• Communications of Mathematical Education
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• v.24 no.3
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• pp.611-626
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• 2010

The purpose of this study is to explore the composite properties of linear functions using CAS calculators. The meaning and processes in which technological tools such as CAS calculators generated to instrument are reviewed. Other theoretical topic is the design of an exploring model of observing-conjecturing-reasoning and proving using CAS on experimental mathematics. Based on these background, the researchers analyzed the properties of the family of composite functions of linear functions. From analysis, instrumental capacity of CAS such as graphing, table generation and symbolic manipulation is a meaningful tool for this exploration. The result of this study identified that CAS as a mediator of mathematical activity takes part of major role of changing new ways of teaching and learning school mathematics.

• Journal of Educational Research in Mathematics
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• v.10 no.2
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• pp.229-246
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• 2000

The purpose of this paper is to compare and analyze the two different teaching methods of elementary mathematics in the traditional method and in the constructive view. To do so, the actual class in the constructive view has been made for about four months using a class of 45 students in the second grade of an elementary school. After the class was finished, we collected diverse data from the class, such as the responses from the children(self-evaluation, mathematics diary, observation by the investigator, daily report), class evaluation report by other teacher and so on. The results of this research are as follows: First, the traditional class reaches at the goal of learning in a unit time because the class is guided by the teacher but the class in the constructive view is a little flexible because it is contextual. Second, in the constructive process of mathematical knowledge we knew that small group activities or discussion without intervention of teacher was often ended in exhaustive argument without arriving at valid social consensus. Third, the attitude in mathematics was changed from the passive one to the self-regulated ones. Fourth, the class in the constructive view could extend not only the ability of mathematical communication but also the ability of self-directed learning of children. Fifth, it was a considerable change the role of teacher, that is, guide of instruction instead of unique specialist in the classroom. Sixth, finally, the evaluation was made after finishing a unit class in the traditional instruction but it was integrated in a class in a constructive view.

• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.221-239
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• 2010

Attention to Korean perspective mathematics education has been increasingly paid m international academic meetings or international comparative studies. Personal or intuitive, vague explanation has been given based on limited literature or observations. This increasing attention and Jack of studies warrant the necessity of systematic researches on it. This article aims at clarifying the research issues in searching for Korean perspective on mathematics education and finding the starting point through discussion on mathematical modeling by teacher on researchers and researchers. Firstly, hypothetical perspective will be described. Secondly, Fourteen teacher educators' and seven researchers' opinion on it will be discussed. Findings imply that strong responsibility for Korean mathematics teachers to reveal theoretical aspects of mathematical knowledge, i.e., structure or essence, as well as to pursue efficiency and effectiveness in mathematics teaching and learning is the main aspect of Korean perspective on mathematics education.

• The Mathematical Education
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• v.58 no.1
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• pp.121-138
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• 2019

The purpose of this study was to analyze the trends of domestic research on mathematics teacher education in terms of the period, topics, methods, subjects, and mathematics content strands. For this purpose, a total of 220 research articles dealing with mathematics teacher education were analyzed, which have been published since 2000 by the Korean Society of Mathematics Education in the three journals: (a) The Mathematical Education; (b) Education of Primary School Mathematics; and (c) Communications of Mathematical Education. Regarding the period when the research was conducted, the number of articles on mathematics teacher education has been rapidly increased since the late 2000s. Regarding the topics, research on teacher orientation has been the most frequent topic and the studies dealing with professional development for teachers, teaching practices, or teacher knowledge tend to be popular. Regarding methods, survey and case study have been most frequently employed in studying mathematics teacher education. Regarding subjects, the main participants were in-service teachers, pre-service teachers, elementary school teachers, and secondary school teachers, respectively, who were in charge of a regular class. Finally, regarding mathematics content strands, previous studies on mathematics teacher education were not specific to mathematics content strands. Given these results, this paper closes with important implications for future research directions on mathematics teacher education in Korea.

• Education of Primary School Mathematics
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• v.16 no.1
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• pp.71-86
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• 2013

The use of manipulative materials is one of the most important teaching-learning methods at primary level, and is recommended across all grade levels and for all areas of mathematics. This study looked into specific manipulative materials suggested in Korean elementary mathematics textbooks and analysed perceptions and actual use of the manipulative materials according to the teachers. As a result, although most teachers were fully familiar with mathematical topics for which manipulative materials can be used and actually used those materials in lessons, but their knowledge on the efficiency of manipulatives and the way to use them efficiently was found somewhat insufficient. This suggests that teachers' knowledge on manipulative materials must be enhanced and there should be active measures taken to support the use of it.

• Journal of Educational Research in Mathematics
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• v.26 no.2
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• pp.173-188
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• 2016

Research on didactic transposition in mathematics education has about 25-year and about 35-year long history in and out of Korea, respectively. This study attempts to investigate in trends of those research and to suggest tasks needed to be tackled. Major findings are followed. First, studies done in Korea tended to focus on the application of the didactic transposition theory for proving its effectiveness in understanding mathematics textbooks and mathematics lessons in-depth. It is suggested to conduct meta-analysis of the accumulated results or analysis of further applications of the didactic transposition theory to improve theoretical aspects of didactic transposition. Second, new categories for extreme teaching phenomenon were found and new typology in knowledge to be considered in the didactic transposition was developed in a few studies done in other subject matter education. Application of these to mathematics education may enhance research in didactic transposition of mathematical knowledge. Third, praxeology or a complex of praxeology for Korean school mathematics should be explored as did in other countries. Fourth, there have been rich attempts to link perspectives in didactic transposition to other perspectives or fields such as anthropology, human and education in technology era, praxeology theory in economics, epistemology in other countries but not in Korea. It is suggested to extend the scope of discussion on didactic transposition and to relate various concepts given in other disciplines. Fifth, clarification or negotiation of meaning for the main terms used in the discussion on didactic transposition such as personalization, contextualization, depersonalization, decontextualization, Topaze Effect, Meta-Cognitive Shift is suggested by comparing researchers' various descriptions or uses of the terms.

