Elementary School Education in Rainforest Conservation and Reforestation in Mindanao, Philippines

A series of four interactive interdisciplinary (but based on science books0 for grades two through five were created to provide educational materials on tropical rainforests for elementary schools in the Philippines. The books were produced in conjunction with Philippine and American teachers, administrators, and science education consultants. They were then used and assessed for a year in actual classrooms in a variety of six Philippine schools in Mindanao. Comparative tests before and after using the materials were given to both teachers and students in participating schools. We observed highly significant measurable learning and improvements in understanding about rainforests. There was much variability in outcomes among the different schools. A highly significant general trend among students however, was for greater improvement (gain) for students who had lower pretest scores. That trend for individual students extended to the schools, which reduced the discrepancies between public rural mountain schools and schools in urban or city settings including a private city school

Finite-matrix formulation of gauge theories on a non-commutative torus with twisted boundary conditions

We present a novel finite-matrix formulation of gauge theories on a non-commutative torus. Unlike the previous formulation based on a map from a square matrix to a field on a discretized torus with periodic boundary conditions, our formulation is based on the algebraic characterization of the configuration space. This enables us to describe the twisted boundary conditions in terms of finite matrices and hence to realize the Morita equivalence at a fully regularized level. Matter fields in the fundamental representation turn out to be represented by rectangular matrices for twisted boundary conditions analogously to the matrix spherical harmonics on the fuzzy sphere with the monopole background. The corresponding Ginsparg-Wilson Dirac operator defines an index, which can be used to classify gauge field configurations into topological sectors. We also perform Monte Carlo calculations for the index as a consistency check. Our formulation is expected to be useful for applications of non-commutative geometry to various problems related to topological aspects of field theories and string theories.Comment: 25 pages, 2 figures v2: 2 figures added, version published in JHE