• Journal of Elementary Mathematics Education in Korea
• /
• v.21 no.3
• /
• pp.415-441
• /
• 2017

The purpose of this study is to develop elementary school math classes for the gifted and talented with a focus on social issues to investigate the possibility of character education through specialized subject classes. As suggested in the goals of the math education for social justice, which provide the fundamental theoretical basis, through mathematics activities with a theme of social issues, mathematically gifted and talented young students can critically perceive social issues, express a sense of mathematical and critical agency throughout the course and develop a willingness and mindset to contribute to social progress. In particular, the concept of Figured Worlds and agency is applied to this study to explain the concept of elementary math classes for the gifted and talented with a focus on social issues. The concept is also used as the theoretical framework for the design and analysis of the curriculum. Figured Worlds is defined as the actual world composed of social and cultural elements (Holland et al., 1998) and can be described as the framework used by the individual or the social structure to perceive and interpret their surroundings. Agency refers to the power of practice that allows one to perceive the potential for change within the Figured Worlds that he is a part of and to change the existing Figured Worlds. This study sees as its purpose the fostering of young talent that has the agency to critically perceive the social structure or Figured Worlds through math classes with a theme of social issues, and thus become a social capital that can contribute to social progress.

• Journal of Digital Convergence
• /
• v.14 no.4
• /
• pp.437-448
• /
• 2016

The study conducted Comparative Analysis on the difference of College Scholastic Ability Data divided by type of admission process through the mileage program. Analysis result in following sequence. Leadership and relationships : CSAT(CSAT) > TOSR(subject), CSAT(CSAT+TOSR) is lower than each types ; mainly TOSR(total), TOSR(subject), CSAT(CSAT). Global : CSAT(CSAT+TOSR) & CSAT(CSAT) is higher than mainly TOSR(total) & TOSR(subject). Career and job search : TOSR(total) & TOSR(subject) is higher than mainly CSAT(CSAT+TOSR). Sum of mileage score : CSAT(CSAT) is higher than TOSR(subject) & CSAT(CSAT). Given this as a result, If you look simply at the activities of joint participation of leadership and relationships, student of mainly TOSR(total) admission do well college life with existing research. But with analysis results of K-Leader mileage this research shows that students of mainly CSAT(CSAT) admission do well college life. * CSAT(College Scholastic Ability Test), TOSR(a transcript of school records)

• Journal of Elementary Mathematics Education in Korea
• /
• v.16 no.3
• /
• pp.491-509
• /
• 2012

The purpose of this study is to analyze some Korean elementary pre-service teachers' Mathematical Knowledge for Teaching(MKT). For this purpose, we selected the MKT items on number and operations which were adapted for Korean in-service teachers by Lee(2011). The survey consisting of those items was administered to 76 Korean elementary pre-service teachers at Teachers College, J University. The results are the following: First, the respondents, elementary pre-service teachers, showed that the preference for the MKT items was very affirmative, but the percentages of correct answers to the MKT items weren't generally high. Second, the preference for the instructional consultation by experienced teachers was very affirmative. Third, the percentages of correct answers to KCS, SCK, CCK and KCT were 70.13%, 55.71%, 43.87% and 29.27%, respectively. Fourth, the percentages of correct answers to type 5, 6, and 7 were more than 60%, but those of correct answers to type 1, 2, 3, 4, and 8 were less than 60%. This means we need to strengthen type 1, 2, 3, 4, and 8 in education of elementary mathematics subject at Teachers College of J University.

• Communications of Mathematical Education
• /
• v.31 no.3
• /
• pp.257-277
• /
• 2017

The purpose of this research is divide into two kinds. First, develop the mathematical modeling program for mathematically gifted students focused on Voronoi diagram and Delaunay triangulation, and then gifted teachers can use it in the class. Voronoi diagram and Delaunay triangulation are Spatial partition theory use in engineering and geography field and improve gifted student's mathematical connections, problem solving competency and reasoning ability. Second, after applying the developed program to the class, I analyze gifted student's core competency. Applying the mathematical modeling program, the following findings were given. First, Voronoi diagram and Delaunay triangulation are received attention recently and suitable subject for mathematics gifted education. Second,, in third enrichment course(Student's Centered Mathematical Modeling Activity), gifted students conduct the problem presentation, division of roles, select and collect the information, draw conclusions by discussion. In process of achievement, high level mathematical competency and intellectual capacity are needed so synthetic thinking ability, problem solving, creativity and self-directed learning ability are appeared to gifted students. Third, in third enrichment course(Student's Centered Mathematical Modeling Activity), problem solving, mathematical connections, information processing competency are appeared.

