (EPIA-2005); 01/2005
[Show abstract][Hide abstract] ABSTRACT: We present a solver for arithmetic and membership constraints over real numbers, for computer assisted learning (CAL) in math. The solver works as a rewrite system. What makes it novel are the proposed rewriting rules that go beyond simple algebraic reductions. Instead they work at high abstraction level and use some knowledge about the functions behaviour to shortcut solving steps. Designed with pedagogic concerns, they are useful to produce step-by-step solutions that look like ones worked out by students. In this way the solver may be more advantageous in some learning environments than sophisticated mathematical software, which is certainly the choice for scientic applications and advanced algebraic manipulations. The proposed solver is correct and although it is complete for a relevant set of problems arising in high-school math curricula, it is incomplete in general. Indeed, this is inherent to the addressed problem. A prototype is being developed in Prolog for a specic application domain, reusing some modules of Demomath (14) for symbolic manipulation of sets and exact arithmetic, that employ CLP(Q) and CLP(R) to some extent. This work is part of AGILMAT project in which a web application to automatically generate and solve math drills is being developed.