• Journal of the Korean School Mathematics Society
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• v.20 no.4
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• pp.495-519
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• 2017

The purpose of this study is to analyze the concept of the real number e and to investigate the understanding of pre-service teachers about the real number e. 28 pre-service teachers were asked to take a test based on the various ideas of the real number e and 8 pre-service teachers were interviewed. The results of this study are as follows. First, a large number of pre-service teachers couldn't recognize relation between the formal definition and the representations of the real number e. Secondly, pre-service teachers judged appropriately for the irrationality and the construction impossibility of the real number e, but they couldn't provide reasonable evidence. Lastly, pre-service teachers understood the continuous compounding context and exponential function context of the real number e, but they had a difficulty in understanding the geometric context and natural logarithm context of the real number e.

• School Mathematics
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• v.16 no.3
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• pp.491-502
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• 2014

This paper analyzed pre-service teachers' justification of $0.99{\cdots}$=1 from their disproof of $0.99{\cdots}$ <1. Some pre-service teachers thought of the difference between $0.99{\cdots}$ and 1 as an infinitesimal. On the contrary, the others claimed that the difference between $0.99{\cdots}$ and 1 was zero as the standard real, but were content with their intuitive justifications. The pre-service teachers' limitation revealed in the process of disproving $0.99{\cdots}$ <1 can be closely related to the orthodox view: the standard real number system is the only absolutely true number system. The existence of nonstandard real number system in which $0.99{\cdots}$ is less than 1, shows that the plain question of whether or not $0.99{\cdots}$ equals 1, cannot be properly answered by common explanations of textbooks or teachers' intuitive justification.

• Journal of Educational Research in Mathematics
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• v.25 no.3
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• pp.263-279
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• 2015

The introduction of real numbers is one of the most difficult steps in the teaching of school mathematics since the mathematical justification of the extension from rational to real numbers requires the completeness property. The author elucidated what questions about real numbers can be unanswered as the "institutional didactic void" in school mathematics defining real numbers as the union of the rational and irrational numbers. The pre-service teachers' explanations on the extension from rational to real numbers and the raison d'$\hat{e}$tre of arbitrary non-recurring decimals showed the superficial and fragmentary understanding of real numbers. Connecting school mathematics to university mathematics via the didactic void, the author discussed how pre-service teachers could break the illusion of transparency about the real number.

• School Mathematics
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• v.17 no.2
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• pp.309-329
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• 2015

This study is to provide didactical implications for teaching and learning of radian through a analysis of investigation result about pre-service teachers' understanding of radian. The results of this study are as follows. First, pre-service teachers understood the radian as ${\frac{180^{\circ}}{\pi}}$, rather than as the definition. Secondly, the definition style of radian affected the problem solving strategy for the measurement of the angle. Thirdly, pre-service teachers had insufficient content knowledge about properties of measurement as a pure number of radian. Lastly, They failed to describe the usefulness of circular measure. We suggested the definition of radian in textbooks should be changed from ${\frac{180^{\circ}}{\pi}}$ to mathematical definition of radian. And the general angle should be stated as the reason why the domain of trigonometric function is real numbers.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.20 no.2
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• pp.336-345
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• 2019

To extend the potential benefits of error, the current study examined factors that affect students' error perception in classroom. An experimental design was used to measure relations of classroom goal structure, feedback, and social relationships on students' perception of error. A total 316 fourth, fifth, and sixth graders attending elementary schools participated as part of their regular class curriculum. Self-reported questionnaires were administered to measure students' perception of errors and relationships with teacher and peers, then students were manipulated by classroom goal structure and feedback. Results from multiple regression suggest that students' perception of learning from error has affected by relationships with peers at the most, then relationships with teacher and the type of feedback. Students' perception of risk taking for error also affected by relationships with peers and teacher, then the classroom goal structure. However, no classroom goal structure and feedback affect on their perception of thinking about error to improve their learning as well as error strain. These results imply how classroom climate should be structured to improve perception of errors to improve student's learning.

