• Education of Primary School Mathematics
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• v.20 no.4
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• pp.253-266
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• 2017

The purpose of the study was to investigate the perceptions of Elementary school teachers on mathematics instruction. To do this, 7 test items were developed to obtain data on teacher's perception of mathematics instruction and 73 teachers who take mathematical lesson analysis lectures were selected and conducted a survey. Since the data obtained are all qualitative data, they were analyzed through coding and similar responses were grouped into the same category. As a result of the survey, several facts were found as follow; First, When teachers thought about 'mathematics', the first words that come to mind were 'calculation', 'difficult', and 'logic'. It is necessary for the teacher to have positive thoughts on mathematics and mathematics learning, and this needs to be stressed enough in teacher education and teacher retraining. Second, the reason why mathematics is an important subject is 'because it is related to the real life', followed by 'because it gives rise to logical thinking ability' and 'because it gives rise to mathematical thinking ability'. These ideas are related to the cultivating mind value and the practical value of mathematics. In order for students to understand the various values of mathematics, teachers must understand the various values of mathematics. Third, the responses for reasons why elementary school students hate mathematics and are hard are because teachers demand 'thinking', 'because they repeat simple calculations', 'children hate complicated things', 'bother', 'Because mathematics itself is difficult', 'the level of curriculum and textbooks is high', and 'the amount of time and activity is too much'. These problems are likely to be improved by the implementation of revised 2015 national curriculum that emphasize core competence and process-based evaluation including mathematical processes. Fourth, the most common reason for failing elementary school mathematics instruction was 'because the process was difficult' and 'because of the results-based evaluation'. In addition, 'Results-oriented evaluation,' 'iterative calculation,' 'infused education,' 'failure to consider the level difference,' 'lack of conceptual and principle-centered education' were mentioned as a failure factor. Most of these factors can be changed by improving and changing teachers' teaching practice. Fifth, the responses for what does a desirable mathematics instruction look like are 'classroom related to real life', 'easy and fun mathematics lessons', 'class emphasizing understanding of principle', etc. Therefore, it is necessary to deeply deal with the related contents in the training courses for the improvement of the teachers' teaching practice, and it is necessary to support not only the one-time training but also the continuous professional development of teachers.

• Journal of Gifted/Talented Education
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• v.5 no.2
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• pp.37-54
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• 1995

The radical development of modern mathematics is due to the appearance of Collection Theory by George Cantor. The Set Theory is independent as an area and also closely interrelated with other areas. So its content becomes a common sense and a basic part across the whole area of modern mathematics. Accordingly, the basic element of modern mathematics is helping young children get familiar with set as early as possible. The thinking of set by which children can categorize, make partial sets and correspondences, understand the general characteristic, and conceptualize the discovered relationships is very important for young children. At this point where the Math education for young children is emphasized under the influence of the modernization movement of Math education, the systematic education for building up the set concept as the basic background of number concept during the early childhood is required. On current mathematics education for young children, graphs, the foundation of geometry, time, and patterns have been included in the traditional and practical content related to numbers. However, the education on collection which is the foundation of number concept is insufficient. A study shows that the level of young children's understanding on set is quite high, but the set concept isn't reflected in current Math curriculum for young children. And basic activities neccesary on building up the set concept, such as categorization, comparison, etc. are conducted in kindergardens but unsatisfactory because of those kindergarden teachers' premature understanding on the set concept. In conclusion, the curriculum for young children should be reorganized based on the set concept as the kernel concept. Also, the reappraisal of the training curriculum and the supplementary efucation for kindergarden teachers are urgent for raising the teaching ability of those kindergarden teachers.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.553-563
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• 1998