• Journal of Educational Research in Mathematics
• /
• v.9 no.2
• /
• pp.383-404
• /
• 1999

This study began with an epistemological question about the nature of mathematical cognition in relation to the learner's activity. Therefore, by examining Piaget's 'reflective abstraction' theory which can be an answer to the question, we tried to get suggestions which can be given to the mathematical education in practice. 'Reflective abstraction' is formed through the coordination of the epistmmic subject's action while 'empirical abstraction' is formed by the characters of observable concrete object. The reason Piaget distinguished these two kinds of abstraction is that the foundation for the peculiar objectivity and inevitability can be taken from the coordination of the action which is shared by all the epistemic subjects. Moreover, because the mechanism of reflective abstraction, unlike empirical abstraction, does not construct a new operation by simply changing the result of the previous construction, but is forming re-construction which includes the structure previously constructed as a special case, the system which is developed by this mechanism is able to have reasonability constantly. The mechanism of the re-construction of the intellectual system through the reflective abstraction can be explained as continuous spiral alternance between the two complementary processes, 'reflechissement' and 'reflexion'; reflechissement is that the action moves to the higher level through the process of 'int riorisation' and 'thematisation'; reflexion is a process of 'equilibration'between the assimilation and the accomodation of the unbalance caused by the movement of the level. The operational learning principle of the theorists like Aebli who intended to embody Piaget's operational constructivism, attempts to explain the construction of the operation through 'internalization' of the action, but does not sufficiently emphasize the integration of the structure through the 'coordination' of the action and the ensuing discontinuous evolvement of learning level. Thus, based on the examination on the essential characteristic of the reflective abstraction and the mechanism, this study presents the principles of teaching and learning as following; $\circled1$ the principle of the operational interpretation of knowledge, $\circled2$ the principle of the structural interpretation of the operation, $\circled3$ the principle of int riorisation, $\circled4$ the principle of th matisation, $\circled5$ the principle of coordination, reflexion, and integration, $\circled6$ the principle of the discontinuous evolvement of learning level.

• The Mathematical Education
• /
• v.59 no.3
• /
• pp.237-254
• /
• 2020

The current study investigated the relationships between mathematical knowledge for teaching and the mathematical quality in instruction in order to gain insight about teacher education for secondary teachers in South Korea. We collected and analyzed twelve high school teachers' scores of the multiple-choice assessment for mathematical knowledge for teaching developed by the Measures of Effective Teaching project. Their instruction was video recorded and analyzed with the mathematical quality in instruction developed by the Learning Mathematics for Teaching project. We also interviewed the teachers about how they planned and assessed their instruction by themselves in order to gain information about their intention and interpretation about instruction. There was a statistically significant and positive association between the levels of mathematical knowledge for teaching and the mathematical quality in instruction. Among three dimensions of the mathematical quality in instruction, mathematical richness seemed most relevant to mathematical knowledge for teaching because subject matter knowledge plays an important role in mathematical knowledge for teaching. Furthermore, working with students and mathematics as well as students participation were critical to decide the quality of instruction. Based on these findings, the current study discussed offering opportunities to learn mathematical knowledge for teaching and philosophy about how teachers need to consider students in high schools particularly in terms of constructivism.

