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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]

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]

Pedagogical content knowledge (PCK) is one form of teachers' professional knowledge in subject teaching, and teachers' rich PCK enables effective instruction and improves students' academic performance. However, there has been limited research on the relationships of individual difference characteristics of teachers to PCK among in-service elementary school teachers. Therefore, in addition to the demographic variables (gender and years of teaching experience) and psychological variables (beliefs about teaching and learning and teacher efficacy) examined in previous studies, this study attempted to clarify whether motivation for teaching is related to PCK. We conducted a web survey of inservice elementary school teachers in Japan (n D 267). The results showed that the traditional beliefs that students are to be controlled by their teachers and indifference, which describes a state of lack of motivation to prepare for class, were negatively associated with two elements of mathematical PCK (knowledge of learners and knowledge of instruction). Furthermore, multiple regression analysis revealed that traditional beliefs about teaching and learning were negatively associated with the knowledge of learners and indifference to subject instruction with knowledge of instruction. This suggests that teachers' motivation for teaching is related to PCK, in addition to the variables that have been previously examined. [ABSTRACT FROM AUTHOR]

Let G be a group. An automorphism α of G is called a commuting automorphism if [α(g), g] = 1 for all g ∈ G. Let A(G) denote the set of all commuting automorphisms of G. A group G is said to be an A(G)-group if A(G) forms a subgroup of Aut(G), where Aut(G) denotes the group of all automorphisms of G. In [Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), no. 5, 57-60] Rai proved that a finite p-group G of co-class 2 for an odd prime p is an A(G)-group. We prove that a finite p-group G of co-class 3 for an odd prime p, under some conditions, is an A(G)-group. [ABSTRACT FROM AUTHOR]

The two studies examined in this paper compare the different mathematical opportunities provided in preschool classrooms in China, Japan, and the United States, with an emphasis on mathematical-themed books in classroom libraries. Study one presents the results of an online survey to examining the content of preschool classroom libraries in China (N = 134), Japan (N = 168), and the United States (N = 291). Study two presents data obtained from semi-structured interviews of teachers in China (N = 8), Japan (N = 8), and the United States (N = 8). The interviews examined teacher perceptions of how they teach mathematics, the importance of teaching mathematics, and the use of the classroom library as a venue for mathematics. Study one results indicated that teachers from all three countries encourage classroom library use; however, teachers from China reported more mathematics storybooks than their Japanese or United States counterparts. Study two results indicated that teachers from all three countries viewed mathematics as important and provided various mathematics learning opportunities to children throughout the school day. Chinese teachers reported providing the most mathematics learning opportunities using whole group instruction, mathematics centers, and free play. Japanese teachers reported few whole group forms of instruction other than circle time but reported providing opportunities for using mathematics during free play and other embedded activities. United States teachers indicated that mathematics learning occurred using whole group instruction and mathematics centers. [ABSTRACT FROM AUTHOR]

Pupils' ability to represent mathematical concepts in multiple ways is a central aspect of mathematical competence and communication. Thus, classroom instructions should be able to support learners in using multiple representations (MRs) to increase the quality and quantity of connections to a network of ideas. Given the importance of bansho (board writing and organisation) in Japanese mathematics classrooms, this study aimed to investigate how MRs are presented as bansho in a mathematics classroom. Guided by a coding scheme of MRs on bansho content, the analysis revealed the ways the MRs are facilitating (or hindering) pupils' understanding. In considering the effect of the sequence and translation of MRs identified in this study, it is important to focus on these aspects of lesson design in the future. The relevant findings are also crucial to illustrate to the educators and researchers how to explore the processes involved in the use of MRs and the critical factor that contribute to the success/failure of such processes through a detailed examination of the bansho. [ABSTRACT FROM AUTHOR]

Research indicates that mathematical understanding before formal schooling influences later attainment. This study investigated the mathematical activities of preschool-aged children in Japan, a neglected topic despite the high mathematical attainment of Japanese children. Preschool activities were investigated using surveys, observations, and staff interviews; activities at home and use of non-preschool educational providers were investigated using surveys of parents. The results showed that preschools overwhelmingly followed the government curricula, seeking to develop children's interest in and sense of number, quantity, and shape through activities embedded in play and daily life; more directed teaching using workbooks was rare. Many children frequently engaged in informal mathematics-related activities at home. An unexpectedly high proportion of children engaged with learning materials from non-preschool educational providers. Results were broadly consistent across the two locations studied, despite the contrasting attainment of children in these areas in national mathematics tests. The results demonstrate that preschools in different parts of Japan avoid directed mathematical teaching. Further research is needed into the development of the mathematical understanding of preschool-aged children in Japan, especially in relation to non-preschool educational providers. [ABSTRACT FROM AUTHOR]

We reflect on our experience in Japan and the UK in raising mathematics funding, from the public and private sectors, and establishing new mathematics institutes. We hope that some of this information and relevant examples will be of use for mathematicians in other countries. [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]