A Study on the Answer Type of Math Test

—Analysis Focusing on Answer Strategy in Free-Response Math Questions—

Abstract

For free-response questions (longer answer non-multiple choice questions) in mathematics, as long as logical reasoning leading to the correct final answer is indicated, independent of the particular choice of problem-solving strategy, the same evaluation (scores) is assigned. However, we all know, in the course of grading exams, that there are responses worthy of certain evaluation because of their mathematical thinking, decision making skills, and problem-solving skills, etc., even if the final solution is not correctly reached. In this research, to search for means of evaluation different from the usual “scoring”, focusing on problem-solving strategies, we reanalyzed students' answers in free-response questions by classifying them by their problem-solving strategies. As a result, we observed a stronger correlation between the choice of problem-solving strategy and overall academic performance in mathematics (e.g. scores on the mathematics section of the National Center for University Entrance Examination) than between the correct answer ratio of a particular question and overall academic performance in mathematics.