• Journal of the Korean School Mathematics Society
• /
• v.16 no.1
• /
• pp.157-185
• /
• 2013

This study was to investigate novice teachers' Specialized Content Knowledge for Teaching in High School Calculus Lessons. The lessons of two novice teachers in Kyunggi Do were observed from July, 2011 to Feb. 2012. All observed lessons were audeotaped and transcribed into word files. Their calculus lessons were analyzed into three kinds of knowledge consisting of SCKT. Their SCKT just copied the contents of the textbook and other additional SCKT were not found for teaching. Even though students asked a question that they did not understand, the teacher just repeated the previous contents that already he used. But this study included possible contents of SCKT within the areas these teachers covered so that teachers in school may use for teaching of Calculus. The novice teacher do not have sufficient experience, the program of the college of education and the contents of the teacher certificate-examination should include multi-dimensional approaches in SCKT to pre-service teachers in order to raise better specialized teachers in mathematics.

• School Mathematics
• /
• v.18 no.4
• /
• pp.839-856
• /
• 2016

In 2009 revision and 2015 revision mathematics national curriculum, 'proof' was moved to high school from middle school in consideration of the cognitive development level of students, and 'proof by contradiction' was stated in the "success criteria of learning contents" of the first year high school subject while it had been not officially introduced in $7^{th}$ and 2007 revision national curriculum. Proof by contradiction is known that it induces a cognitive conflict due to the unique nature of rather assuming the opposite of the statement for proving it. In this article, based on the logical, mathematical and historical analysis of Proof by contradiction, we looked about the introductions and the applications of the current textbooks which had been revised recently, and searched for improvement measures from the viewpoint of discovery, explanation, and consilience. We suggested introducing Proof by contradiction after describing the discovery process earlier, separately but organically describing parts necessary to assume the opposite and parts not necessary, disclosing the relationships with proof by contrapositive, and using the viewpoint of consilience.

• Journal of Educational Research in Mathematics
• /
• v.13 no.3
• /
• pp.247-265
• /
• 2003

The purpose of this study is to analyze the essence of ratio concept from educational viewpoint. For this purpose, it was tried to examine contents and organizations of the recent teaching of ratio concept in elementary school text of Korea from ‘Syllabus Period’ to ‘the 7th Curriculum Period’ In these text most ratio problems were numerically and algorithmically approached. So the Wiskobas programme was introduced, in which the focal point was not on mathematics as a closed system but on the activity, on the process of mathematization and the subject ‘ratio’ was assigned an important place. There are some educational implications of this study which needs to be mentioned. First, the programme for developing proportional reasoning should be introduced early Many students have a substantial amount of prior knowledge of proportional reasoning. Second, conventional symbol and algorithmic method should be introduced after students have had the opportunity to go through many experiences in intuitive and conceptual way. Third, context problems and real-life situations should be required both to constitute and to apply ratio concept. While working on contort problems the students can develop proportional reasoning and understanding. Fourth, In order to assist student's learning process of ratio concept, visual models have to recommend to use.

• The Mathematical Education
• /
• v.43 no.2
• /
• pp.115-137
• /
• 2004

In this paper, we verified the effect and appropriateness of the scheme to cure the math. disliking disposition which is the cause of underachievement in learning. We choose 3 middle schools as the subject of experiment for this research. Each experiment class consists of 27∼30 students(underachievers) whose final test results of 1st school year in the middle school are 30∼60 points. In this case, we also select some middle level students whose test results are more than 60 points for the normal experimental condition. For this research, we developed the suitable test materials to cure the mathematics disliking disposition of underachievers. We applied those test materials to the experiment schools during 2.5 months and we analysed the variation of disliking disposition, the variation of math. dislike students' number and the cure rate of the math. disliking disposition. From the results of this experimental study, we find that the factors of teacher and math recognition environment have only the significant difference of math. disliking disposition between experiment class and comparison class under the 5% significance level in one middle school. We understand that this results caused by teachers' careful advice and guidance in that middle school. We also find that the number of student who dislike mathematics decreased in two middle schools. Furthermore 50% of math. disliking dispositions are cured for 9 disliking factors in the lower grade group(the group of underachievers) and as a whole, we can see that 50% of cure rate for the 7 factors of math. disliking in two middle schools. So we can understand that the experiment of our research was performed successfully in two middle schools. In this research, we find out that the scheme to cure the disliking dispositions for the factors of math. disliking depends on the factors of teacher who take charge of cure. So teachers must take interest in and must have careful concern to students and their math. disliking.