VISUAL IMAGES AS EDUCATIONAL MATERIALS IN MATHEMATICS     

Kazutoshi Aso 《Community College Journal of Research & Practice》2013,37(5-6):355-360

In general, students in school learn mathematical concepts by words. Some mathematical concepts, however, are difficult to understand by words. This is especially true of some of the more complicated concepts in mathematics taught in higher education. For students who are studying to become engineers, it is very important to understand mathematics intuitively. Ways must be found for them to learn mathematics that will promote intuitive understanding. We often find that a figure helps us understand mathematical concepts and provides important clues for solving problems. A figure may serve as a concrete expression of an abstract mathematical concept; it is a visual image of the mathematical concept. A visual image is a figure with no words but its title. The aim of this article is to introduce some visual images that are effective in mathematical education.  相似文献   

Pitching form determines probabilistic structure of errors in pitch location     

Masahiro Shinya  Shinji Tsuchiya  Yousuke Yamada  Kimitaka Nakazawa  Kazutoshi Kudo  Shingo Oda 《Journal of sports sciences》2017,35(21):2142-2147

According to recent motor control studies, it is important to know probabilistic structure of his/her own motor errors to choose an optimal motor plan (i.e., where you aim at) to maximise the expected gain. In this study, we questioned if pitching form determines the probabilistic structure of pitching errors in baseball pitchers. Eighteen collegiate baseball pitchers with various pitching forms including right- and left-handed overarm, sidearm and underarm throwers threw 100 pitches aiming at a target located 90 cm above the ground. Two dimensional distribution of pitch location was fitted by using bivariate normal distribution and 95% confidence ellipse was calculated. In order to quantify the pitching form, the direction of the throwing arm trajectory in frontal plane was calculated. The direction of the long axis was dependent on each participant’s pitching form (e.g., right overarm pitchers pitched along a right-up–left-down ellipse and left overarm pitchers pitched along a left-up–right-down ellipse). This was confirmed by circular correlation analysis (P = 0.98). These results suggest that different mechanisms, potentially errors in pitching mechanics and errors in ball release timing, might contribute to errors along the long axis and those along the short axis.  相似文献