The purpose of this study is to develop a mathematical assessment and correction materials according to the mathematics learning hierarchy. The scope of the study is set to 'function' in 7th grade of middle school. The researchers developed a draft of the mathematical assessment and correction materials based on the mathematics learning hierarchy through the pilot test and the expert review. Using the results of the expert review, the researchers modified and supplemented the math assessment and correction materials to produce the final version. The mathematics assessment and correction material developed in this study is expected to build an effective guidance system for students with mathematics deficits. In addition, by presenting a mathematical assessment and correction materials to the teachers in the field, it is possible to reduce the effort for the management of underachievers and to provide guidance for the education of students with a lack of math learning.

In this study, we investigate the latus rectum, one of the geometric measures of the conics, as one of the ways in which learners harmonize the geometric and algebraic approaches to conics from a pedagogical point of view. We also introduce the conical curve of Biot as presented in 'The Discourse on the Latus Rectum in conics(2013)' by Takeshi Sugimoto and reinterpret it for visualization and use as teaching material. Therefore, we expect that the importance of mathematical concepts will be recognized in conics and students can experience geometry learning that is explored in the school field and have a positive effect in developing the power to apply even in the context of applied problems.

This study is to establish the items on class critiques based on the mathematical competencies according to the mathematics curriculum revised in 2015. Namely, this study deals with the items on how pre-service or in-service teachers understand and comment on mathematics instruction on their own instruction or peers' instruction. To accomplish this, first of all the draft items on instructional reviews was developed by researchers of this study on the basis of the previous study(Hwang, 2018). In order to revise and develop the draft items, the experimental study was executed. The experimental study was done by the subject of 11 groups who are undergraduate students in the educational college of C University. The subject was supposed to watch an in-service middle school mathematics teacher's excellent instruction(study) video and to comment the instruction video on the draft items on class critiques. While analyzing the comments of the subject, the revised items on the class critiques were to be develop. Based on this study, from now on, the final and ideal items on the class critiques would be establish to reflect and comment teachers' instruction.

The reason for this study is that the learning content of geometric construction in school mathematics is very insufficient. Geometric construction not only enables in-depth understanding of shapes, but also improves deductive proof skills. In school mathematics education, geometric construction is a very important learning factor, and educational significance is very high in that it can develop reasoning skills essential to the future society. Nevertheless, the reduction of geometric construction learning content in Korean curriculum and mathematics textbooks is against the times. Therefore, the purpose of this study is to analyze the transition of geometric construction learning contents in middle school mathematics curriculum and mathematics textbooks. In order to achieve the purpose of this study, the following studies were conducted. First, we analyze the characteristics of geometric construction according to changes in curriculum and textbooks. Second, we develop a framework for analyzing geometric construction tasks. Third, we explore geometric construction tasks according to the developed framework. Through this, it is expected to provide significant implications for the geometric areas of the new middle school curriculum that will be developed in the future.

The 2015 revised mathematics curriculum had newly introduced the term 'process-focused assessment'. The official document, however, did not offer an explicit definition of the new term, but only by virtue of narrative. This has encouraged practitioners and researchers to figure out themselves what it is and how it differs from those in use, formative assessment and performance assessment in particular, in use. In consequence, many versions of interpretation, all of which are not necessarily consistent, have been developed and implemented in schools, This, in turn, still has created a chaotic situation carrying out the process-focused assessment. This study attempted to make the meaning of the process-focused assessment more explicit by conducting a comprehensive review of the related literature, for implementing it in its intended way.