37,139 research outputs found
Integrating DGSs and GATPs in an Adaptative and Collaborative Blended-Learning Web-Environment
The area of geometry with its very strong and appealing visual contents and
its also strong and appealing connection between the visual content and its
formal specification, is an area where computational tools can enhance, in a
significant way, the learning environments.
The dynamic geometry software systems (DGSs) can be used to explore the
visual contents of geometry. This already mature tools allows an easy
construction of geometric figures build from free objects and elementary
constructions. The geometric automated theorem provers (GATPs) allows formal
deductive reasoning about geometric constructions, extending the reasoning via
concrete instances in a given model to formal deductive reasoning in a
geometric theory.
An adaptative and collaborative blended-learning environment where the DGS
and GATP features could be fully explored would be, in our opinion a very rich
and challenging learning environment for teachers and students.
In this text we will describe the Web Geometry Laboratory a Web environment
incorporating a DGS and a repository of geometric problems, that can be used in
a synchronous and asynchronous fashion and with some adaptative and
collaborative features.
As future work we want to enhance the adaptative and collaborative aspects of
the environment and also to incorporate a GATP, constructing a dynamic and
individualised learning environment for geometry.Comment: In Proceedings THedu'11, arXiv:1202.453
Automated Theorem Proving in GeoGebra: Current Achievements
GeoGebra is an open-source educational mathematics software tool, with millions of users worldwide. It has a number of features (integration of computer algebra, dynamic geometry, spreadsheet, etc.), primarily focused on facilitating student experiments, and not on formal reasoning. Since including automated deduction tools in GeoGebra could bring a whole new range of teaching and learning scenarios, and since automated theorem proving and discovery in geometry has reached a rather mature stage, we embarked on a project of incorporating and testing a number of different automated provers for geometry in GeoGebra. In this paper, we present the current achievements and status of this project, and discuss various relevant challenges that this project raises in the educational, mathematical and software contexts. We will describe, first, the recent and forthcoming changes demanded by our project, regarding the implementation and the user interface of GeoGebra. Then we present our vision of the educational scenarios that could be supported by automated reasoning features, and how teachers and students could benefit from the present work. In fact, current performance of GeoGebra, extended with automated deduction tools, is already very promising—many complex theorems can be proved in less than 1 second. Thus, we believe that many new and exciting ways of using GeoGebra in the classroom are on their way
Using Automated Reasoning Tools in GeoGebra in the Teaching and Learning of Proving in Geometry
ABSTRACT: This document introduces, describes and exemplifies the technical features of some recently implemented automated reasoning tools in the dynamic mathematics software GeoGebra. The new tools are based on symbolic computation algorithms, allowing the automatic and rigorous proving and discovery of theorems on constructed geometric figures. Some examples of the use in the classroom of such commands are provided, including one describing how intuitive handling of GeoGebra automated reasoning tools may result in unexpected outputs. In all cases the emphasis is made in the potential utility of these tools as a guiding stick to foster student activities (exploration, reasoning) in the learning of elementary geometry. Moreover, a collection of appendices describing other, more sophisticated, low-level GeoGebra tools (Prove, ProveDetails), as well as instructions on how to obtain the translation of GeoGebra commands into other languages, and details about debugging, are included.Work partially supported by the grant MTM2017-88796-P from the Spanish MINECO and the ERDF (European
Regional Development Fund)
Deciding geometric properties symbolically in GeoGebra
It is well known that Dynamic Geometry (DGS) software systems can be useful tools in the teaching/learning of
reasoning and proof. GeoGebra 5.0 was recently extended by an Automated Theorem Prover (ATP) subsystem that is able to compute proofs of Euclidean geometry statements. Free availability and portability of GeoGebra has made it possible to harness these novel techniques on tablets, smartphones and computers. Then, we think it is urgently necessary to address the new challenges posed by the availability of geometric ATP?s to millions of students worldwide
EuclidNet: Deep Visual Reasoning for Constructible Problems in Geometry
In this paper, we present a deep learning-based framework for solving
geometric construction problems through visual reasoning, which is useful for
automated geometry theorem proving. Constructible problems in geometry often
ask for the sequence of straightedge-and-compass constructions to construct a
given goal given some initial setup. Our EuclidNet framework leverages the
neural network architecture Mask R-CNN to extract the visual features from the
initial setup and goal configuration with extra points of intersection, and
then generate possible construction steps as intermediary data models that are
used as feedback in the training process for further refinement of the
construction step sequence. This process is repeated recursively until either a
solution is found, in which case we backtrack the path for a step-by-step
construction guide, or the problem is identified as unsolvable. Our EuclidNet
framework is validated on complex Japanese Sangaku geometry problems,
demonstrating its capacity to leverage backtracking for deep visual reasoning
of challenging problems.Comment: Accepted by 2nd MATH-AI Workshop at NeurIPS'2
Improving QED-Tutrix by Automating the Generation of Proofs
The idea of assisting teachers with technological tools is not new.
Mathematics in general, and geometry in particular, provide interesting
challenges when developing educative softwares, both in the education and
computer science aspects. QED-Tutrix is an intelligent tutor for geometry
offering an interface to help high school students in the resolution of
demonstration problems. It focuses on specific goals: 1) to allow the student
to freely explore the problem and its figure, 2) to accept proofs elements in
any order, 3) to handle a variety of proofs, which can be customized by the
teacher, and 4) to be able to help the student at any step of the resolution of
the problem, if the need arises. The software is also independent from the
intervention of the teacher. QED-Tutrix offers an interesting approach to
geometry education, but is currently crippled by the lengthiness of the process
of implementing new problems, a task that must still be done manually.
Therefore, one of the main focuses of the QED-Tutrix' research team is to ease
the implementation of new problems, by automating the tedious step of finding
all possible proofs for a given problem. This automation must follow
fundamental constraints in order to create problems compatible with QED-Tutrix:
1) readability of the proofs, 2) accessibility at a high school level, and 3)
possibility for the teacher to modify the parameters defining the
"acceptability" of a proof. We present in this paper the result of our
preliminary exploration of possible avenues for this task. Automated theorem
proving in geometry is a widely studied subject, and various provers exist.
However, our constraints are quite specific and some adaptation would be
required to use an existing prover. We have therefore implemented a prototype
of automated prover to suit our needs. The future goal is to compare
performances and usability in our specific use-case between the existing
provers and our implementation.Comment: In Proceedings ThEdu'17, arXiv:1803.0072
Automated Generation of Geometric Theorems from Images of Diagrams
We propose an approach to generate geometric theorems from electronic images
of diagrams automatically. The approach makes use of techniques of Hough
transform to recognize geometric objects and their labels and of numeric
verification to mine basic geometric relations. Candidate propositions are
generated from the retrieved information by using six strategies and geometric
theorems are obtained from the candidates via algebraic computation.
Experiments with a preliminary implementation illustrate the effectiveness and
efficiency of the proposed approach for generating nontrivial theorems from
images of diagrams. This work demonstrates the feasibility of automated
discovery of profound geometric knowledge from simple image data and has
potential applications in geometric knowledge management and education.Comment: 31 pages. Submitted to Annals of Mathematics and Artificial
Intelligence (special issue on Geometric Reasoning
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