find why we cannot see obvious relationships between entrance examination
scores and academic records in universities in mathematics subjects,
we have investigated three testing records of the placement test,
the learning check test, and term examinations. First, irreducible
probabilistic fluctuations of academic scores are analyzed by using
the placement test and term examinations. As a result, we have
noticed the magnitude of irreducible probabilistic fluctuations.
Next, we have compared the score distributions of the three testing
scores in equally split classes using the placement test scores.
In testings in this paper, unlike the ordinary testing style of
the description type in mathematics subjects, the multiple choice
type testings were performed. Then, we have found two important
things. One is that we can eliminate teacherfs evaluation biases.
The other is that the studentfs academic growth could be seen more
clearly using the multiple choice type testing than using the description
type testing. In addition, we have proposed a fundamental equation
on studentfs ability including irreducible probabilistic fluctuations.
answer rate, item response theory, irre- ducible probabilistic
fluctuation, evaluation bias, description type testing, multiple
choice type testing, academic growth, ability equation, learning