In this thesis, I examined Bruner's EIS theory from the viewpoint of epistemology based on Piaget's genetic epistemology. Although Bruner's ideal thought which insisted ‘to teach the structure’accepted Piaget's theory in the methodology of realization, it is different from Piaget in understanding knowledge. The difference is shown from understanding the meaning of ‘structure’. Piaget's concept of structure is something that has overcome the realistic viewpoint of the traditional epistemology and is reconstructed through endless self-regulative transformational process. However Bruner's is used as a realistic meaning as we can see in the Plato's recollection theory. Therefore Piaget's ‘stage of development’means the difference of structure which lies in the generative process and it includes the qualitive difference of level. On the other hand, Bruner, who is trying to translate and suggest the fixed structure to the children understood Piaget's stage of development as the difference in the ways of representation. Piaget's operational constructivism insists that the children should ‘construct’the knowledge through their activity, and especially in case of the lohico-mathematical recognition, the source should be internalized activity, that is, operation. In view of this assertion, Burner's idea which insists to accept the structure of knowledge as a fixed reality and to suggest the translated representation proper to the cognitive structure of the children to teach them, has a danger of emphasizing only the functional aspects to deliver the given knowledge ‘quickly’. And it also has the danger of damaging ‘the nature of the knowledge’in the translated knowledge.

• Journal of the Korean School Mathematics Society
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• v.15 no.4
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• pp.643-671
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• 2012

The purpose of this study was to examine How the exploratory activities using Excel and GSP which are exploratory software, in learning analytic geometry affected on the underachievers' analytic geometry concept development process. The subjects of 5 students who received the 8th~9th grades from their examination of the last semester, participated in a total of 7 units based on Skemp's intelligent learning model. The results of the study showed that there were two important cases found to nearly achieve the category $R_2$. One was reflective thinking could happen through exploratory software in category $R_1$. The other was the exploratory activities which could have the same effectiveness as the relational understanding in category $I_2$, as Skemp mentioned that there is a room to be achieved in the elementary level when such relational understanding is achieved.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1245-1252
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• 2011

Consider the $L^2$-adjoint $s_g^{'*}$ of the linearization of the scalar curvature $s_g$. If ker $s_g^{'*}{\neq}0$ on an n-dimensional compact manifold, it is well known that the scalar curvature $s_g$ is a non-negative constant. In this paper, we study the structure of the level set ${\varphi}^{-1}$(0) and find the behavior of Ricci tensor when ker $s_g^{'*}{\neq}0$ with $s_g$ > 0. Also for a nontrivial solution (g, f) of $z=s_g^{'*}(f)$ on an n-dimensional compact manifold, we analyze the structure of the regular level set $f^{-1}$(-1). These results give a good understanding of the given manifolds.

• The Mathematical Education
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• v.61 no.2
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• pp.339-357
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• 2022

This study explores pre-service secondary mathematics teachers (PSTs)' noticing competency. 17 PSTs participated in this study as a part of the mathematics teaching method class. Individual PST's essays regarding the question 'what effective mathematics teaching would be?' that they discussed and wrote at the beginning of the course were collected as the first data. PSTs' written analysis of an expert teacher's teaching video, colleague PSTs' demo-teaching video, and own demo-teaching video were also collected and analyzed. Findings showed that most PSTs' noticing level improved as the class progressed and showed a pattern of focusing on each key aspect in terms of the Teaching for Robust Understanding of Mathematics (TRU Math) framework, but their reasoning strategies were somewhat varied. This suggests that the TRU Math framework can support PSTs to improve the competency of 'what to attend' among the noticing components. In addition, the instructional reasoning strategies imply that PSTs' noticing reasoning strategy was mostly related to their interpretation of noticing components, which should be also emphasized in the teacher education program.

• School Mathematics
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• v.13 no.1
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• pp.189-206
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• 2011

