Early understanding of base-10 concept has been shown to be associated with superior mathematical achievement among East Asian children. In addition to their base-10 structured number system, teacher support in kindergarten is also crucial to children's development of this complex mathematical concept. Therefore, this study examined how Japanese…

Studies have found that problems exist with respect to elementary school teachers' understanding of proportions and their knowledge of the appropriate methods for teaching the concept. This study aims to help aspiring elementary school teachers form a healthy mathematical identity and deepen their understanding of mathematics. This quantitative…

Recently a team of third- and fourth-grade teachers tested instructional ideas on the topic of division with remainders (DWR) using lesson study. The Common Core State Standards for Mathematics give little attention to the concept of the remainder, specifying only that students are to solve problems for which remainders must be interpreted (NGA…

This paper explores the use of gamification in math lessons for children in order to highlight the relationship between math education and its application to society. In school education, there is an existing problem about how to relate concepts learned in math to everyday life. One of the reasons for this problem is that it is difficult for…

Structured problem-solving lessons are used to explore mathematical concepts such as pattern and relationships in early algebra, and regularly used in Japanese Lesson Study research lessons. However, enactment of structured problem-solving lessons which involves detailed planning, anticipation of student solutions and orchestration of whole-class…

Given the distinctive characteristics of Japanese mathematics lessons found by the international studies and the subsequent focus of the attention to Lesson Study in mathematics education community, the author discusses the relationships between the scientific studies and improvement of mathematics teaching and learning from an insider's…

Proof and proving are important components of school mathematics and have multiple functions in mathematical practice. Among these functions of proof, this paper focuses on the discovery function that refers to invention of a new statement or conjecture by reflecting on or utilizing a constructed proof. Based on two cases in which eighth and ninth…

On the basis of the construct of "discursive focus" by Sfard (2000), this study explores how students' attention is brought to new mathematical content in whole-class interaction between the teacher and the children. In a sixth-grade lesson introducing the concept of constancy of proportion, we analyzed the progression of social…

This study aims to describe how the learning study model can be used to improve lesson design and children's learning outcomes by enabling them to perceive and define the critical aspects of the object of learning, guided by variation theory. Three lesson designs were used with three groups of children (A = 24, B = 13, C = 14) from two schools.…

This paper describes a pedagogical framework that teachers can use to support students who are engaged in solving open-ended problems, by explaining how two Japanese expert teachers successfully apply open-ended problems in their mathematics class. The Open-Ended Approach (OPA) framework consists of two main sections: Understanding Mathematical…

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) identifies the strategic use of appropriate tools as one of the mathematical practices and emphasizes the use of pictures and diagrams as reasoning tools. Starting with the early elementary grades, CCSSM discusses students' solving of problems "by drawing." In later…

This study combines the Japanese lesson study approach and mathematics teachers' professional development. The first year of a 4-year project in which 3 Dutch secondary school teachers worked cooperatively on introducing making sense of the calculus is reported. The analysis focusses on instrumental and relational student understanding of…

Although the importance of mathematical problem solving is now widely recognised, relatively little attention has been given to the conceptualisation of mathematical processes such as representing, analysing, interpreting and communicating. The construct of Mathematical Knowledge for Teaching (Hill, Ball & Schilling, 2008) is generally…

This is an account of events in a real classroom when the notion that there is a distinction between calculation by counting, and calculation by structuring is a focus for learning. Pupils have "hands-on" experiences that support their understanding of "number". The teaching "aid" might be unfashionable in…

This study examined how types of tasks influenced student activities/thinking and defined the role of Seatwork in mathematics lessons. It used 60 lessons from the TIMSS videotaped Study. These data indicated that practice was the most prevalent form of tasks in the U.S. In Germany, students completed mathematical calculations after a complex…