Michael H. G. Hoffmann

A crucial problem of conflict management is that whatever happens in negotiations will be interpreted and framed by stakeholders based on their different belief-value systems and world views. This problem will be discussed in the first part of this article as the main cognitive problem of conflict management. The second part develops a general semiotic solution of this problem, based on Charles Peirce's concept of "diagrammatic reasoning." The basic idea is that by representing one 's thought in diagrams, the conditions that determine interpretations can become visible, we can "experiment" with them, and we can change them eventually. The third part, finally, focuses on a concrete tool, called Logical Argument Mapping , that can be used in conflict management to perform such diagrammatic reasoning and to cope with the cognitive problems discussed in the first part. The Israeli-Palestinian conflict on the sovereignty over Jerusalem will be used as an example to show how LAM could work in practice

The paper aims to show how by elaborating the Peircean terms used in the title creativity in learning processes and in scientific discoveries can be explained within a semiotic framework. The essential idea is to emphasize both the role of external representations and of experimenting with those representations , and to describe a process consisting of three steps: First, looking at diagrams "from a novel point of view" offers opportunities to synthesize elements of these diagrams which have never been perceived as connected before. Second, by forming those observed syntheses to "new objects" of thinking, and by signifying these objects through new signs , new means of thinking and acting are created . And finally, by applying these new means – in proofs, for instance – the "intelligibility" of new discoveries and their power to explain problematic facts must be tested

In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's own representations of mathematical problems. As a paradigmatic example, we apply a Peircean semiotic framework to answer the question of how students learned the concept of "distribution" in a statistics course by "diagrammatic reasoning" and by developing "hypostatic abstractions," that is by forming new mathematical objects which can be used as means for communication and further reasoning. Peirce's semiotic terminology is used as an alternative for notions such as modeling, symbolizing, and reification. We will show that it is a precise instrument of analysis with regard to the complexity of learning and of communication in mathematics classroom.

Different situations — like school and workplace — demand different forms of knowledge. Even more important, in particular for lifelong learning, are forms of knowledge we need for managing movements between those situations. To develop a better understanding of how to ‘navigate’ knowledge boundaries, this paper analyzes, firstly, interviews with scientists interpreting familiar and unfamiliar graphs. Our goal is to identify those forms of knowledge that should receive special attention in education. Secondly, the article elaborates — based on Peirce’s semiotics — an epistemologically reflected semiotic model to describe the role and conditions of knowledge necessary for crossing knowledge boundaries.

Abductive reasoning takes place in forming``hypotheses'''' in order to explain ``facts.'''' Thus, theconcept of abduction promises an understanding ofcreativity in science and learning. It raises,however, also a lot of problems. Some of them will bediscussed in this paper. After analyzing thedifference between induction and abduction (1), Ishall discuss Peirce''s claim that there is a ``logic''''of abduction (2). The thesis is that this claim can beunderstood, if we make a clear distinction between inferential elements and perceptive elements of abductive reasoning. For Peirce, the creative act offorming explanatory hypotheses and the emergence of``new ideas'''' belongs exclusively to the perceptive side of abduction. Thus, it is necessary to study the roleof perception in abductive reasoning (3). A furtherproblem is the question whether there is arelationship between abduction and Peirce''s concept of``theorematic reasoning'''' in mathematics (4). Both forms of reasoning could be connected, because both arebased on perception. The last problem concerns therole of instincts in explaining the success ofabductive reasoning in science, and the question whether the concept of instinct might be replaced bymethods of inquiry (5).