Level: Beginner
[Presenter] Kazuo Amma, Professor, Faculty of International Liberal Studies, Dokkyo University
[Presentation summary] This is an attempt to classify events that occur continuously but have no cycle and whose scale is unpredictable. Thirty-six major grammatical items in junior high school English textbooks (6 items in total) were targeted, and the frequency of appearance after the introduction was tracked. Even if the frequency of these grammatical items is measured for each lesson, it is impossible to generalize the tendency, and it is impossible to compare them with a common standard. In this study, by regressing a cubic curve on the cumulative frequency distribution, we identified the linear, secondary, and cubic term coefficients and intercepts of the curve as new variables to explain the item. A factor analysis was performed on all items using these variables, and the patterns of occurrence were obtained by plotting the factor scores on a two-dimensional plane. One is a convex cumulative distribution, in which the corresponding item occurs frequently at the time of introduction, but after that, the occurrence decreases. The other one is a concave cumulative distribution, which gradually increases in frequency after its introduction. This includes many of the high-frequency items (universal items such as definite articles and past tenses) that are introduced at the beginner's level, and it is assumed that students will approach natural English as they progress in their studies. Looking at the distribution of textbooks for each item, many textbooks are concentrated in a narrow range or are arranged along a straight line from the origin. It turned out to be an explanatory factor.
[Profile of the presenter] I have analyzed problems related to language learning and language measurement using statistical methods centered on multivariate analysis, and made proposals for educational programs. As a recent work, there is a paper on a partial scoring method for permutation problems using matrices (IntechOpen, May 2022). The research in the previous stage of this paper was awarded the Best Presentation Award at ICICT 2019 (Hawaii). I have been a user of JMP since version 2, and have learned a lot from the multivariate analysis study group.
