Rina Kim

The History of Base-Ten-Blocks: Why and Who Made Base-Ten-Blocks?

In recent years social, economic and environmental considerations have led to a reevaluation of the factors that contribute to sustainable urban environments. Increasingly, urban green space is seen as an integral part of cities providing a range of services to both the people and the wildlife living in urban areas. The use of urban green space, and especially increasing the use, has become a hot topic for many green space managers during the past few years as the assumed link between use of urban green space and sustainable urban development is becoming more visible. Up to this time, there is little systematic information about urban green space including natural water bodies in the City of Kazan, Russia, its use and the main factors that influence this use. As green spaces play a crucial role in supporting urban ecological and social systems, it is important to make investigations in the amount of provision, the distribution and characteristics of urban green space in the city. The main concern of this paper is to address the importance of urban nature for citizens’ well being and for the sustainability of the city they inhabit. DOI: 10.5901/mjss.2014.v5n24p356

A Hierarchy of South Korean Elementary Teachers Knowledge for Teaching Mathematics

The purpose of this study is to develop a framework for understanding teachers’ knowledge for teaching mathematics (MKT) by examining a hierarchy of 317 South Korean elementary teachers’ knowledge for teaching mathematics. Through a web-based survey, the teachers were asked to rank order their beliefs about and use of knowledge subdomains for teaching mathematics. Findings show that teachers’ beliefs about knowledge for teaching mathematics are divergent from current research trends. Also, their beliefs about the subdomains of knowledge for teaching mathematics were ranked differently in comparison to their actual use of the subdomains. Their hierarchy for MKT presents suggestions for the type of curriculum that might be offered to teachers to develop their knowledge at the pre-and in-service level.

A Pedagogical Overview of Relevant Literature

This literature reviewed in this chapter is an examination of conceptual and empirical studies in the area of elementary teachers’ knowledge for teaching mathematics; it includes a discussion of the implications and implementations emerging from the review. The literature review is divided into four major sections: sociocultural theory, a history of research on teachers’ knowledge for teaching mathematics, studies about elementary teachers’ knowledge for teaching mathematics, and an interpretive summary and critical analysis. Taken together, these sections of literature provide a historical and theoretical context for this study.

Summary, Conclusions, and Implications

This chapter summarizes the study, emphasizing the importance of the findings, and discusses how they contribute to existing research about elementary teachers’ knowledge for teaching mathematics. It also includes conclusions drawn from the findings and their implications as well as recommendations for future research.

Knowledge for Teaching Mathematics Categories IV and V: Mathematics Pedagogical Content Knowledge and Mathematics Pedagogical Procedural Knowledge

This chapter explores the notion that mathematics pedagogical content knowledge is a conjunctive form of knowledge that intersects mathematics curriculum knowledge, mathematics learner knowledge, and fundamental mathematics conceptual knowledge. We put forth the claim that the intersection of the knowledge categories is where mathematics pedagogical content knowledge is located. Then drawing on this claim, the proposition that mathematics pedagogical procedural knowledge designates how the teachers’ knowledge is related to common procedures the teachers might use in the development of mathematics pedagogical content knowledge is discussed. From the analysis of lesson plans, we presented several multilayer models that illustrated how mathematics pedagogical content knowledge along with mathematics pedagogical procedural knowledge influenced planning and teaching.

Mathematics Teaching and Learning

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Knowledge for Teaching Mathematics Category II: Mathematics Learner Knowledge

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Knowledge for Teaching Mathematics Category I: Mathematics Curriculum Knowledge

Mathematics learner knowledge (MLK) is related to teachers’ understanding of the characteristics of mathematics learners and how that knowledge is used in mathematics instruction. This study demonstrated that there are key subcategories of MLK based on the analyses of the lesson plans: students’ mathematical knowledge, students’ mathematical skills, and students’ mathematical attitude. Therefore, students represent mathematics learners who are learning mathematics in formal classroom settings according to the National Mathematics Curriculum. In addition, students’ mathematical knowledge represents students’ conceptual understanding of mathematics, while mathematical skills indicate both students’ procedural understanding and skills needed to solve mathematics problems. Students’ mathematical attitude involves students’ preference for and value of mathematics. These three key subcategories were useful to the teachers participating when developing lesson plans, teaching the lesson, and assessing student learning.

Knowledge for Teaching Mathematics Category III: Fundamental Mathematics Conceptual Knowledge

Mathematics curriculum knowledge indicates teachers’ understanding of the sequence among mathematical concepts that exist both inter-grade and intra-grade according to the National Mathematics Curriculum. Mathematics curriculum knowledge is divided into two subcategories, which are referred to as vertical mathematics curriculum knowledge and horizontal mathematics curriculum knowledge. Vertical mathematics curriculum knowledge represents the general order of what students learn across grade levels (e.g., mathematics topics across grades one to three). Horizontal mathematics curriculum knowledge is composed of the mathematics curriculum at one grade level (e.g., mathematics topics for first grade). Findings emerging from the data analysis are that the teachers’ Mathematics curriculum knowledge served as a catalyst for investigating their students’ mathematical backgrounds and experiences. In particular, Mathematics curriculum knowledge provided the scope of the content to consider when the teachers worked with their students to help them make mathematical connections.

Context of Elementary Mathematics Education in South Korea

Fundamental mathematics conceptual knowledge defines teachers’ understanding of mental representations of mathematics topics and the relationship among them. It also includes knowledge that may convert abstract mathematics concepts into a form, which supports learners’ understanding of them. Fundamental mathematics conceptual knowledge is divided into two subcategories: intrinsic mathematics conceptual knowledge and extrinsic mathematics conceptual knowledge. A key finding is that the teachers used fundamental mathematics conceptual knowledge when they planned mathematics lessons, considering both the mathematics concepts and the relationship among them. During mathematics instruction, the teachers used their fundamental mathematics conceptual knowledge while engaging in conversations with students. Thus from our analysis of these conversations, we found that fundamental mathematics conceptual knowledge might include embryologic origins of mathematics concepts.