@article{oai:miyazaki-u.repo.nii.ac.jp:00000176,
 author = {Uda, Hirohumi and 宇田, 廣文 and Uda, Hirofumi},
 journal = {数学教育学研究紀要},
 month = {Mar},
 note = {In the preceding paper I investigated on understanding equivalence of fractional numbers for university students and discussed levels of understanding this in three viewpoints - properties of fractional numbers, functions of fractional numbers and calculations of fractional numbers -. Many of them interpreted equivalence of factional numbers by means of reduced representatives. Moreover, I showed the difference between mathematical definition of equivalence of fractional numbers and introductions of ones in a primary school.
In this paper, therefore, investigate and discuss the following matters.
(I) I investigate levels of understanding inequivalence of fractional numbers written by reduced representatives for university students who belong to an elementary education teachers training course.
(2) I discuss the difference between equivalence and inequivalence of fractional numbers from mathematical viewpoints and educational ones. The outline of conclusions is as follows.
(i) Main methods of interpretations by university students on inequivalence of fractional numbers by reduced representatives are reduction to common denominator, a decimal representation and geometric representations. This implies the difference between interpretations of equivalence and ones of inequivalence of fractional numbers.
(ii) Interpretations on inequivalence by means of indirect comparisons are troublesome, because inequivalence is not an equivalence relation. Therefore, guidance of interpretations of direct comparisons is important for children.
(iii) Understanding equivalence (or inequivalence) of fractional numbers from the viewpoint of mathematics is not equal to understand that from the viewpoint of mathematical education. In this way, understanding mathematical concepts from these two viewpoints differs a little in that methods of definitions of mathematical concepts are different. Therefore, it is requisite to study mathematical contents which imply neither "mathematics" nor "educational conceptualizations".},
 pages = {123--128},
 title = {分数の相等性II-大学生の意識を中心に-},
 volume = {17},
 year = {1991},
 yomi = {ウダ, ヒロフミ}
}