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这是一种屡见不鲜的现象:一个具备良好基础和数学能力的学生,为解答一个数学试题或课本上的习题大感困惑,因为这些习题或条件不足,或叙述不清,……,质言之,不符合科学性的要求。十年动乱,祖国语言不纯的现象有所发展,同样的,在数学读物和各种考试中。题目违反科学性要求的现象也有所发展。笔者工作的教学研究机构,每年都要收到许多来信,询问某些有争议的习题,或者对课本中的习题提出质疑。人们还记得,一九八○年全国高等学校招生理科数学第九题,由于措词不清,曾在全国范围内引起相当广泛的不同解释,该题为“抛物线的方程是y~2=2x,有一个半径为1的圆:圆心在x轴运动,问这个圆运动到什么位置时,圆与抛物线在交点处的切线互相垂直。”对上面加着重号的句子,按命题人的原意是“圆与抛物线在同一交点处的切线互相垂直,”由于缺少“同一”两字,以黑龙江省为例,大约有15％的考生无可责怪地理解为“在一个交点处圆(或抛物线)的切线与另一个交点处的抛物线(或圆)的切线互相垂直。”对这个试题的详评可在文[1]、[2]中读到,恕不在此赘述。
This is a common phenomenon: a student with a good foundation and mathematics ability is very puzzled to answer a mathematics problem or a problem in a textbook, because these problems or conditions are insufficient or unclear,... , does not meet the scientific requirements. Ten years of turmoil, the phenomenon of imperfect language in the motherland has developed, as well as in math readings and examinations. The phenomenon of violation of scientific requirements has also developed. The teaching and research institution that the author works for receives many letters every year, inquires about some controversial exercises, or questions the exercises in textbooks. People still remember that in the 1980’s, the National Mathematical Physics Mathematics Question 9 of the National Institute of Higher Learning had caused quite a wide range of different interpretations due to unclear wording. The title of the parabolic equation is y~2=2x. There is a circle with a radius of 1: the center of the circle moves in the x-axis and when asked where the circle moves, the tangents at the point of intersection of the circle and the parabola are perpendicular to each other. “For the sentence with a heavy sign above, the original intention of the proposition is ” The tangents at the same intersection point between the circle and the parabola are perpendicular to each other. “Because of the lack of the word ”same,“ in Heilongjiang Province, approximately 15% of the candidates unexplainably interpreted it as ”circular (or parabolic) at an intersection point." The tangent line is perpendicular to the tangent line of the parabola (or circle) at another intersection.” A detailed review of this question can be read in [1], [2], and will not be repeated here.