Watanabe (2019) revealed that the pattern of item difficulty of Japan does not have observable changes between PISA2003 and PISA2012 in whole by making international comparison.  Looking at common items between PISA2003 and PISA2012 to examine the pattern of item difficulty in more detail, one of the items of the area ‘uncertainty and data’ that related with probability and statistics has remarkable change of being easy item in only the result of Japan.  The results suggest that the revised course of study in 2008 has a gradual effect on the pattern of item difficulty.  Because this course of study is newly revised with the area ‘uncertainty and data’.  However, the students that took PISA2012 learned mathematics under the revised course of study in a period of its advanced implementation.  

　　The aim of this study is to verify the effect of the revised course of study in 2008 after its full implementation focusing on the area ‘uncertainty and data’ by analyzing PISA2015 data.  In order to consider the pattern of item difficulty in the area ‘uncertainty and data’, the method of multiple group item response theory is used to detect the differences of item difficulty between PISA2003, PISA2012 and PISA2015.   

　　The results revealed that the pattern of item difficulty in the area ‘uncertainty and data’ does not have observable changes among PISA2003, PISA2012 and PISA2015 in whole by making international comparison. However, focusing on common items, the item of the area ‘uncertainty and data’ that has remarkable change in the study of Watanabe (2019) became easer in the results of PISA2015 as well.  In conclusion, the effect of the revised course of study in 2008 is revealed that the specific item of the area ‘uncertainty and data’ become easer among PISA2003, PISA2012 and PISA2015.

　　The purpose of this paper is to construct the framework grasping collective mathematical understanding process (MUP).  Then, analysis and consideration of practical example is shown by them.  For this purpose, two big theoretical ideas are used; one is the transcendental recursive theory and other is the classification of mathematical representation register (MMR).  The framework capturing collective MUP is constructed by them. In addition, learner thinking can be divided into three semiotic ones.  They are semantic thinking, syntactic thinking, and pragmatic thinking.  The semiotics refined by Morris have been classified into three categories to analyze the semiotic process.  However, these are not only used to analyze of the symbolic process, but it is also possible to assume that humans think from a similar perspective when interpreting the sign.  On the other hand, when learners in a small group interpret, there are various types.  There are five main cases when classifying learner situations that appear during group learning; Individual-type, absorption-type, confrontation-type, agreement-type, idling-type.   

　　Taking into account a number of factors as described above, a framework describing a collective MUP was constructed.  Until now, PK model (Pirie and Kieren, 1994b) was able to capture only one-dimensional MUP of an individual, but the framework created in this paper can visualize two-dimensional MUP of a group.  By analyzing the practical case described, it was visualized the transition of the registers used in the group and the appearance of folding back.  From this aspect, the following features were found.  First, learners tend to use syntactic thinking to raise their level of mathematical understanding.  Second, if the group produces many agreement-type or absorption-type interpretations, it is possible to judge that a good group mind is working.  Third, semantic thinking tended to be heavily used when the conversion between registers occurred.

　　The aim of this article is to discuss a significance of mathematical thinking (MT) and computational one (CT) from a perspective of modern literacy and suggest the major roles of school mathematics education.  The authors have a standpoint that MT and CT are different modes of thinking; MT works when constructing an academic knowledge system, while CT brings forth when dealing with practical problems.  So, we could suppose that there is a mutually complemental relationship between MT and CT.  From this theoretical standpoint, we pointed out the varieties of meaning of computation by referring to a brief history of computation, computation instructed in school mathematics, and computer science.  As a result, computation is essentially a series of possible processing in an automatic manner.  Then, we characterized modern society from the three viewpoints: unavoidableness, implicitness, and agnosticism, which were drawn from the nature virtuality of modern society we identified. Computation is definitely a disembodied, technical operation, but recent data science takes humanity into consideration when simulating and making a useful model of phenomena.  That implies the importance of emotional aspects such as intention, creativity, crisis, aesthesis, and so on, when we think within various contexts.  So, we should form school mathematics education while appreciating the nature of mathematical and computational activity. 　 

　　Finally, we identified three dimensions of literacy: cognitive, material, and socio-cultural and suggested that school mathematics education should have the role to let students have enough experience reflecting a mutual relationship between mathematics and computation.  The authors described literacy having both individual, collective competence depending on a form of expression as a cultural product and an aggregation of knowledge permeating every part of our civilization.  As stating above, actual human activity involves emotion, so school mathematics education should encourage students behave as authentic mathematical and computational actors, rather than encouraging acquisition of some new competences.

　　The purpose of this study is to identify the characteristics of the processes of student valuing development and the influences of their teacher valuing on the students’ value formations in mathematics education in Japan. This study is conducted as a part of International Comparative Study “The Third Wave”. 

　　This paper shows the data analysis of questionnaire survey in Miyazaki prefecture using the questionnaire “What I Find Important (in mathematics learning) too” (WIFItoo) developed by “The Third Wave”.  The survey was conducted for 3 junior high school mathematics teachers and their students in Miyazaki prefecture.

　　Through the data analysis using the dimension “Mathematics educational values” in the conceptual framework “Values in mathematics education” developed by “The Third Wave”, the followings were found as common characteristics among the cases of the 3 teachers and their students: the sub-dimension Exposition in the dimension “Mathematics educational values” was shared by both teachers and students; and the sub-dimensions Ability, Hardship, Facts/Truths, Ideas/Practice and Creating were not shared by both teachers and students.  In addition, the following patterns were found as possible processes of student valuing development: 1) teacher has a valuing, students recognize that the teacher has the valuing, then the students also have the valuing; 2) teacher has a valuing, students do not recognize that the teacher has the valuing, but the students have the valuing; 3) teacher has a valuing, students do not recognize that the teacher has the valuing, then the students do not have the valuing; 4) teacher does not have a valuing, but students recognize that the teacher has the valuing, then the students have the valuing; 5) teacher does not have a valuing, but students recognize tha teacher has the valuing, however, the students do not have the valuing; and 6) teacher does not have a valuing, students do not recognize that the teacher has the valuing, then the students also do not have the valuing.

　　The purpose of this paper is to construct a framework and set viewpoints for understanding views of mathematics from the perspective of lifelong learning. Views of mathematics have originally been discussed in the context of students’ mathematics learning in schools and also in it of adults’ mathematics learning. The framework enabled to integrate these contexts and analyse individual views of mathematics in detail. The meaning of “mathematics” in lifelong learning can be classified into four categories. This is based on the two characteristics of the environment where people learn mathematics, and the time period of the learning. In the time-oriented category, in school means the period of elementary and secondary education, and out of school means the opposite. On the other hand, in the spatial category, in school means the student is under structured education, whereas out of school the student is not. 　

　　In addition, we identified the viewpoints of ‘person’, ‘role’, and ‘situatedness’ to analyse the individual views of mathematics. Further, in order to characterise the categories, we analysed these individual views on the categories using the viewpoints.