中外数学教科书“用圆弧表示角”本质的比较研究

A Comparative Study on the Essence of“Representation of Angle with Arc”in Chinese and Foreign Mathematics Textbooks

中小学数学教科书中用圆弧表示角的方式尚未统一,无法凸显角的本质,主要原因在于“用圆弧表示角”的本质尚不明确.“用圆弧表示角”的本质为:用圆弧长度(圆弧所对半径相等)表示角的大小;带有方向(箭头)的圆弧,既可表示角的方向,也可表示角的优劣.对中国近百年(15个版本)教科书的比较发现:“用圆弧表示角”的编排逐渐统一,但角的静态定义不利于体现“用圆弧表示角”的本质;对“圆弧所对半径相等”的认识仍不清晰.国外教科书的情况也大致相同.提出建议:早早引入角的动态定义,统一圆弧所对半径,凸显角的本质.

Representation of Angle with arc in primary and secondary school mathematics textbooks has not been unified,and the essence of angle cannot be highlighted.The main reason is that the essence of“using arcs to represent angles”is still unclear.The essence of“using arc to represent angle”is as follows:arc length(the radius of the arc is equal)represents angle size;the arc with a direction(arrow)can represent both the direction of the angle and the minor and reflex angle.A comparison of Chinese textbooks over the past century(15 versions)found that the arrangement of“representation of angle with arc”has gradually become unified,but the static definition of angle is not conducive to reflecting the essence;it is still not clear that the radius of the arc is equal.The situation of foreign textbooks is roughly the same.The following suggestions are put forward:introduce the dynamic definition of angles early,unify the radius of arc,and highlight the essence of angle.