Conceptual knowledge discovery and data analysis

In this paper, we discuss Conceptual Knowledge Discovery in Databases (CKDD) in its connection with Data Analysis. Our approach is based on Formal Concept Analysis, a mathematical theory which has been developed and proven useful during the last 20 years. Formal Concept Analysis has led to a theory of conceptual information systems which has been applied by using the management system TOSCANA in a wide range of domains. In this paper, we use such an application in database marketing to demonstrate how methods and procedures of CKDD can be applied in Data Analysis. In particular, we show the interplay and integration of data mining and data analysis techniques based on Formal Concept Analysis. The main concern of this paper is to explain how the transition from data to knowledge can be supported by a TOSCANA system. To clarify the transition steps we discuss their correspondence to the five levels of knowledge representation established by R. Brachman and to the steps of empirically grounded theory building proposed by A. Strauss and J. Corbin.

Analysis of applications and of conceptions for an application-oriented mathematics instruction

In connection with the (revived) demand for considering applications in the teaching of mathematics, various schemata or lists of criteria have been developed since the end of the sixties, which set up requirements about closeness to the real world or about the type of mathematics being used, and which have made it possible to analyze the available applications in their light. After having stated the problem (in section 1), we present (in section 2) a sketch of some of the best known of these and of some earlier schemata, although we are not aiming for a complete picture. Then (in section 3) we distinguish among different dimensions.in the analysis of applications. With this as a basis, we develop (in section 4) our own suggestion for categorizing types of applications and conceptions for an application-oriented mathematics instruction. Then (in section 5) we illustrate our schemata by some examples of performed evaluations. Finally (in section 6), we present some preliminary first results of the analysis of teaching conceptions.