• Education of Primary School Mathematics
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• v.24 no.1
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• pp.43-69
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• 2021

The purpose of this study is to confirm the influences of learner-centered instruction on learners' achievement and reason ability. In order to accomplish them, the fraction unit and the polygonal unit in the fourth grade were implemented with teaching methods and materials suitable for learner-centered mathematics instruction. Some conclusions could be drawn from the results as follows: First, learner-centered mathematics instruction has a more positive effect on learning of learned knowledge and generating unlearned knowledge in the experimental period than teacher-centered instructions. Second, learner-centered instruction makes an influence of low learning ability on getting achievement positively. Third, as the experimental treatment is repeated, learner-centered instruction has a positive effect on students' reasoning ability. The reasoning ability of students showed a difference in the comparison between the experimental group and the comparative group, and within the experimental group, there was a positive effect of the extension of the positive reasoning ability. Fourth, it can be estimated that the development of students' reasoning ability interchangeably affected their generation test results.

• Journal of the Korean School Mathematics Society
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• v.17 no.2
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• pp.251-274
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• 2014

The purpose of this study is to analyze characteristics of PCK before class, investigate how these characteristics are enacted in classrooms when beginning and experienced teachers teach mathematical functions, and provide pedagogical implications. Two beginning teachers and two experienced teachers participated in the study. In order to analyze characteristics of PCK before class, interviews and survey research were conducted. An investigation of classroom discourse was used to examine how the PCK characteristics appear in classrooms. Results show that experiences teachers enacted their PCK about learner, curriculum, teaching methods, and teaching environment in classrooms, whereas beginning teachers could not show their PCK. These results suggest practical implications for the developments of teacher education curriculum and teacher training program.

• Korean Journal of Child Education & Care
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• v.17 no.4
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• pp.145-161
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• 2017

The purpose of this study was to analyze the relationship among NCS basic vocational competencies, Teaching Personality Aptitude and DISC behavior type of pre-preschool teachers. The subjects were 110 pre-preschool teachers attended in D university located in Kyonggido. 'NCS basic vocational competencies scale', 'Teaching Personality and Aptitude scale', and 'DISC behavior type scale' were used in the collection of data. It used Pearson's correlation Analysis to analyze the data. The results of this study are as follows; first, there was positive correlations between dominance trait and mathematical competency. And, there was positive correlations between interaction trait and self-development competency. And there were negative correlations between support traits and NCS basic vocational competencies. Second, it was revealed that positive correlations between almost sub scale's of NCS basic vocational competencies and teacher teaching personality aptitude. Third, there was positive correlations between dominance trait and sub scale of teaching personality aptitude(e.g.: problem solving/ inquiry skills, judgment, creativity/practical ability, leadership, knowledge/information ability, planning ability, sincerity/responsibility). And there were negative correlations between support traits and sub scale of teaching personality aptitude(e.g.: problem solving/ inquiry skills, judgment, creativity/practical ability, leadership, sincerity/responsibility).

• Journal of Educational Research in Mathematics
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• v.15 no.3
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• pp.251-272
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• 2005

Given that cognitive demands of mathematical tasks can be changed during instruction, this study attempts to provide a detailed description to explore how tasks are set up and implemented in the classroom and what are the classroom-based factors. As an exploratory and qualitative case study, 4 of six-grade classrooms where high-level tasks on ratio and proportion were used were videotaped and analyzed with regard to the patterns emerged during the task setup and implementation. With regard to 16 tasks, four kinds of Patterns emerged: (a) maintenance of high-level cognitive demands (7 tasks), (b) decline into the procedure without connection to the meaning (1 task), (c) decline into unsystematic exploration (2 tasks), and (d) decline into not-sufficient exploration (6 tasks), which means that the only partial meaning of a given task is addressed. The 4th pattern is particularly significant, mainly because previous studies have not identified. Contributing factors to this pattern include private-learning without reasonable explanation, well-performed model presented at the beginning of a lesson, and mathematical concepts which are not clear in the textbook. On the one hand, factors associated with the maintenance of high-level cognitive demands include Improvising a task based on students' for knowledge, scaffolding of students' thinking, encouraging students to justify and explain their reasoning, using group-activity appropriately, and rethinking the solution processes. On the other hand, factors associated with the decline of high-level cognitive demands include too much or too little time, inappropriateness of a task for given students, little interest in high-level thinking process, and emphasis on the correct answer in place of its meaning. These factors may urge teachers to be sensitive of what should be focused during their teaching practices to keep the high-level cognitive demands. To emphasize, cognitive demands are fixed neither by the task nor by the teacher. So, we need to study them in the process of teaching and learning.