Finite field computation technique for exact solution of systems of linear equations and interval linear programming problems

An error-free computational approach is employed for finding the integer solution to a system of linear equations, using finite-field arithmetic. This approach is also extended to find the optimum solution for linear inequalities such as those arising in interval linear programming probloms.

Complimentary collaborations: Teachers and researchers co-developing best practices in art education

Australia is currently experiencing a huge cultural shift as it moves from a State-based curriculum, to a national education system. The Australian State-based bodies that currently manage teacher registration, teacher education course accreditation, curriculum frameworks and syllabi are often complex organisations that hold conflicting ideologies about education and teaching. The development of a centralised system, complete with a single accreditation body and a national curriculum can be seen as a reaction to this complexity. At the time of writing, the Australian Curriculum is being rolled out in staggered phases across the states and territories of Australia. Phase one has been implemented, introducing English, Mathematics, History and Science. Subsequent phases (Humanities and Social Sciences, the Arts, Technologies, Health and Physical Education, Languages, and year 9-10 work studies) are intended to follow. Forcing an educational shift of this magnitude is no simple task; not least because the States and Territories have and continue to demonstrate varying levels of resistance to winding down their own curricula in favour of new content with its unfamiliar expectations and organisations. The full implementation process is currently far from over, and far from being fully resolved. The Federal Government has initiated a number of strategies to progress the implementation, such as the development of the Australian Institute for Teaching and School Leadership (AITSL) to aid professional educators to implement the new curriculum. AITSL worked with professional and peak specialist bodies to develop Illustrations of Practice (hereafter IoP) for teachers to access and utilise. This paper tells of the building of one IoP, where a graduate teacher and a university lecturer collaborated to construct ideas and strategies to deliver visual arts lessons to early childhood students in a low Socio- Economic Status [SES] regional setting and discusses the experience in terms of its potential for professional learning in art education.