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Some global error bounds with undetermined parameters, which are not always valid, for the extended vertical linear complementarity problems (LCP) of CKV-type matrices and CKV-type B -matrices, are presented by Yan and Wang (Jpn. J. Ind. Appl. Math. 41:129–150, 2024). In this paper, new global error bounds for the extended vertical LCP of CKV-type matrices and CKV-type B -matrices are given, which depend only on the entries of the involved matrices. Numerical examples show that the new bounds are better than those provided in Zhang et al. (Comput. Optim. Appl. 42(3):335–352, 2009) and Wang et al. (Comput. Appl. Math. 40:148, 2021) in some cases. [ABSTRACT FROM AUTHOR]

The growing interest in classroom discourse reflects a wide recognition within the mathematics education community of the critical role of social interactions in the joint construction of mathematics knowledge. An extensive body of empirical and theoretical work has been undertaken in the last two decades to characterise the types of classroom talk that are conducive to learning. Yet, a key challenge remains for mathematics teachers to orchestrate whole-class discussions so that student responses to instructional tasks can be utilised to advance the disciplinary understanding of the entire class. This is especially the case when the mathematics task in focus is both open and cognitively challenging. Drawing upon a complementary accounts methodology, we analysed the Learner's Perspective Study (LPS) classroom and interview data from two classrooms in the United States and Japan to explore teacher orchestration of student responses to rich mathematics tasks. Significantly influenced by a body of literature on classroom microculture in mathematics education, this paper employed two complementary conceptual tools, coherence and meta-discursive rules, to develop an analytical framework for the purpose of exploring epistemic coherence of classroom discourse across diverse settings. The findings demonstrated that both teachers' orchestration of whole-class discussion supported the macro-structuring of students' experience at the level of topic coherence and contextual, organisational and conceptual connectedness, whilst the meta-narratives allowed the teacher to connect their goals for mathematics teaching and learning with the ongoing classroom activities and interactions. [ABSTRACT FROM AUTHOR]

Presents information on the symposium "New Trends in Computational and Optimization Algorithms (NTOC2001)," organized and sponsored by the Institute of Statistical Mathematics, Tokyo, Japan from December 9 to 13, 2001. Topics of the symposium; Introduction to papers presented at the symposium.

This paper reports on how the geometry component of the National Curricula for mathematics in Japan and in one selected country of the UK, specifically England, is interpreted in school mathematics textbooks from major publishers sampled from each country. The findings we report identify features of geometry, and approaches to geometry teaching and learning, that are found in a sample of textbooks aimed at students in Grade 8 (aged 13-14). Our analysis raises two issues which are widely recognised as very important in mathematics education: the teaching of mathematical reasoning and proof, and the teaching of problem-solving. In terms of the teaching of mathematical reasoning and proof, our evidence indicates that this is dispersed in the textbook in England while it is concentrated in geometry in the textbook in Japan. In terms of the teaching of mathematical problem-solving and modeling, our analysis shows that it is more concentrated in the textbook from England, and rather more dispersed in the textbook from Japan. These findings indicate how important it is to consider ways in which these issues can be carefully designed in the geometry sections of future textbooks. [ABSTRACT FROM AUTHOR]

Lesson study (LS), a teacher-oriented, student-focused professional development (PD) approach that originated in Japan, has spread globally. However, existing literature on the implementation of LS and its effectiveness provides inconsistent results, suggesting a need to review current research on LS. With a focus on LS in mathematics education, we examined 75 recent LS studies using Lewis's (ZDM Mathematics Education 48:571–580, 2016. https://doi.org/10.1007/s11858-016-0792-x) framework to understand how LS is implemented and the pathways by which LS can impact teaching practice and student learning. We found that new developments have taken place in LS implementation, although challenges persist throughout its process. Regarding the implementation of LS, even though the examined LS studies generally contained four phases (study, plan, teach, and reflect), we found many LS lacked a research question, and the study of teaching materials was sometimes invisible. Across phases, studies shared a consensus that it is most critical to focus on students' thinking and learning, yet reported challenges in maintaining this focus. In addition, the role of knowledgeable others (KOs) was recognized but inconsistently understood. Collaboration was also widely reported as a challenge. Finally, there were large variations in LS duration, with some LS implementing overly brief cycles. Regarding LS impact, the literature has more frequently reported changes in teachers' knowledge and beliefs and less frequently in curriculum, learning community/professional norms, teaching practice, and student learning outcomes. The above challenges reflect a need for culturally relevant systemic support for developing sustainable and large-scale LS. We suggest future directions for continued research and practice improvement. [ABSTRACT FROM AUTHOR]

