Computational understanding and manipulation of symmetries

Attila Egri-Nagy, Chrystopher L Nehaniv, "Computational Understanding and Manipulation of Symmetries", in Chalup S. K., Blair A. D., Randall M. (Eds) Artificial Life and Computational Intelligence ACALCI, First Australasian Conference, Newcastle, NSW, Australia, February 5-7 2015, Proceedings, Lecture Notes in Computer Science, Vol. 8955, 2015 © Springer International Publishing Switzerland 2015 Final, published version of this paper is available online via doi: 10.1007/978-3-319-14803-8_2For natural and artificial systems with some symmetry structure, computational understanding and manipulation can be achieved without learning by exploiting the algebraic structure. This algebraic coordinatization is based on a hierarchical (de)composition method. Here we describe this method and apply it to permutation puzzles. Coordinatization yields a structural understanding, not just solutions for the puzzles. In the case of the Rubik’s Cubes, different solving strategies correspond to different decompositions

Creating Your Own Symbols: Beginning Algebraic Thinking With Indigenous Students

Because mathematics education devalues Indigenous culture, Indigenous students continue to be the most mathematically disadvantaged group in Australia. Conventional wisdom with regard to Indigenous mathematics education is to utilise practical and visual teaching methods, yet the power of mathematics and the opportunities it brings for advancement lie in symbolic understanding. This paper reports on a Maths as Story Telling (MAST) teaching approach to assist Indigenous students understand algebra through creating and manipulating their own symbols for equations. It discusses effective Indigenous mathematics teaching, describes the MAST approach, analyses it in terms of Ernest’s (2005) semiotic processes, discusses its applications, and draws implications for Indigenous mathematics learning