基于劣构问题的生物学课堂教学实践

劣构问题源于生活实际,是一种开放性问题,其解决途径具有不确定性。劣构问题的解决能有效地促进学生深度学习的发生,提升学生的生物学核心素养。本文基于对劣构问题的解读,以“生态系统中的物质能被循环利用”一节为例进行教学实践,以期为高中生物学课堂教学实践提供参考。

培养核心素养的弹力教学设计之哲学探析

精准设计并有效落实弹力的课堂教学,不仅是学生认识物质及其相互作用、形成物质观的重要载体,还是培养学生物理学科核心素养的有效时机。不同形变的刚柔相济特征,反映了多样性的物质观念,蕴含着多样性与统一性的辩证思想;相互作用的弹力、形变的对称性,体现了物体间相互作用的观念,蕴含着相互依存的矛盾观,是"宇称守恒"的具体体现;二力平衡求弹力的和谐稳定,反映了运动与相互作用的核心素养,蕴含着平衡和谐的哲学思想;胡克定律的大道至简,培养学生模型建构核心素养,蕴含着表象与本质的思辨。故有必要从哲学高度来全方位审视弹力的课堂教学设计,以期有效培养学生的物理学科核心素养,促使学生形成辩证的认识与探究自然的世界观,提升高中物理的教育教学质量。

Competition Numbers of Several Kinds of Triangulations of a Sphere

It is hard to compute the competition number for a graph in general and characterizing a graph by its competition number has been one of important research problems in the study of competition graphs. Sano pointed out that it would be interesting to compute the competition numbers of some triangulations of a sphere as he got the exact value of the competition numbers of regular polyhedra. In this paper, we study the competition numbers of several kinds of triangulations of a sphere, and get the exact values of the competition numbers of a 24-hedron obtained from a hexahedron by adding a vertex in each face of the hexahedron and joining the vertex added in a face with the four vertices of the face, a class of dodecahedra constructed from a hexahedron by adding a diagonal in each face of the hexahedron, and a triangulation of a sphere with 3n (n≥2) vertices.