• Journal of The Korean Association For Science Education
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• v.30 no.7
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• pp.908-919
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• 2010

The objectives of this study were to investigate what kind of background concepts is necessary to help that high school students easily understand meiosis and to find out how these background concepts affect students' understanding of meiosis. To achieve these objectives, first this study surveyed meiosis background concepts that high school teachers think. Based on 8 background concepts - nuclear phases, chromosome, mitosis, reproduction, gamete, gene, mother/daughter cell - of previous survey, the questionnaire was made for the 10th(724) and 11th(862) grade students and then was analyzed for the effect of meiosis background concepts on the high school students' understanding of meiosis. Results of the analysis revealed that the influential background concepts are as follow; cell cycle, chromosome in the advanced level, mother/daughter cell, mitosis, chromosome, nuclear phases in the intermediate level, mother/daughter cell, nuclear phases, gene in the low level. And the achievement according to item types was differed not by meiosis achievement, but by each background concepts.

• The Mathematical Education
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• v.42 no.1
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• pp.11-18
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• 2003

One of the terms that are most often used in mathematics classrooms by either teachers or students might be about 'understanding' of mathematical concepts. Although 'understanding' in mathematics teaching and learning has been highly emphasized by many people, there is no exact and undebatable definition of 'understanding' as of yet. This paper tries to contribute to unfolding the meaning and the structure of understanding in mathematics education along with various literature and finally enhance our understanding of 'understanding' in mathematics education.

• Journal of Korean Elementary Science Education
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• v.35 no.4
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• pp.389-405
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• 2016

The purpose of this study was to analyze elementary school teachers' understanding, certainty, and familiarity with 13 key concepts of wave physics that are presented in textbook and teacher's guidebook. 123 elementary school teachers answered concept tests and questionnaires. In the results to these tests and questionnaires, teachers demonstrated a high level of understanding and high certainty in understanding with regard to the concepts of sound generation, effect of medium on wave, timbre, wavelength, and trough and crest of wave. For the topics of sound velocity, wave reflection and wave transmission, teachers demonstrated a high level of understanding but low certainty in understanding. With regard to sound propagation, teachers demonstrated a low level of understanding and an improperly high certainty in that low understanding. Teachers lacked knowledge, i.e., displayed a low level of understanding and low certainty in sound strength, sound frequency, constructive interference and destructive interference. In constructive and destructive interference, the teachers also displayed a low level of familiarity. We analyzed the differences in teacher's understanding, certainty, and familiarity according to teacher demographics defined by the teacher's gender, teaching experience with concepts of sound, career, curriculum track while in high school, and major in university. There were no significant differences in understanding, certainty, or familiarity as defined by gender, teaching experience, and career. However, these displays of knowledge were affected by the teacher's curriculum track in high school and their major. These results suggest that the teacher's understanding of, familiarity with, and certainty in wave physics concepts are more influenced by their learning experience than by their teaching experience. Therefore, we suggest additional learning opportunities for teachers (such as teacher training programs) in order to improve teacher knowledge and correct teacher misconceptions in wave physics.

• East Asian mathematical journal
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• v.29 no.2
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• pp.207-239
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• 2013

This research is a study on student's understanding fundamental concepts of mathematical curriculum, especially in geometry domain. The goal of researching is to analyze student's concepts about that domain and get the mathematical teaching methods. We developed various questions of descriptive assessment. Then we set up the term, procedure of research for the understanding student's knowledge of geometric figures. And we analyze the student's understanding extent through investigating questions of descriptive assessment. In this research, we concluded that most of students are having difficulty with defining the fundamental concepts of mathematics, especially in geometry. Almost all the students defined the fundamental conceptions of mathematics obscurely and sometimes even missed indispensable properties. And they can't distinguish between concept definition and concept image. Prior to this study, we couldn't identify this problem. Here are some suggestions. First, take time to reflect on your previous mathematics method. And then compile some well-selected questions of descriptive assessment that tell us more about student's understanding in geometric concepts.

• School Mathematics
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• v.12 no.4
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• pp.547-561
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• 2010

Even though statistics is considered as one of the areas of mathematical science in the school curriculum, it has been well documented that statistics has distinct features compared to mathematics. However, there is little empirical educational research showing distinct features of statistics, especially research into the understanding of statistical concepts which are different from other areas in school mathematics. In addition, there is little discussion of a relationship between the ability of mathematical thinking and the ability of understanding statistical concepts. This study extracted some important concepts which consist of the fundamental statistical reasoning and investigated how mathematically high achieving students understood these concepts. As a result, there were both kinds of concepts that mathematically high achieving students developed well or not. There is a weak correlation between mathematical ability and the level of understanding statistical concepts.

