Integrative Methods of Inquiry in Education: SYMMETRY
Symposium at Akita International University, Akita Japan
March 29-30, 2017
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. FULL SYNOPSIS
||Symmetry as a compression tool (Attila Egri-Nagy)
||Bacterial genome rearrangements and phylogeny in the Cayley graph (Andrew Francis, Western Sydney University)
||LUNCH (Cycling Terminal)
||Symmetry in Visual Arts (Kuniko Abe)
||The concept of symmetry in Physics (Yasushi Nara)
||WORKSHOP: Structuralism - Its prominent past, sad present, and bright future (Marcin Schroeder)
||Symmetry and Symmetry Breaking in Biology (Andy Crofts)
||Can we future-proof phylogenetic consensus trees? (Andrew Francis, Western Sydney University)
||LUNCH (Cycling Terminal)
||Reforming Calculus Textbook of High Schools and Colleges in Japan (Akihiro Yamamura, Mahito Kobayasahi, Akita University)
||The difference of class makes carelessness (Saaya Konno, Szilárd Zolt Fazekas, Akihiro Yamamura, Akita University)
||Symmetry in Serious Economics - Fixed points in functional spaces as a description of the economy (Nori Tawara)
||Identity, Equivalence, Orders and Similarities (Florent Domenach)
||Symmetry in Language (Shunsuke Nakata)
||Questioning Ontic Realism (Akiko Frischhut)
Professor Andrew R. Francis Director of Centre for Research in Mathematics,
School of Computing, Engineering and Mathematics, Western Sydney University, Australia
Abstracts (partial list)
- Symmetry in Visual Arts (Kuniko Abe)
In visual arts, through time, spiral or helical patterns fascinate creators in both the East and the West. These patterns represent continuity as seen in the growth processes of biological forms and organism. Physical world shows a plenty of spiral patterns, from gigantic curling arms of galaxies to twisted biological molecules, to be identified, measured, and finally defined in scientific terms. Spiral or helical is a type of symmetry. It is a special kind of similarity symmetry that simple mathematical formulas can reveal with a variety of beautiful shapes and images. Human creations are greatly inspired by these unbroken shapes, used as symbols by some, for magnifying the world, rational or spiritual. Exploring concrete examples in Art and Architecture, I will demonstrate how humans are capable to create new forms of spirals and helixes which have no counterparts in the natural world.
- Symmetry and Symmetry Breaking in Biology (Andy Crofts)
Symmetry in the living world is pervasive, yet conveying an engaging and relevant understanding of the mechanism by which it is generated, maintained, and broken, poses many pedagogical challenges. For example, to what extent must students first be introduced to stereochemistry – a subdiscipline of chemistry which addresses the chirality or “handedness” of molecules? This is an important question to consider, since ultimately the three-dimensional shape of organic molecules such as proteins, and the nucleic acids which encode them, plays a central role in determining their biological function.
In addition to addressing this and other questions related to which topics and depth of knowledge may be most appropriate to ensure the active engagement of students, this presentation will also seek to identify and present connecting points to other disciplines, as well as highlight aspects of symmetry that are especially interesting due to their profusion or scarcity in the natural world.
- Identity, Equivalence, Orders and Similarities (Florent Domenach)
- Symmetry as a compression tool (Attila Egri-Nagy) The precise notion of symmetry underlies most of modern mathematics and several other scientific fields (e.g. physics, chemistry). Despite its fundamental role, symmetry is easy to explain on an intuitive level. The traditional introduction to symmetry operations begins with studying geometrical transformations of regular polygons and polyhedra, then proceeds to the algebraic notation. This approach emphasizes the beauty aspect of symmetry. There is another way based on the notion of efficiency. Here we describe how the simple idea of relabelling elements of a combinatorial structure can make computer programs way faster, and how we can store the same amount of information in less space. For the argument, only the mathematical notion of function is assumed. Therefore, similarly to the geometrical approach, the ideas are accessible without abstract algebra background.
- Bacterial genome rearrangements and phylogeny in the Cayley graph (Andrew Francis, Western Sydney University) Group-theoretical and combinatorial approaches are finding more and more application in the biological sciences. For instance, modelling bacterial genome rearrangement operations as group actions on the space of all possible genomes provides a one-to-one correspondence between genome space and the group that acts. This means that a subset of genomes defines a set of points on the Cayley graph of the group, and a phylogeny on those genomes is represented by a Steiner tree on those points. In this talk I will describe this viewpoint and several related results. First, I will show how group theory can be used to calculate the “minimal distance” between genomes. Then I will describe a more nuanced view of the distance between genomes through a maximum likelihood estimate, and finally, I will describe some algorithmic results relating to the median problem for three genomes on the Cayley graph.
