Suzukawa et al. (2008) found that Japan has unusual pattern of item difficulty among 13 countries and area (namely, Australia, Canada, Finland, France, Germany, Hong Kong, Ireland, Italy, Japan, Korea, Netherland, New Zealand and the United States) by making secondary analysis of PISA2003 data.  Following this research, Watanabe (2012) focused on the area of probability and statistics, and then mentioned that the items of outlier and sample collection have different patterns compared to other items thorough analysing PISA2003 data of the same 13 countries and area.  However, the data of PISA2012 has not been analysed to reveal the secular changes between PISA2003 and PISA2012.  

　　The aim of this study is to reveal the secular changes of the pattern of item difficulty that Japanese students have between PISA2003 and PISA2012 by making cross-national comparison with above 13 countries and area.  In order to consider the pattern of item difficulty of Japanese students, the method of multiple group item response theory is used to detect the differences of item difficulty between PISA2003 and PISA2012.   

　　Analysis revealed that the pattern of item difficulty of Japan does not have observable changes between PISA2003 and PISA2012 in whole.  Looking at common items between PISA2003 and PISA2012 to examine the pattern of item difficulty in more detail, one of the items of probability and statistics has remarkable change in only the result of Japan.  The results suggest that revised course of study has a gradual effect on students’ pattern of item difficulty.

　　The purpose of this study is to identify the characteristics of mathematics teachers’ noticing and its changes, to find out the factors for the changes of their noticing, and to develop teacher training programme for improving mathematics teachers’ noticing finally.  In this article, we examined the noticing of 9 elementary school teachers who participated a teacher training based on lesson study about the elementary grade three content “addition of fractions with same denominator” conducted at a national attached elementary school.  We conducted qualitative data analysis for the participants’ talks on their observations of two mathematics lessons in order to identify the characteristics of their noticing on the implemented lessons and students’ learning activities.   

　　As the result, we identified the characteristics of their noticing in terms of “students”, “lesson objectives”, “learning content” and “teacher” in the context of the lessons on “addition of fractions with same denominator”. In terms of “students”, their noticing was about the degree of learning achievement, students’ thinking process, and students’ expressions of their thinking.  In terms of “lesson objectives”, their noticing was focused on the aims and objectives of the conducted lesson, goal setting considering the whole teaching unit, and the content of textbook.  In terms of “learning content”, their noticing was related to the interpretation of fraction, the procedure of calculation, and the simplification from the meaning to the procedure on the addition of fractions with same denominator.  And, in terms of “teacher”, their noticing was on the review of previous knowledge, lesson objectives, outlook of learning, individual problem solving, group and whole discussion for problem solving, summary, and mastering and becoming proficient at learning content.   

　　In addition, we also examined and found out the factors of stimulating or improving their noticing in terms of “observations of real lessons and students learning”, “social interaction of teachers”, “infliences of instractors” and “knowledge, experience and expectations of teachers”.

　　The article mainly proposed the theoretical framework for continuous professional development of preschool teachers in early childhood mathematics education in Japan, utilizing the three components of theory and methodological perspectives: Legitimate Peripheral Participation (LPP), Pedagogical Content Knowledge (PCK), and the ALACT model. It also examined how the framework can successively depict teachers’ changes and growth for offering mathematical activities in practice. In this article, particularly focusing on PCK and ALACT model to examine how they can work, the authors qualitatively analysed the children’s mathematical activity regarding the comparison and measurement of various areas of rectangles by non-universal unit and the transcriptions of a teacher’s talks, followed by the analytical procedure through the interpretive phenomenological lenses. The analysis showed that the proposing frameworks could work to see preschool teacher’s professional development and some improved points for the future practices.

　　The purpose of this paper is to understand how much the elementary school students of the second grade can solve through the problem which Takahashi stated in 2015.  Furthermore, in order to achieve the suggestion of teaching, we also conducted lessons about the relationship between two quantities based on the representation written by children.  

　　In this paper, the purpose was achieved through the following ３ steps.  First, the examination designed from the viewpoints of precious research was held.  After that, the teacher practiced the lesson based on the results of the first examination.  Secondly, the second examination and the lesson were held as above.  

　　At last, we held the final inquiry and compared the whole results through the analysis framework which composed two division, score, and level designed by the author.   As for the framework, the division of score is evaluated according to the 3-grade system.  We conducted three symbols, ◎, △, ×, to represent the children’s attending.  The first grade, ◎ is for each correct answer. The second grade, △ is for the answer including some mistakes.  The last grade, × is for no solution.  The division of the level of their pictures is used to evaluate the answer according to the 4-grade system.  We considered that if the solution written by children was confirmed by verbal representation and geometric representation.  As the result, the successful problem solving and the effectiveness were confirmed.

　　This study examines the applicability of inferentialism to mathematics education in Japan.  Inferentialism, which R. Brandom originally proposed in pure philosophy and J. Derry introduced to educational contexts, has been applied to mathematics education, and especially in statistics education.  In this paper, we identified four characteristics of Derry’s inferentialism: 1) it denies representationalism, namely, conceptual platonism; 2) it entails that understanding a concept is defined as possessing practical know-how for making inferences and that a process of making knowledge explicit is interpreted as a process of conceptualization; 3) it is assumed that using a concept requires us to understand many other concepts from a holistic perspective; 4) judgements in learning environments are considered important opportunities for learning.  We then drew two findings from these characteristics: 1) inferentialism is highly consistent with mathematics education research in Japan, which focuses on know-how in learning environments; 2) we should value not only mathematical (context-free) concepts but also context-specific concepts in both research and practice.  

　　Considering these findings, we analyzed the ski jump problem from the 2012 National Assessment of Academic Ability, a well-known statistical word problem.  We found that the problem lacked information necessary for determining a unique optimal solution.  Our findings imply that teachers should consider how we treat non-statistical concepts in statistical word problems and how we teach statistical activities.  As a future research task, we propose to contrast inferentialism with existing epistemologies in mathematics education such as constructivism or the theory of commognition.

　　This study aims to propose a perspective for describing and analyzing mathematics teachers’ reflection focusing on mathematical knowledge.  For this purpose, the notion of praxeology which is used within the Anthropological Theory of the Didactic (ATD) is employed for modelling both teachers’ activity and their knowledge.  In this paper, we conduct following two research tasks: 1) Setting up the perspective from the theoretical implication of praxeology, especially of paradidactic praxeology; 2) Validating the perspective through a case study which analyzes a post-lesson discussion by preservice teachers.  For the first task, we focus on relationships between different kinds of praxeologies: mathematical praxeology, didactic praxeology, and paradidactic praxeology.  As a rule, didactic praxeology refers to knowledge and activities for elaborating mathematical praxeology, and, paradidactic praxeology refers to that of didactic praxeology.  Thus, the subjects of paradidactic praxeology can be described as didactic praxeology (or elements of that).  Similarly, mathematical praxeology can be described as the viewpoints of that paradidactic practice.  For the second task, we use the lesson plan and the transcription of the post-lesson discussion as empirical date.  As a result, we could get a figure which showed the structure of knowledge constructed in the post-lesson discussion (Fig. 2). Moreover, the analysis suggested that persistence in practical aspects was one of the characteristics of reflection by preservice teachers.  With reference to validity of the analytical perspective, the case study showed its usefulness for considering relationships between praxeologies and elements of that.  Particularly, the value of the analytical perspective consisted in availability for considering not only observed phenomenon but also non-realized phenomenon.