Integrative Methods of Inquiry in Education: SYMMETRY


Symposium has as its main goal an exchange of views and opinions, sharing knowledge and discussion of the methods to integrate curriculum helping to educate new generations in the manner propagating a holistic world view. Mathematics and increased level of abstraction are natural sources of the methods of unification of knowledge and of curriculum. The concept of symmetry provides an example of the program of unification of the methods of inquiry across virtually all disciplines of human intellectual activity. Whether successful or not, it can serve as a starting point for the discussion of the curricular reforms. We invite contributions to the discussion in the form of oral presentations of relevant papers.

Another symbol of our time is losing its meaning. Globalization was supposed to bring together entire human population in a coordinated effort to eliminate poverty, dangers of wars, destruction of environment, to promote sustainable economic development and to generate wealth and happiness accessible to all. Recent political events show that instead the majority, or at least a large part of human population prefers to mend neglected fences, to build walls separating nations and to maintain traditional divisions. We live no more in the era of globalization, but rather the world enters the era of fragmentation.

The dangers of fragmentation was recognized in the past, in particular as a result of reflection on the atrocities of the Second World War. Political, economic, civilizational fragmentation was identified as a source of tendencies to use power and violence instead of discourse and negotiation in resolving conflicts of interests at inter- and intra-national level. This fragmentation was in turn diagnosed as a result of the dissociation of culture into domains of specialization. Although C. P. Snow was not the first who presented this diagnosis, he was the most successful in its propagation and popularization, and his vision of the separation of the drifting apart Two Cultures (humanistic and techno-scientific) became a symbol of the problem. There is no doubt that this separation was not reversed in the following decades in spite of many efforts, including curricular reforms, and the fragmentation is now deeper, wider and more dangerous.

There are many reasons why educational reforms failed in the bridging of the Two Cultures, but without doubt the most important was a naïve conviction that the mandatory participation in classes presenting both cultures would suffice. Thus, students may learn about the different perspectives on the problems of the world developed in a variety of disciplines belonging to different fragments of human inquiry, but it does not mean that they will automatically gain a consistent, holistic world view, especially when their teachers do not have one. We have to develop a new holistic methodology of inquiry and to use it in our (teacher’s) scholarly activity, and only then we can propagate a unified vision of the world among students.

Symmetry became a universal intellectual tool in practically all techno-scientific disciplines and remains a foundation for their cohesion. It became a central concept in the humanistic inquiry at the time when structuralism conquered intellectual world, but lost its prominent position, except as a target of common attacks. This reversal of interest did not inflict applications of geometric symmetry studies in art, but rather there was decline in support for using symmetry as a general intellectual tool for the analysis of creative processes in the humanities.

Only very recently there is a revival of the interest in its methods and increased recognition that symmetry was more a metaphor than a methodological tool in the works of even most accomplished propagators of humanistic structuralism of the past. Thus, the fact that philosophers of humanistic orientation prefer to present themselves now as belonging to “post-structuralism” cannot be used as an argument that all what symmetry concept could offer to the humanities is already known or even that a consistent, mature methodology based on the concept of symmetry was ever developed and effectively applied in this domain.

The symposium is intended as a forum for the discussion of the role of symmetry in the task to integrate curriculum and of pedagogies necessary to implement its integrative power. However, we invite contributions presenting other ideas of integration of curriculum, in particular the methods to employ mathematics for this purpose.

The non-exhaustive list of topics of special interest for the discussion and presentation at the symposium is as follows. For each topic pedagogical issues are of specific significance.