• Communications of Mathematical Education
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• v.22 no.3
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• pp.311-335
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• 2008

The importance of students' precise understanding of mathematical definitions, formulas, and theorems can not be underestimated. In this survey research, we attempted to evaluate students' understanding of the concepts of five topics -limit, continuity and intermediate theorem, derivative, application of derivative and integral. On the basis of the research result, this paper suggests that we need to 1) be more inventive and speculative in making test problems, 2) explain the examples and counter-examples more concretely, 3) stress and repeat the basic concepts on the stage of introducing new concepts, 4) develop more effective problems for the measure of students' understanding of mathematical concepts, 5) use developed problems in actual teaching.

• The Mathematical Education
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• v.40 no.2
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• pp.241-252
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• 2001

Many high school students are having difficulties for studying advanced mathematics concepts. It is more complicated than in junior high school and they are losing interest and confidence. In this paper, advanced mathematics concepts are not just basic concepts such as natural numbers, fractions or figures that can be learned through life experience but concepts that are including variables, functions, sets, tangents and limits are more abstract and formal. For the students to understand these ideas is too heavy a burden and so many of the students concentrate their efforts on just memorizing and not understanding. It is necessary to search for a meaningful method of teaching for advanced mathematics that covers deductive methods and symbols. High school teachers are always asking themselves the following question, “How do we help the students to understand the concept clearly and instruct it in a meaningful way?” As a solution we propose the followings : I. To ensure they have the right understanding of concept image involved in the concept definition. II. Put emphasis on the process of making mental representations and the role of intuition. III. To instruct students and understand them as having many chance of the instructional conversation. In conclusion, we studied the meaningful method of teaching with the theory of Ausubel related to the above proposed methods. To understand advanced mathematics concepts correctly, the mutual understanding of both teachers and students is necessary.

• Research in Mathematical Education
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• v.17 no.1
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• pp.63-78
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• 2013

Trigonometric ratios are difficult concepts to teach and learn in middle school. One of the reasons is that the mathematical terms (sine, cosine, tangent) don't convey the idea literally. This paper deals with the understanding of a concept from the learner's standpoint, and searches the orientation of teaching that make students to have full understanding of trigonometric ratios. Such full understanding contains at least five constructs as follows: skill-algorithm, property-proof, use-application, representation-metaphor, history-culture understanding [Usiskin, Z. (2012). What does it mean to understand some mathematics? In: Proceedings of ICME12, COEX, Seoul Korea; July 8-15,2012 (pp. 502-521). Seoul, Korea: ICME-12]. Despite multi-aspects of understanding, especially, the history-culture aspect is not yet a part of the mathematics class on the trigonometric ratios. In this respect this study investigated the effect of history approach on students' understanding when the history approach focused on the mathematical terms is used to teach the concept of trigonometric ratios in Grade 9 mathematics class. As results, the experimental group obtained help in more full understanding on the trigonometric ratios through such teaching than the control group. This implies that the historical derivation of mathematical terms as well as the context of mathematical concepts should be dealt in the math class for the more full understanding of some mathematical concepts.

• School Mathematics
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• v.11 no.2
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• pp.261-280
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• 2009

This study was motivated by recognizing the weakness of teaching and learning about the concepts of statements in high school mathematics curriculum. To report the reality of students' understanding about statements, this study investigated the 33 first-year undergraduate students' understanding about the concepts of statements by giving them 22 statement problems. The problems were selected based on the conceptual framework including five types of statement concepts which are considered as the key ideas for understanding mathematical reasoning and proof in college level mathematics. The analysis of the participants' responses to the statement problems found that their understanding about the concepts of prepositions are very limited and extremely based on the instrumental understanding applying an appropriate remembered rule to the solution of a preposition problem without knowing why the rule works. The results from this study will give the information for effective teaching and learning of statements in college level mathematics, and give the direction for the future reforming the unite of statements in high school mathematics curriculum as well.

• Journal of the Korean Chemical Society
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• v.61 no.1
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• pp.34-44
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• 2017

The purpose of this study was to analyze the conception type change and to investigate the effect of understanding on concepts in electrochemistry after general chemistry lessons. The significant differences in concept understanding of electrochemistry were shown in both groups. Statistically significant gains in both groups were as shown in distinguishing the chemical cell, in identifying the anode and cathode, and in understanding current formation and flow, while, significant achievements in understanding the role of the salt bridge, and the need for a standard half-cell were not found. Taking elective chemistry II in high school had an effect on understanding related concepts of electrochemistry in general chemistry lessons. It was shown that many freshmen had difficulties in understanding exact related concepts in several kinds after general chemistry lessons. In order to solve these problems, it is necessary to teach contents of the basic concepts in electrochemistry exactly and to hold supplementary lessons.