More Accurate Evaluation of Student’s Ability Based on A Newly Proposed Ability Equation

To 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 teacher’s evaluation biases. The other is that the student’s 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 student’s ability including irreducible probabilistic fluctuations.