This study is to setup a mathematics PBL model that is right for elementary students. PBL models are developed and applied to actual courses and analyzed. So, a specific plan and practical understanding of PBL mathematics textbooks will be presented. But in order for this to happen, first the mathematics PBL model, that can realize 7th revised curriculum's goal, needs to setup and divided into knowledge, skill and attitude domains. Through this study, the general PBL model and the PBL model appropriate for elementary mathematics was amended and supplemented, this was then applied to courses and analyzed, and the below conclusions were realized. First, mathematical idealization stage is needed for mathematical PBL model. Since an elementary student is shortcoming in problem understanding and mathematical activity, a middle step that allows the student to understand the problem situation mathematizing and find a solution mathematically is desperately needed. Therefore, in this study, we named it the mathematical idealization stage and had it setup. Second, a mathematics information collection stage needs to be prepared for a successful PBL. Through this stage, the students will have an opportunity to gather the necessary information needed and restructure it to solve the problem. Third, the organization stage in mathematical PBL model needs to be strengthened. PBL is not just completed, through the best use of mathematics subject matter to solve the problem. Organization time is needed to allow the students to grow to a more deepened and advanced level. In conclusion, there is significance in providing a specific plan for mathematical PBL model, which can be seen through this study on applying and analyzing elementary mathematics and appropriate PBL models.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.1
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• pp.39-56
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• 2015

The aim of the study presented in this paper was to explore South Korean elementary teachers' knowledge regarding educational theory in mathematics. An independent t-test and ANOVA are applied to examine elementary teachers' knowledge regarding educational theory in mathematics. Findings of this study suggest that there is a negative correlation between the teachers' knowledge regarding educational theory in mathematics and their teaching experiences as well as the teacher certification level. However, there is a little affect of the teachers' gender and educational backgrounds on the teachers' knowledge regarding educational theory in mathematics. The results of this quantitative study may broaden our understanding of the South Korean elementary teachers' knowledge for teaching mathematics, which have a deep impact on their teaching practice.

• Journal of the Korean School Mathematics Society
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• v.21 no.4
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• pp.469-483
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• 2018

The purpose of this study is to find out how pre-service mathematics teachers should prepare for the teaching of probability and statistics in school mathematics and to help improve teacher education. To do this, questionnaires and evaluation of probabilistic and statistical curriculum were conducted for pre-service teachers, and regression analysis and correlation between them were examined. Through the investigation, the items with low evaluation results due to level of difficulty were extracted and analyzed. As a result, first, it is necessary to teach pre-service mathematics teachers with link the contents curriculum of college and secondary school about probability and statistics. Second, accurate diagnosis of pre-service mathematics teachers' understanding of probability and statistics is needed. Third, the misconceptions and causes of pre-service mathematics teachers were analyzed in detail. And suggests that various follow-up studies related to this are needed.

• Communications of Mathematical Education
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• v.26 no.1
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• pp.109-135
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• 2012

On the standards or elements of teaching evaluation, the Korea Institute of Curriculum and Evaluation(KICE) has carried out the following research such as : 1) development of the standards on teaching evaluation between 2004 and 2006, and 2) investigation on the elements of Teacher Knowledge. The purposes of development of evaluation standards for mathematics teaching through those studies were to improve not only mathematics teachers' professionalism but also their own teaching methods or strategies. In this study, the standards were revised and modified by analyzing the results of those studies focused on the knowledge of subject matter knowledge, knowledge of learners' understanding, teaching and learning methods and assessments, and teaching contexts. For this purpose, the part of subject matter knowledge was consisted of four evaluation domains such as the knowledge of curriculum reconstruction, knowledge of mathematical contents, methodological knowledge, mathematical value. The part of Learners' unders tanding included the evaluation domains such as students' intellectual and achievement level, students' misconception in math, students' motivation on learning, students' attitude on mathematics learning, and students' learning strategies. The part of teaching methods and evaluation was consisted of seventh evaluation domains such as instruction involving instructional goal and content, instruction involving problem-solving activity, instruction involving learners' achievement level and attitude, instruction on communication skills, planning of assessment method and procedure, development on assessment tool, application on assessment result in class were new established. Also, the part of teaching context was consisted of four evaluation domains such as application of instructional tools and materials, commercial manipulatives, environment of classroom including distribution and control of class group, atmosphere of classroom, management of teaching contexts including management of student. According to those evaluation domains of each teacher knowledge, elements on teaching evaluation focused on the teacher's knowledge were established using the instructional evaluation framework, which is developed in this study, including the four areas of obtaining, planning, acting, and reflecting.