Exercises in mathematics are often solved using a standard
procedure, such as for example solving a system of linear equations by
subtracting equations from top to bottom, and then substituting variables
from bottom to top. Students have to practice such procedural
skills: they have to learn how to apply a particular strategy to an exercise.
E-learning systems offer excellent possibilities for practicing procedural
skills. The first explanations and motivation for a procedure that
solves a particular kind of problems are probably best taught in a class
room, or studied in a book, but the subsequent practice can often be
done behind a computer. There exist many e-learning systems or intelligent
tutoring systems that support practicing procedural skills. The
tools vary widely in breadth, depth, user-interface, etc, but, unfortunately,
almost all of them lack sophisticated techniques for providing
immediate feedback. If feedback mechanisms are present, they are hard
coded in the tools, often even with the exercises. This situation hampers
the usage of e-learning systems for practicing mathematical skills.
This paper introduces a formalism for specifying strategies for solving
exercises. It shows how a strategy can be viewed as a language in which
sentences consist of transformation steps. Furthermore, it discusses how
we can use advanced techniques from computer science, such as term
rewriting, strategies, error-correcting parsers, and parser combinators to
provide feedback at each intermediate step from the start towards the
solution of an exercise. Our goal is to obtain e-learning systems that give
immediate and useful feedback
Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.