A Study on Improving Teaching of Geometry with an Emphasis on Cooperation across Primary and Secondary Schools

1.本研究的目的是提出改进几何教学的建议。我们发现在六年级学生中能够准确画出素描的学生寥寥无几，这说明了在教学中对三维图形进行投射概念处理的重要性。此外，我们还分析了英国《国家课程标准》和《国家算术策略》中关于形状、空间和措施的内容，并阐明了英国小学低年级开始教授数字对称性的特点。我们把小学和中学的十二年分为三个阶段，第一阶段是从一年级到四年级，第二阶段是从第五到第八，第三阶段是从第九到第十二。然后，我们提出了17条改进几何教学的建议，强调中小学之间的合作；我们在这里展示了17个项目中的8个是针对第二阶段的。(3)第二阶段要了解平面图形的同余和相似性。(4)从第一阶段开始接近对称的形状。(5)理解图形的概念，并通过学习图形的测量来提高他们对图形的兴趣。(6)更加重视素描和阅读。(7)通过二维投影、横截面和展开来积极地分析三维图形。(8)使用平行线和角度，即第七年多边形的角度和；这些都放在了论证的内容中。(9)了解实际演示和证明方式的区别。(10)更加重视先建构，再证明。

1. The purpose of this research is to recommend improving teaching of geometry.2. We find there are few students who can draw a sketch exactly in sixth grade, and indicate the importance of teaching projective idea treated 3-D shapes. Moreover, we analyze the contents of Shape, space and measures in The National Curriculum for England and National Numeracy Strategy, and clarify, for example, the characteristic the symmetry of figures are taught from lower grade of primary school in UK.3. We divide twelve years to three periods across primary and secondary schools ; the first period is from year 1^<st> to forth, the second is from fifth to eighth, and the third is from ninth to twelfth. Then, we propose 17 recommendations for improving teaching of geometry with an emphasis on cooperation across primary and secondary schools; we here show eight items of 17, which are for the second period.Pupils should be taught to(3) understand congruence and similarity of plane figures in the second period.(4) get close to shapes of symmetry from the first period.(5) understand the concepts of figures, and raise their interest about it through learning the measures of figures.(6) be attached greater importance to drawing and reading sketches.(7) analyze 3-D shapes positively through 2-D projections, cross-section, and expanding.(8) use parallel lines and angles, the angle sum of a polygon in year seven; these are placed in the content of reasoning.(9) understand the differences between the way of practical demonstrations and proofs.(10) be attached greater importance to constructing first, and then proving.