@article{oai:nittaidai.repo.nii.ac.jp:00001511,
 author = {島田, 功 and Shimada, Isao},
 issue = {1},
 journal = {日本体育大学大学院教育学研究科紀要, Bulletin of the Graduate School of Education, Nippon Sport Science University},
 month = {Sep},
 note = {Bishop (1988) pointed out the importance of research on values in mathematics education. Based on this idea, Shimada and Baba (2012) developed three “socially open-ended problems.”1 Shimada and Baba (2015) gave them to fourth graders, and examined how students appreciated others’ values2 and transformed their own values during a lesson. Furthermore, Shimada and Baba (2016) studied the issue of the long-term transformation of values and mathematical models across grades. As an extension of this long-term transformation, Shimada (2017) compared the values and ideas of mathematical models of elementary school students with those of university students. Similarly, Shimada and Baba (2018) compared the values and ideas of mathematical models of elementary school students with those of junior high school students. 
Following these studies, the aim of this paper is to study university students' values and ideas of mathematical models3 through comparison with those of elementary school students and junior high school students,4 and the research results reveal four characteristics. 
The first characteristic is that the ratio of students who express the value “fairness and equality” increases as they (elementary school students, junior high school students, and university students) became older (Table 1). This can be expressed statistically.5 The second characteristic is that the ideas of mathematical models of the university students are the same as those of the junior high school students, and there is no uniqueness in the university students (Table 2). However, there are some explanations according to “the perspective of a school teacher,” which can be slightly seen only among the university students (Table 4). The third characteristic is that “Generalization of scenes” tends to increase as students became older (Table 5). This can be expressed statistically.6 The fourth characteristic is that “Generalization of mathematical formulae” is not seen in junior high school students or elementary school students (Shimada, 2017), but is slightly seen only in university students, and it became clearer that this is particular to university students (Table 6)., Shimada and Baba (2012,2015)では，社会的オープンエンドな問題（的当て問題）を用いて，小学4年生の子ども達の社会的価値観や数学的モデルの実態とその変容（1時間の問題解決過程に於ける変容）を明らかにした。また，Shimada and Baba (2016)では，縦断的研究法を用いて小学4年生時の価値観と数学的モデルを記録しておき，その子ども達が6年生卒業時にどのような価値観や数学的モデルに変容しているかの比較研究を行った。更には，島田 (2017)では，小学生と大学生との価値観と数学的モデルの比較研究をし，Shimada and Baba (2018) では，小学生と中学生との価値観と数学的モデルの比較研究を行った。今回の研究は，これらの研究を更に発展させ，中学生と大学生の価値観と数学的モデルの比較を中心に，小学生と中学生と大学生の価値観と数学的モデルの比較をし，大学生の思考の特徴を明らかにすることを目的とした。研究の結果，4つの知見を得た。
①　平等・公平の価値観は小学生，中学生，大学生と年齢を重ねると増えていく傾向が見られる。これは統計的にも言える（表１）。
②　大学生の考える数学的モデルの背景となる考えは中学生と同じで大学生独特のものは見られないが（表２），中学生や小学生には見られない大学生特有の「小学校教師の視点」による説明が見られる（表４）。
③　場面の一般化は大学生になるにつれて増えていく傾向が見られる。これは統計的にも言える（表５）。
④　数式の一般化は，小学生同様（島田，2017），中学生にも見られず，大学生特有なものであることがより明確になった（表６）。, 原著論文},
 pages = {121--133},
 title = {Characteristics of university students' values and ideas of mathematical models through comparison with those of elementary school students and junior high school students},
 volume = {2},
 year = {2018},
 yomi = {シマダ, イサオ}
}