- Can we future-proof phylogenetic consensus trees? (Andrew Francis, Western Sydney University) Consensus methods are widely used for combining phylogenetic trees into a single estimate of the evolutionary tree for a group of species. But how robust are these methods to future information? If additional species are added to the original set of trees, will the expanded consensus tree simply be an expansion of the original consensus tree? In this talk I will formalise and answer this question. Joint work with David Bryant andMike Steel.
- The difference of class makes carelessness (Saaya Konno, Szilárd Zolt Fazekas, Akihiro Yamamura, Akita University) We can see some difference in the class between university and high school. The first difference is how often the classes are given. We have a class once a week in the university, but three or four times a week in high school. The second difference is how wide the classroom is, and how many students take the class in the same room. It is very different because the teacher cannot remember each student’s face and name, so some students are likely to take a class without being nervous, and skip it. It is bad. The third difference is how long the class has the review time. In high school, we often had the review time in the class, sometimes some of us had to write on the blackboard. I think these three things give the freshmen “carelessness”. It is natural to come up the difference, so the side which has to adapt it is the student side. I believe we can cover the differences to make use of the things we have been given until high school, so to enjoy studying the field which we are interested in, it is important to attend the class without accepting the “carelessness”.
- The concept of symmetry in Physics (Yasushi Nara) The concept of symmetry in physics serves as the most crucial concept, since natural laws are determined by symmetries. Fundamental forces in nature is deduced from the symmetries. Conservation laws in physics is also related to symmetry. One of the most important theorem regarding symmetry is known to be the Noether’s theorem (discovered in 1918) that tells us that if there is a symmetry, there is a corresponding conservation law. The first law of thermodynamics is known to be total energy conservation which according to Noether’s theorem, is the consequence of the invariance of the natural law in time. I will discuss how to introduce Noether’s theorem at an introductory physics course as a part of Liberal Arts education.
- Structuralism - Its prominent past, sad present, and bright future (Marcin Schroeder)
- Reforming Calculus Textbook of High Schools and Colleges in Japan (Akihiro Yamamura, Mahito Kobayasahi, Akita University) High school students learn elementary algebra and single variable calculus in Japan. Thus they already have advanced knowledge when they enter colleges. However, most of them loose their motivation to learn more calculus through college education. We consider that our conventional textbooks in Japan do not emphasize understanding of concepts in calculus, its modeling and applications in various fields such as natural and social phenomena and force students to devote too much time in exercising template problems. Accordingly, many students cannot relate the contents of calculus to science and technology even though these are their major areas. Turning our attention to education in the United States, we noticed that they experienced the so-called Calculus Reform and teaching of calculus was substantially scrutinized during 1990’s. Not like in the United States we have not changed teaching style of calculus in Japanese high schools and colleges and we now face difficulty in teaching calculus because the student’s ability varies in broad spectrum and slow learners cannot follow the traditional teaching style. Therefore, we have started to revise teaching method of calculus. Taking Calculus Reform into consideration, we complied a new college textbook, which can be an advanced teaching material in high schools as well. In this talk we report concepts, features and effects of our new textbook in our classroom uses and the future prospects.
Submission of Abstracts:
Please send your extended abstract of your presentation with 200-500 words formatted as a Word document or pdf as an attachment to e-mail message addressed to either of the members of Organizing Committee listed below.
Presentations may be of the work in progress. High quality papers with the content of broadly understood philosophical significance presented at the symposium may be published after peer review, but without publication fee, in the open access journal Philosophies (MDPI, Switzerland).
Deadline for abstract submission March 1, 2017
Language of the symposium: English
Important dates: Deadline for abstracts March 1, 2017
Notifications of acceptance within a week from submission.
Registration by e-mail: March 15, 2017
Symposium March 29-30, 2017
Venue: Campus of Akita International University, Akita city, Japan (detailed information will be sent to participants with the confirmation of registration)
No conference fee (we will request only for optional donations for coffee, tea, etc. at coffee breaks)
Kuniko Abe (kunikoabe)
Andy Crofts (acrofts)
Florent Domenach (fdomenach)
Attila Egri-Nagy (egri-nagy)
Yasushi Nara (nara)
Marcin J. Schroeder (mjs)
(email addresses all end with @aiu.ac.jp)