• Communications of Mathematical Education
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• v.25 no.2
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• pp.323-339
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• 2011

The expansion of exponential law as the law of calculation of integer numbers can be a good material for the students to experience an extended configuration which is based on an algebraic principle of the performance of equivalent forms. While current textbooks described that exponential law can be expanded from natural number to integer, rational number and real number, most teachers force students to accept intuitively that the exponential law is valid although exponent is expanded into real number. However most teachers overlook explaining the value of exponent of rational number or exponent of irrational number so most students have a lot of questions whether this value is a rational number or a irrational number. Related to students' questions, most teacher said that it is out of the current curriculum and students will learn it after going to college instead of detailed answers. In this paper, we will present several examples and the values about irrational exponents of a positive rational and irrational exponents of a positive irrational number, and study the recognition and fallacy of would-be teachers about the cases of irrational exponents of a positive rational and irrational exponents of a positive irrational number at the expansion of exponential law.

• Korean Journal of Childcare and Education
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• v.9 no.2
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• pp.23-46
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• 2013

The purpose of this study was to obtain basic information for novice teachers' adjustment. The data from five novice teachers were collected by in-depth interviews of each subject, as well as reviewing a memo diary, journal and class diary. The results indicated that the novice teachers' experiences were categorized into difficulties in social relationships, heavy workload, stress related to making mistakes, obtaining support and assistance, adequate understanding of their field of work and so on. The model theory for their process of adjustment was found by grounded theory approach. The causal conditions include mistakes in performance of work and immaturity of managing social relationships. The contexts include age of the children, work conditions(i.e. time and space), amount of workload, unfamiliarity of new work assignments, personalities of colleagues, and high frequency of meeting parents of children. The intervening conditions are composed of a guidance program for novice teachers, support from colleagues, work rewards, and the personalities of novice teachers. The novice teacher use three strategies: trying to ignore, sharing difficulties and accessing support from friends or family, as well as willful efforts to transfer negative emotions into positive ones. The consequences of the strategies include: successful career progression, survival, and desire for leaving the field of work.

• Journal of Educational Research in Mathematics
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• v.22 no.2
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• pp.163-178
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• 2012

The efforts to represent the numbers based on the decimal system give us fundamental understanding to construct and teach the concept network on the related knowledge of elementary and secondary school mathematics. In the process to represent natural numbers, integers, rational numbers, real numbers as decimal system, we will classify the extended decimal system. Moreover we will obtain the view to classify real numbers. In this paper, we will study the didactical significance of mathematical knowledge, which arise from process to represent real numbers as decimal system, starting from decimal system representation of natural numbers, and provide the theoretical base about the classification of real numbers. This study help math teachers to understand school mathematics in critical inside-measurement and provide the theore tical background of related knowledge. Furthermore, this study provide a clue to construct coherent curriculum and internal connections of related mathematical knowledge.

• Journal of The Korean Association For Science Education
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• v.25 no.3
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• pp.364-370
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• 2005

The purpose of this study was to examine middle school students' (N= 153) perceptions of motivational climate (teacher learning/teacher comparison/peer learning/peer comparison/peer worry) and their achievement goals (task/performance/performance-avoidance). The influence of perceptions of motivational climate emphasized by science teachers and/or peers on achievement goals was explored by stepwise regression. Although there was no difference in male/female perceptions of motivational climate, there was significant difference in their achievement goals. Regression result indicated that the pursuit of learning by peers made the strongest contribution to students' task goal. On the other hand, promotion via comparison by science teachers or peers had little effect on inducing performance goal. Anxieties about mistakes were found to be the strongest contribution to predictions on students' performance-avoidance goal. The promotion of comparison by science teachers was related to not only performance goal, but also performance-avoidance goal. Lastly educational implications for intervention efforts designed to enhance the quality of student motivational development in science education are discussed.

• Journal of Digital Convergence
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• v.14 no.1
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• pp.25-31
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• 2016

This study aims to suggest the improvement plan for the future church schools and the teachers after examining the reality and the situation of the teachers in church schools in Korea. In order to do this, the study examined the factors of the changes in Christian population in Korea, the factors of reduced number of Christian population and the factors of the reduced number of students in church schools. It also conducted the survey on the teachers in church schools to find the actual problems and situation of them. Based on the result and analysis of the survey, the study will suggest the alternative plans for improvement. The study asked 12 questions of 534 teachers to examine the real situations of the teachers in church schools in Korea and based on the analysis and result of it, the study will suggest a couple of alternatives to the teachers.