Usability of the front-end

If you consider to contribute to the development of ISAC, you might be interested not only in the (3) topics for development, but also in the  (1) practical effect and in some  (2) background information.

Practical effect of development
ISAC is an academic development project of mid-level size, where you can pursue academic interests as well as you can get familiar with professional development tools and processes --- and you will contribute to practical effects inevitably:

TU Graz, remarkably triggered by "STEOP" (Studieneingangs- und Orientierungsphase) in Telematik, identified an issue in education for engineering sciences: The first semesters introduce basic mathematics knowledge (where time is lacking for demonstration of how these basics are used in engineering) and higher semesters' advanced courses rely on these basics (where the basics of mathematics are forgotten frequently).

TODO



TODO

common and well known issue in math education, which extends to all science studies, polytechnic universities and even high-school mathematics.

Background information on development
ISAC is a prototype of an emerging generation of (educational) mathematics assistants based on the Theorem Proving (TP) technology of Isabelle. The prototype has been under construction at TUG already since 2002. The process of prototyping also clarifies theoretic foundations and contributes to the emergence of a new academic field “TP-based educational mathematics systems” addressed by two workshops presently, one focusing technology and one focusing education.

Characteristics of TP-based math assistants
By now the characteristics of the new TP-based generation has been clarified as follows:
 * 1) TP-based systems cover the whole range of mathematical problem solving: The range starts from formal specification of the problem (more or less prepared and hidden from the learner), continues through stepwise construction of a solution within a logical context and finishes with an automated proof that the solution found fulfills the post-condition of the specification.
 * 2) TP-based systems have all underlying mathematics knowledge in a human readable format: Following the LCF-paradigm [GMW79] this knowledge is mechanically proved from “first principles”; thus this knowledge is structured by deductive aspects in analogy to comprehensive textbooks in mathematics, but with links which can be followed interactively. ISAC experiments with separate structures for specifications (application-oriented aspect) and for methods (algorithmic aspect).
 * 3) TP-based systems allow to check user input generously and reliably: Given a logical context from Pt.1 above, user input establishes a proof situation: Can the input step be derived from the context ? TP technology is the most general technology to answer such a question reliably. The automation of such checks by TP technology enables to model stepwise problem solving in software. (Without TP technology the check for each step required separate code, which cannot be accomplished for variants desirable in problem solving.)
 * 4) TP-based systems can combine deduction and computation such that automated generation of next steps is possible [Neu12] in general at any step of problem solving. So we can expect such a system to suggest a next step if the learner gets stuck at some step in problem solving. “Automated generation” of these steps requires one program describing the solution of the respective problem class, a program written in an emerging kind of TP-based programming language. Lucas-Interpretation of such a program can cope with a very wide range of variants of user input within steps towards a solution of the respective problem class.

Footnotes reference the TP-based programming language and Lucas-Interpretation.

Challenges for cooperation with Cognitive Science
Given the above features, TP-based systems have the potential to tackle a kind of questions which are out of reach for systems like CAS (Computer Algebra Systems), DGS (Dynamic Geometry Systems) and Spreadsheets, the most general tools available for the construction of educational systems. Here are some examples drawn from early work on dialogs in ISAC: the formula resulting from rule application ? The rule at which level (elementary, a whole simplifier, etc) ?
 * Which parts of the next step shall be presented to the learner, the rule to apply or
 * Which part of formula or rule should be omitted ? Does the current step concern difficulties encountered (error patterns) in previous sessions of the individual learner, or in the respective course ?
 * In which situations is the learner allowed to request a next step ? During assessment sessions (written exams, etc) learners won’t be allow in general, but how establish a continuum between learning and evaluating ?
 * How can the wealth of research and experience in didactics of mathematics concerning instructional design and design of learning scenarios made be fruitful for user modeling and dialog design ?
 * How can the wealth of research and experience in didactics of mathematics concerning misconceptions made be fruitful for dialog design ? Error patterns ?
 * Etc.

Such questions are not meant to be tackled by software engineers; serious approaches to such questions can only be expected by experts in cognitive and educational science. These experts have a rich set of authoring tools at their disposal for creating instructional software without expertise in software engineering. Such tools are widely used for various topics in academia and in schools, in business and in military. But there are no such authoring tools for stepwise problem solving in mathematics an in applications of mathematics to engineering problems. So the essential goal for the present phase of development is formulated as follows:

Prepare the rule-based system and the logger in ISAC such that non-programmers can start experimenting with dialog design.

This goal has successfully been tackled in a joint effort of two Baccalaureate Theses, one introduces a rule-based system for future design of dialogs the other establishes logging of high-level steps for approaching learning histories

Topics for projects and theses
See Development_Front-end