Lesson study is a Japanese concept to improve teaching and learning mathematics through a particular form of activity in which a group of teachers works collaboratively to plan, implement, observe, and reflect on the proposed research lessons. Although lesson study is internationally acknowledged as providing key learning opportunities for teachers, there is limited information on post-lesson discussion and its contribution toward teachers' professional growth. This study has the aim of describing the key features of post-lesson discussions. An entire group of teachers at a public elementary school in Japan participated in three lesson study cycles. During the post-lesson discussion in each cycle, the teachers were invited to write down what they believed was significant in the planned lesson and their comments regarding the lessons, for the discussion. The writings and comments were collected and analyzed. This method helped capture teachers' 'voices' better compared to recordings of oral discussion. The results of the analyses of teachers' writings and comments revealed that a major part of post-lesson discussions involved issues related to pedagogies, and teachers' reflections tended to focus more on students' thinking and mathematical topics over time as the cycles of lesson study proceeded. The results suggested that teachers' professional growth can be related to their recognition of the importance of understanding students' thinking and their perspectives on mathematics, in order to improve teaching. [ABSTRACT FROM AUTHOR]

Lesson study has been implemented in schools around the world as a method of professional development for teachers. Lesson study consists of five steps, among which the "Research Lesson" and "Post-lesson Discussion" are central. During the Post-lesson Discussion, after the teacher has commented on the lesson, all of the observers discuss the lesson, and the "knowledgeable other" (koshi), a specially invited expert, provides final comments. The quality of these final comments is critical to the learning of the lesson-study participants, and, consequently, the koshi plays an extremely important role. However, few studies have examined the nature and structure of the final comments that koshis provide. This study analyzed the final comments made in three elementary-school research lessons in Japan by a highly distinguished university mathematics educator with considerable teaching experience and an outstanding reputation as a koshi. We found that his final comments clustered into seven categories, which we named: (1) considering the didactical value of mathematical content; (2) use of representations; (3) fostering positive attitudes to learning; (4) incorporating students' ideas into whole-class discussions; (5) giving attention to what students write down; (6) giving attention to the content of the board-work; and (7) teacher growth through reflection. These categories provide insight into the nature of final comments that are regarded as being particularly useful and may form the basis for less-experienced koshis to structure their final comments in lesson study. [ABSTRACT FROM AUTHOR]

We study the ODE/IM correspondence for all states of the quantum g ^ -KdV model, where g ^ is the affinization of a simply-laced simple Lie algebra g . We construct quantum g ^ -KdV opers as an explicit realization of the class of opers introduced by Feigin and Frenkel (Exploring new structures and natural constructions in mathematical physics, Math. Soc. Japan, Tokyo, 2011), which are defined by fixing the singularity structure at 0 and ∞ , and by allowing a finite number of additional singular terms with trivial monodromy. We prove that the generalized monodromy data of the quantum g ^ -KdV opers satisfy the Bethe Ansatz equations of the quantum g ^ -KdV model. The trivial monodromy conditions are equivalent to a complete system of algebraic equations for the additional singularities. [ABSTRACT FROM AUTHOR]

210Pb geochronology is described mathematically, but how to cut a sediment core is not explicit. Thick sectioning may reduce dating reliability; but on the contrary, thin sectioning is time-consuming. Considering the counting error of excess210Pb, a new method was proposed for the determination of meaningful thickness for sectioning. The authors applied this method to a core from Tokyo Bay. To increase the thickness with depth, the treatment is helpful in reducing the sample number for measurement and improving the dating accuracy. In addition, the averaging effect involved in sectioning was discussed, and it was confirmed that the averaging effect in the new method on210Pb geochronology may generally be neglected. [ABSTRACT FROM AUTHOR]

The Third International Mathematics and Science Study (TIMSS) reports that the mathematics teaching in Japan is distinctly different from that found in the United States. They attribute part of that difference to the professional development practice of Lesson Study. However, is the pre-service preparation of Japanese mathematics teachers also different? In an effort to understand the Japanese secondary mathematics student teaching process better, the author spent two weeks in Japan at three different universities and their affiliated junior high schools observing student teachers as they interacted with their cooperating teachers. This article is a description of that process as seen through the eyes of an American mathematics teacher educator. The author found that the main focus of student teaching at the observed junior high schools is on the preparation, teaching and reflection on the lesson itself. [ABSTRACT FROM AUTHOR]