Level: Beginner
This is an attempt to classify phenomena that occur continuously, but have no periodicity and whose scale is unpredictable. We targeted 36 major grammar items from junior high school English textbooks (6 in total) and tracked their frequency of occurrence since their introduction. Even if the frequency of these grammar items is measured for each lesson, it is impossible to generalize their trends, much less compare them with a common standard. In this study, by regressing a cubic curve on the distribution of cumulative frequencies, we identified the linear, quadratic, and cubic term coefficients and intercepts of the curve as new variables that explain the items in question. We performed a factor analysis of all items using these variables and obtained patterns of occurrence by arranging the factor scores in two dimensions. One is a convex cumulative distribution, in which the corresponding items occur frequently mainly at the time of introduction, but their occurrence decreases thereafter. The other is a concave cumulative distribution, in which the frequency of occurrence gradually increases after introduction. Many of the high-frequency items (universal items such as definite articles and past tense) introduced at the beginner's level fall into this category, and it is expected that English sentences will become more natural as learning progresses. When examining the arrangement of textbooks for each item, it was found that for many items the textbooks were concentrated in a narrow range or arranged along a straight line from the origin, and that the classification criterion of convex versus concave was a fundamental explanatory factor for this subject.
He has analyzed issues related to language learning and language measurement using statistical methods, primarily multivariate analysis, and has made recommendations for educational programs. His most recent publications include a paper on partial scoring methods for rearrangement problems using matrices (IntechOpen, May 2022). The research prior to the paper won the Best Presentation Award at ICICT 2019 (Hawaii). He has been a JMP user since version 2, and has learned a great deal from participating in multivariate analysis study groups.
