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The purpose of this paper is to examine how lesson study can lead to teacher learning and improvement of instruction by developing teachers’ mathematical-task knowledge and by supporting teachers’ selection, modification, and implementation of mathematical tasks. Mathematical-task knowledge includes knowledge needed to use tasks that require a high level of thinking and reasoning.

A qualitative case study design was used to explore the learning and instruction of three teachers as they went through the process of lesson study, developed knowledge around mathematics tasks, and made changes to their instruction. Methods included direct observation of lessons, semi-structured interviews, and participant observation.

This lesson study project supported teachers in developing mathematical-task knowledge and in making change to instructional practice. The teachers discussed in this paper added to their understanding of mathematical tasks and changed how they implemented tasks after lesson study. The teachers began to challenge students to go beyond memorizing or executing procedures to deepen the students’ understanding of mathematical concepts. Teachers developed key insights and understandings of mathematical tasks, triggering shifts in their thinking, and changes to instruction. Collaboration and reflection altered the selection, modification, and implementation of mathematical tasks.

This study reveals the connections between features of lesson study and the pathways that lead to learning and improvements to instruction. Limitations included the demands of the school district’s pacing guide and curriculum, and a limited number of interviews and observations were conducted after lesson study.

There are many different ways lesson study has been implemented in the USA, yet the effectiveness of many lesson study projects is still unclear. This study reveals more about the lesson study process, what features are important, and how these features lead to development of knowledge and practice. This study examines how teachers within the same lesson study group added to their knowledge and practice and how different features of lesson study prompt them to make changes.

Being numerate involves the ability to use mathematical knowledge meaningfully across multiple contexts allowing us to order our day, optimise our health and well-being, and function in technology rich environments. Addressing numeracy from the early years of learning, and across all areas of the education curriculum, is key to lifelong learning and quality of life. Being numerate, however, is more than mathematical knowledge; the language that underpins it heavily impacts how we become numerate. This chapter examines numeracy, or mathematical literacy, investigating how literacy can include, and exclude, students from opportunities to learn at school and beyond. This chapter will also examine how numeracy can be used to provide access to educational curricula and personalised goals for students with diverse learning needs in ways that many have ignored.

The purpose of this paper is to highlight the ways racialization in K-12 mathematics classrooms has narrowed the understanding of mathematical learning for Black children.

Drawing on situated learning theory and funds of knowledge, the authors argue that the social learning context of mathematics classrooms has limited the understanding of what Black children are capable of mathematically. The authors suggest that as a community of practice, mathematics classrooms may be marginalizing Black children, as well as other students of color, by devaluing their community-based knowledge and ways of knowing.

The extant literature portrays Black children as struggling in mathematics; however, this research is overwhelmingly conducted based on school performance measures. Yet, if one looks beyond the classroom to Black children's homes and communities, a plethora of mathematical knowledge tied to cultural and community practices may be found. As such, Black children who struggle in mathematics classroom may be experiencing misalignment across contexts, rather than a lack of mathematical knowledge altogether.

This paper has implications for classroom practice, particularly teacher ideologies pertaining to community-based knowledge. The authors urge mathematics education researchers and practitioners to look beyond the classroom, as community-based mathematical practices may provide more insight into students’ mathematical capabilities. These implications are particularly important for educating students of color, who often experience a subpar classroom education.

In this paper, the authors provide a critical lens to situated learning theory, pushing mathematics education research to examine the underexplored topic of Black children's out-of-school mathematical practices.

The purpose of this paper is to report a case study of how learning study was incorporated in teacher education programs in Hong Kong. It aims to share the success of the program and to disseminate how pre‐service teachers enhanced their mathematical content knowledge and pedagogical content knowledge by practising learning study. Building on the work, this paper suggests incorporating the framework of learning study, a theory‐guided pedagogical principle, as an integrated subject of mathematics pedagogy and teaching practice in teacher education programs.

In total 32 pre‐service teachers’ learning journals of their reflections of learning processes were analyzed. The analysis of data and reporting of findings are linked tightly to how pre‐service teachers enhanced their mathematical content knowledge and pedagogical content knowledge by practising learning study.

The 32 pre‐service teachers noted that the learning study subject fostered their understanding of relationship between theory and practice and their understanding of transforming knowledge into action. In particular, they came to understand that knowledge of pupils and content involves a particular mathematical idea or procedure and familiarity with students’ prior knowledge and misconceptions. They also reported that they understood better what mathematics pedagogy content knowledge means and what components it includes.

The suggestions of incorporating the framework of learning study in teacher education programs is supported and manifested by the positive feedback and comments of the 32 pre‐service teachers who underwent the entire learning process of learning study in Hong Kong. The findings demonstrate how pre‐service teachers’ mathematical content knowledge and pedagogical content knowledge were enhanced by practising learning study.

In his discussion of early lexical development in children Barrett (1995) notes that utterances can be of the following types: an expression of an internal state, a response to a specific context, a social-pragmatic utterance and a referential utterance. A referential utterance can be thought of in the following way: the thing referred to, a mental representation, a word representation and a word sound. An utterance may refer to an object, an action, an attribute or an event. Some utterances are used as the names of classes of objects while other utterances are used as the proper names of individual objects. Looking at this in abstract we might say that, in the early years of childhood, language is used to refer to elements, sets, functions and relations – in other words to the mathematical structures which were discussed in Chapter 2. Of course although early language is used to refer to mathematical objects, the character of the language itself takes the form of ordinary language.

