E-mail: web@matr
E-mail: web@matrIn other sections are the ones written during work, and translations to Spanish of other people's writings.
(Included corrections for typos and grammar from Bachelor's Thesis submission at 2010-12-23)
Mathematical formula editing remains a laborious and frustrating task which requires extensive familiarization with the exact formula editor provided with a web application.
Direct manipulation formula editors are on most cases based on an internal model of the formula that dictates how the user can modify it [PS04]. The exact steps depend on the internal model of the formula which is not visible to the user. This means that it is possible to get stuck into a state where a seemingly obvious modification of the formula requires specific steps to be done. This has been reported among others in [PWY07] (page 4) and mentioned by our colleages in the ActiveMath1 project, where during evaluation studies in schools, students have been observed to get stuck while building fractions and having to scrape the whole expression and start over.
A multimodal user interface combines “different input or output channels in order to make using a computer more efficient, easier or both”[Rai99], and in this thesis we explore what can be done within the limitations of web browsers.
In this report we describe the extensions of the eLearning system ActiveMath that we developed [...] focused on the generation of parameterized exercises [...] by adding two different mechanisms: picking random numbers from given intervals (open, closed, continuous and discrete) and composing arbitrarily complex mathematical expressions using an iterative term rewriting algorithm.
Furthermore, our implementation takes into account the user model and provides a set of guarantees for what is picked depending on information from the user model. Also, expressions generated by our algorithm are checked for validity with a Computer Algebra System.
Besides the in-depth description of the implemented changes, we present some problems we encountered and the respective solutions that we found.
Sentido is an integrated environment for browsing, searching, and editing collections of OMDoc documents. It is implemented as an extension for the Mozilla/Firefox browsers to avoid the biggest problems found when using QMath: the need to compile the program for installing, the batch mode of interaction that made small corrections consume much of the author's time, and the lack of any support for document navigation and search.
QMath is a batch processor that produces an OMDoc file from a plain Unicode text document, in a similar way to how TEX produces a DVI file from a plain text source. Its purpose is to allow fast writing of mathematical documents, using plain text and a straightforward syntax (like in computer algebra systems) for mathematical expressions.
We present an exercise description language suitable for the representation of interactive exercises which involve mathematical entities, and have complex structures. One of the goals of the language is to provide primitives for support of interactive environments where adaptive presentation of steps and feedback is required. Using this scheme, exercises can be generated from static documents, in what can be seen as a layered scheme: the interactivity layer is applied over the static layer, yielding an interactive version of the content. This significantly speeds up the authoring process, makes the document management process easier, and helps in reusing the document. We believe that the information model presented in this paper, as well as the proposed way of deployment, may provide grounds for new extensions of today's standards helping to overcome some of the limitations that they currently have.
These are articles written during my work at the Universtät des Saarlandes and the DFKI (Deutsches Forschungszentrum für Künstliche Intelligenz):
We present how the mathematical semantic wiki SWiM has been enhanced towards support for editing content dictionaries (CDs) in the semantic markup language OpenMath.
The ongoing revision of the OpenMath CDs for the 3rd version of the standard has motivated several enhancements to the SWiM user interface: a structural editor for CDs and their most common elements, particularly addressing notation definitions for symbols, the integration of a visual OpenMath formula editor, and a form-based editor for metadata.
We show how OpenMath CDs imported from the filesystem or a Subversion repository are split into handy fragments that are convenient to edit and navigate, and reassembled on export.
We present a search engine for mathematical formulae. The MathWebSearch system harvests the web for content representations of formulae and indexes them with substitution tree indexing. In version 0.4 we have parallelized and distributed the search server and augmented the web interface with a new JavaScript-based visual editor for content math formulae. Furthermore, we have extended the query language by generalization, variants, unification, and text search facilities, which can also be mixed.
Our experiments show that this architecture results in a scalable application.
In this paper we describe several existing knowledge representation formats for interactive exercises and how these address the representational needs of mathematical exercises. The paper also provides an overview of existing tools that support these formats such as players, rendering exercises and the role of mathematical services assisting these players. Since most of the developers of this family of languages have the same goal, it is now more possible than before, to reach a common representation format. Having this in mind, we discuss features, limitations and the interoperability between them.
Interactive exercising is one of the major ingredients of technology-enhanced learning. It reaches its full potential only, when appropriate feedback is given to the learner. This paper describes a principled approach for representing and processing interactive exercises in ActiveMath. This approach relies (1) on a modular architecture of the exercise player, (2) on a separation of different types of knowledge that have to be handled to generate feedback, and (3) on a generic representation of interactive exercises.
This document describes the design and implementation of a part of the e-Learning system ActiveMath, the exercise sub-system, that was done completely by the report author.
The main goal of this system is to facilitate reuse of both the software components and the exercise content by clear and strict separation of functionality.
It consists of a user interface mediator, that handles the interaction with the user (display of questions and feedback, and parsing of the answers), an answer evaluator/diagnoser, that classifies the answer for choosing the adequate feedback, an exercise generator, that produces the exercise content as needed (such as feedback content based on the diagnosis done by the answer evaluator), and an interaction manager that orchestrates all of them.
The exercises are described by an ``interaction graph'' that is traversed by the interaction manager. The answers from the user are parsed into OpenMath expressions that can be evaluated internally (by the evaluator/diagnoser) or, when required, by an external program such as a Computer Algebra System (CAS) with OpenMath support.
The input parsers implement a variatey of syntaxes similar to those of the Computer Algebra Systems Yacas, Maxima, Axiom, Maple™, Mathematica®, MuPAD, Derive, and REDUCE. The intention is that users already familiar with any of those systems can use ActiveMath without having to learn yet another syntax.
Annotating mathematical knowledge with semantics has obviously become of a major importance for systems dealing with mathematical knowledge management. We investigate various possibilities for authors to produce semantically annotated mathematics using existing general purpose editors such as OpenOffice[2] and TeXmacs[3].
We use the semantic markup language OMDoc[1] for the representation of mathematical knowledge. OMDoc is an XML language which is an extension of an OpenMath standard for representation of mathematical formulas. It classiffies the items of mathematical knowledge in deffinitions, axioms, theorems, lemmas, corollaries, proofs and other types of conceptual markup needed for building the ontology of mathematical knowledge.
Annotating mathematical documents with semantics is a tedious process, since authors have to provide an amount of additional annotations to their documents. We have been investigating different styles of authoring tools that can help authors not familiar with XML languages, since for those editing the XML document directly is a non trivial and expensive process.
We consider two different styles of WYSIWYG editors: OpenOffice which is the open source version of an advanced office program able to import and export Microsoft Office documents and TeXmacs, macro-based editor combining some features of Emacs and LaTeX. Each of these editors have their pros and cons in usability for annotating the documents with semantics and their architectural particularities impose different technical approaches and restrictions.