The purpose of this study was to suggest methods to apply generalizability theory to mathematics teacher evaluation using classroom observations in Korea by analysing mathematics teachers in the U.S. using the instructional quality of assessment instrument as an illustrative example. The subjects were 96 teachers participating in Year 3 and Year 4 from the Middle-school Mathematics and the Institutional Setting of Teaching (MIST) project funded by the National Science Foundation since 2007. The MIST project investigates the following question: What does it takes to support mathematics teachers` development of ambitious and equitable instructional practices on a large scale (MIST, 2007). This study examined data based on both the univariate generalizability analysis using GENOVA program and the multivariate generalizability analysis using mGENOVA program. Specifically, this study determined the relative effects of each error source and investigated optimal measuring conditions to obtain the suitable generalizability coefficients. The methodology applied in this study can be utilized to find effective optimal measurement conditions for the mathematics teacher evaluation for professional development in Korea. Finally, this study discussed limitations of the results and suggested directions for future research.

Recently, with the development of technology, intuitive understanding of abstract mathematical concepts through visualizations is growing in popularity within college mathematics. In this study, we introduce free visualization tools developed for better understanding of topics which students learn in Calculus. We visualize important concepts of Calculus as much as we can according to the order of most Calculus textbooks. In this process, we utilized a well-known, free mathematical software called GeoGebra. Finally, we discuss our experience with visualizations in Calculus using GeoGebra in our class and discuss how it can be effectively adopted to other university math classes and high school math education.

This study aimed to explore the affective characteristics of primary and middle school students in mathematics and to analyze the relationship between the affective characteristics and initiative in mathematics learning. For the purpose of this study, a survey was conducted for students in a primary and a middle school in Incheon area. The questionnaires using in this study consisted of five affective domains of interest, self-efficacy, value, self-regulation, and mathematics anxiety. The results of this study showed that the participant students` affective characteristics tended to be decreased by grades. Moreover, the gender differences were increase as the participant students grew older. Students who take the initiative in mathematics learning showed better affective characteristics in general than students who depends on other assistants.

In this paper, we study the major mathematical history appeared in the elementary school mathematics textbooks. School mathematical history described in the texts reflects the axial age, and deals with mathematical transculture from the ancient Greek into Europe without the Islamic mathematics. We discuss about them through out the elementary school textbooks and give some directions for the problems.

This study is intended to examine 36 in-service secondary school mathematics teachers` conceptions of proof in the context of mathematics and mathematics education. The results suggest that almost teachers recognize the role as justification well but have the insufficient conceptions about another various roles of proof in mathematics. The results further suggest that many of teachers have vague concept-images in relation with the requirement of proof and recognize the insufficiency about the actual teaching of proof. Based on the results, implications for revision of mathematics curriculum and mathematics teacher education are discussed.

Recently, mathematical reasoning has been considered as one of the most important mathematical thinking abilities to be established in school mathematics. This study is to investigate the mathematical problems on the content of `Set and Statement` and `Sequences` in high school according to the four types of reasoning, namely Making Conjectures, Investigating Conjectures, Developing Arguments, and Evaluating Arguments. Those types of reasoning were reconstructed based on Johnson`s six types of reasoning suggested in 2010. The content is dealt with in `Mathematics II` textbook developed and published according to the mathematics curriculum revised in 2009. The subject of this study is nine types of textbooks and mathematical problems in the textbook are consisted of as two parts of `general problem` and `evaluation problem`. Finally, the results of this study can be summarized as follow: First, it is stated that students be establishing a logical justification activity, the highest reasoning activity through dealing with the `Developing Arguments` type of problems affluently in both `Set and Statement` and `Sequence` chapters of Mathematics II textbook. Second, it is mentioned that students have an chance to investigate conjectures and develop logical arguments in `Set and Statement` chapter of Mathematics II textbook. In particular, whereas they have an chance to investigate conjectures and also develop arguments in `Statement`, the `Set` chapter is given only an opportunity of developing arguments. Third, students are offered on an opportunity of reasoning that can make conjectures and develop logical arguments in `Sequences` chapter of Mathematics II textbook. Fourth, Mathematics II textbook are geared to do activities that could evaluate arguments while dealing with the problems relevant to `mathematical process` included in `general problem`.

Mathematical process is an issue in current mathematics education. In this paper discuss how to assess the mathematical process using essay type questions. For this we first suggest the concept of Mathematical Process Oriented Question which is an essay type question and possible to assess mathematical processes, that is, the mathematical communication, reasoning, and problem solving as well as mathematics knowledge. And we develop a framework for developing the mathematical process oriented question and rubric, examples of assessment standards and those questions containing rubric for assessing mathematical processes. The results of this paper can serve as basic data and examples for follow up research about mathematical process assessment.

How will the field of education react to the big data craze that has recently seeped into every aspect of society? To search for ways to use big data in mathematics education, this study first examined the concept of big data and examples of its application, and then pursued directions for future research in two ways. First, changes in the representation and acceptance of data are required because of changes in technology and the environment. In other words, the learning content and methodology of data treatment need to be changed by describing a myriad amount of data visually or by `analyzing and inferring` data to provide data efficiently and clearly. Additionally, the mathematics education field needs to foster changes in curricula to facilitate the improvement of students` learning capacity in the 21st century. Second, it is necessary to more actively collect data on general education and not merely on teaching or learning to identify new information, pursue positive changes in the teaching and learning of mathematics, and stimulate interest and research in the field so that it can be used to make policy decisions regarding mathematics education.