Four examples of physical-knowledge activities are described and analyzed on the basis of Piaget’s theory. These are playful activities like Pick-Up Sticks in which children act on objects mentally and physically to produce a desired effect.

The objective of physical-knowledge activities is to develop children’s logico-mathematical knowledge. Therefore, it is not the activities themselves that are important. What is important is the thinking children do while they play because it is by thinking that children construct logico-mathematical knowledge, and logico-mathematical knowledge serves as the framework for children to construct all knowledge.

Data are presented about the achievement in mathematics of two groups of low-SES first graders who came to school without any number concepts. One group was given physical-knowledge activities during the math hour for half a year instead of math lessons. The other group received traditional math instruction throughout the year. The first group did better in mental arithmetic at the end of the school year, demonstrating the importance of a solid logico-mathematical foundation.

In this chapter, the interplay between the development of the discipline, the development of the field of study, and the emergence of professional fields is examined using the example of mathematics. In connection with the formation of the modern research university, mathematics has emerged as an independent scientific discipline and as an independent field of study. In the process, mathematics attains a high degree of formalization and internal coherence. This is the basis for the penetration of mathematicians into more and more professional fields, even outside science. Real problems or real facts are reduced to aspects that are amenable to mathematical modeling by treating them as quantifiable parameters. As mathematics expands as a field of study, more and more professional sectors become applications of mathematical models. As a consequence, more mathematical fields of study are differentiating themselves, specializing in these application fields. This chapter analyzes this dynamic and its preconditions.

This paper aims to present an open source math-aware Question Answering System based on Ask Platypus.

The system returns as a single mathematical formula for a natural language question in English or Hindi. These formulae originate from the knowledge-based Wikidata. The authors translate these formulae to computable data by integrating the calculation engine sympy into the system. This way, users can enter numeric values for the variables occurring in the formula. Moreover, the system loads numeric values for constants occurring in the formula from Wikidata.

In a user study, this system outperformed a commercial computational mathematical knowledge engine by 13 per cent. However, the performance of this system heavily depends on the size and quality of the formula data available in Wikidata. As only a few items in Wikidata contained formulae when the project started, the authors facilitated the import process by suggesting formula edits to Wikidata editors. With the simple heuristic that the first formula is significant for the paper, 80 per cent of the suggestions were correct.

This research was presented at the JCDL17 KDD workshop.

This paper aims to propose an innovative building information modelling (BIM)-based framework for multi-objective and dynamic temporary construction site layout design (SLD), which uses a hybrid approach of systematic layout planning (SLP) and mathematical modelling.

The hybrid approach, which follows a step-by-step process for site layout planning, is designed to facilitate both qualitative and quantitative data collection and processing. BIM platform is usedto facilitate the determination of the required quantitative data, while the qualitative data are generated through knowledge-based rules.

The multi-objective layout model represents two important aspects: layout cost and adjacency score. The result shows that the model meets construction managers’ requirements in not only saving cost but also assuring the preferences of temporary facility relationships. This implies that the integration of SLP and mathematical layout modelling is an appropriate approach to deliver practical multi-objective SLD solutions.

The proposed framework is expected to serve as a solution, for practical application, which takes the advantage of technologies in data collection and processing. Besides, this paper demonstrates, by using numerical experimentation and applying Microsoft Excel Solver for site layout optimisation, how to reduce the complexity in mathematical programming for construction managers.

The original contribution of this paper is the attempt of developing a framework in which all data used for the site layout modelling are collected and processed using a systematic approach, instead of being predetermined, as in many previous studies.

Teachers in the USA have been conducting lesson study for more than ten years since it was introduced from Japan in the late 1990s. Although interest in conducting lesson study in the USA is still strong and greater numbers of teachers have become involved in this professional learning, there are significant obstacles to conducting high quality and effective lesson study that enhances teachers’ content and pedagogical knowledge, as well as improving their instruction and student learning in classrooms. Because of the needs of improvement in lesson study in the USA, so it can be administered effectively and sustained, the purpose of this paper is to discuss the current status of lesson study in the USA, what high quality and effective lesson study is, and what ideas might be help to improve lesson study in the USA.

In this paper, issues that are common barriers to conducting effective lesson study, such as: US teachers’ misunderstanding or lack of understanding of lesson study; teachers’ insufficient knowledge of content, pedagogical content, curriculum knowledge; lack of support from administrators for lesson study; non‐systematic approach to implement lesson study; and having short‐sighted vision to conduct lesson study will be discussed. The discussions are based on the author's 12 years of experience working with teachers, schools, and school districts in the USA, interactions and information exchanges with other lesson study educators and researchers and professional development coordinators in schools and districts in the USA, and existing research documents in the USA. Through this discussion, the author attempts to provide suggestions for improving lesson study in the USA.

In order for lesson study to be successful, teachers need to think of lesson study as a way to improve their own learning as well as student learning. Spending more time studying mathematical content and curriculum, developing a strong pedagogical content knowledge with colleagues, and establishing a professional community of learning through lesson study will help it to be effective for improving classroom teaching and learning.

The paper provides some helpful suggestions for improving quality and effectiveness of lesson study in order to improve: classroom teaching – teacher's content, pedagogical content and curriculum knowledge; and student learning. The paper is particularly valuable for lesson study practitioners, and administrators and staff developers who are implementing lesson study in schools.