Rating Points for the Logicality of Mathematical Statements based on the Ratings by Mathematicians

K. Kawamoto, N.H. Arai, and Y. Ishigami (Japan)

Keywords

Logical thinking ability, mathematical statements, automated rating system, learning assesment, elearning

Abstract

There are a number of automated rating applications for student essays. However, if we are going to rate mathematical statements written in Japanese, there is no rating applications available at the moment. This study shows what statements are highly rated by mathematics experts, what characteristics such statements have, and what can be used as the points and standards of objective rating: one can rate a statement by looking at the numbers of conjunctions, logical steps, characters in mathematical equation and commas, or whether or not there is any algorithm included in the statements. By using these rating points, it is possible for non-experts or automated rating systems to rate students' statements with a certain accuracy. The authors have built a protitype of a rating application that has the rating points implemented, and tested the software with similar examples and widely-acknowledged mathematical statements to prove that the rating points and standards are valid.

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