20 research outputs found
Automated Generation of User Guidance by Combining Computation and Deduction
Herewith, a fairly old concept is published for the first time and named
"Lucas Interpretation". This has been implemented in a prototype, which has
been proved useful in educational practice and has gained academic relevance
with an emerging generation of educational mathematics assistants (EMA) based
on Computer Theorem Proving (CTP).
Automated Theorem Proving (ATP), i.e. deduction, is the most reliable
technology used to check user input. However ATP is inherently weak in
automatically generating solutions for arbitrary problems in applied
mathematics. This weakness is crucial for EMAs: when ATP checks user input as
incorrect and the learner gets stuck then the system should be able to suggest
possible next steps.
The key idea of Lucas Interpretation is to compute the steps of a calculation
following a program written in a novel CTP-based programming language, i.e.
computation provides the next steps. User guidance is generated by combining
deduction and computation: the latter is performed by a specific language
interpreter, which works like a debugger and hands over control to the learner
at breakpoints, i.e. tactics generating the steps of calculation. The
interpreter also builds up logical contexts providing ATP with the data
required for checking user input, thus combining computation and deduction.
The paper describes the concepts underlying Lucas Interpretation so that open
questions can adequately be addressed, and prerequisites for further work are
provided.Comment: In Proceedings THedu'11, arXiv:1202.453
Proceedings 11th International Workshop on Theorem Proving Components for Educational Software
The ThEdu series pursues the smooth transition from an intuitive way of doing
mathematics at secondary school to a more formal approach to the subject in
STEM education, while favouring software support for this transition by
exploiting the power of theorem-proving technologies. What follows is a brief
description of how the present volume contributes to this enterprise. The 11th
International Workshop on Theorem Proving Components for Educational Software
(ThEdu'22), was a satellite event of the 8th Federated Logic Conference (FLoC
2022), July 31-August 12, 2022, Haifa, Israel ThEdu'22 was a vibrant workshop,
with two invited talk by Thierry Dana-Picard (Jerusalem College of Technology,
Jerusalem, Israel) and Yoni Zohar (Bar Ilan University, Tel Aviv, Israel) and
four contributions. An open call for papers was then issued, and attracted
seven submissions. Those submissions have been accepted by our reviewers, who
jointly produced at least three careful reports on each of the contributions.
The resulting revised papers are collected in the present volume. The
contributions in this volume are a faithful representation of the wide spectrum
of ThEdu, ranging from those more focused on the automated deduction research,
not losing track of the possible applications in an educational setting, to
those focused on the applications, in educational settings, of automated
deduction tools and methods. We, the volume editors, hope that this collection
of papers will further promote the development of theorem-proving based
software, and that it will allow to improve the mutual understanding between
computer scientists, mathematicians and stakeholders in education. While this
volume goes to press, the next edition of the ThEdu workshop is being prepared:
ThEdu'23 will be a satellite event of the 29th international Conference on
Automated Deduction (CADE 2023), July 1-4, 2023, Rome, Italy