山梨医科大学紀要 第6巻，034-043(1989)
入試に関する諸問題の数学的考察
平野光昭
今日、入試改革に関する問題は、国民の多くから関心を寄せられており、マスコミにも絶えず取り上げられているが、各方面から提出された正当な問題点には、前向きの姿勢で取り組むと同時に、正しい情報を提供することも大学の役目の1つであると考える。
入試に関連した問題は、教育学の問題として論じられることが多く、この場合は論ずる者の立場や基本的な考え方の相違により、平行線をたどることもあるが、数学の問題として論ずることにより、だれもが納得できる結論を得ることが多い。
ここでは、受験機会の複数化に関連した問題及び選抜時のウエートが入学後の成績との相関に及ぼす影響について、これまで著者らが研究発表してきたことを数学的側面からまとめて紹介し、入試教科・科目数と受験生の負担の問題及び得点修正の方法について、我々の考えを述べた。特に４節で論じたものは、他に全く類をみない発想に基づいており、問題提起となれば幸いと思っている。
キーワード：数学、確率・統計、入学試験、トレーニング効果、得点修正
A Mathematical Consideration of Some
Problems in Entrance Examination
Teruaki HIRANO
Today the reform of entrance examination is a matter of increasing interest for the great many people of our country. It has been always taken up by journalism and other mass-media. We think it one of the major tasks of the university to tackle positively with the judicious proposals raised up from every point of view and, at the same time, to provide sound informations for the applicants and for the public in general.
We once, in this Journal NO.2, discussed stochastically the problem of the so-called self-estimation system, pointed out its irrationality and proposed its abolition. Afterward many articles on entrance examination appeared from educational side, which naturally tends to be inconclusive according to their different view points. 0n the other hand, we have very few articles, for general readers, of the mathematical consideration on this field.
In this paper at first, we generally summed up, from the mathematical angle, our results of a series of studies on entrance examination : namely on (1) the pluralization of chances to apply for national universities, (2) two-step system for selecting successful students, (3) the rate of the so-called double-pass candidates and stochastics of the renunciation of admission, (4) the influence of weighing various subjects for the correlation between the results of entrance examination and those of graduation, and (5) the predicability, of the results in college from interview-evaluation in entrance examination.
Then we made here quite a fresh approach on (6) the relation between the number of subjects for entrance examination and the load of the applicants and (7) the method to revise the marks in the achievement test. The former one (6), especially, might call for due attention as a unique and entirely original idea which treats the problem theoretically from purely mathematical angle.
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