• Journal of Educational Research in Mathematics
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• v.14 no.2
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• pp.171-185
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• 2004

Students are exposed to a concept of tangent from a specific context of the relation between a circle and straight lines at the 7th grade. This initial experience might cause epistemological obstacles regarding learning concepts of tangent to additional curves. The paper provides a method of how to introduce a series of concepts of tangent in order to lead students to revise and improve the concept of tangent which they have. As students have chance to reflect and revise a series of concepts of tangent step by step, they realize the facts that the properties such as 'meeting the curve at one point' and 'touching but not cutting the curve' may be regarded as the proper definition of tangent in some limited contexts but are not essential in more general contexts. And finally students can grasp and appreciate that concept of tangent as the limit of secants and the relation between tangent and derivative.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.273-289
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• 2001

Given that the culture of the mathematics classroom has been perceived as an important topic in mathematics education research, this paper deals with the construct of sociomathematical norms which can be used as an analytical tool in understanding classroom mathematical culture. This paper first reviews the theoretical foundations of the construct such as symbolic interactionism and ethnomethodology, and describes the actual classroom contexts in which social and sociomathematical norms were originally identified. This paper then provides a critical analysis of the previous studies with regard to sociomathematical norms. Whereas such studies analyze how sociomathematical norms become constituted and stabilized in the specific classroom contexts, they tend to briefly document sociomathematical norms mainly as a precursor to the detailed analysis of classroom mathematical practice. This paper reveals that the trend stems from the following two facts. First, the construct of sociomathematical norms evolved out of a classroom teaching experiment in which Cobb and his colleagues attempted to account for students' conceptual loaming as it occurred in the social context of an inquiry mathematics classroom. Second, the researchers' main role was to design instructional devices and sequences of specific mathematical content and to support the classroom teacher to foster students' mathematical learning using those sequences Given the limitations in terms of the utility of sociomathematical norms, this paper suggests the possibility of positioning the sociomathematical norms construct as more centrally reflecting the quality of students' mathematical engagement in collective classroom processes and predicting their conceptual teaming opportunities. This notion reflects the fact that the construct of sociomathematical norms is intended to capture the essence of the mathematical microculture established in a classroom community rather than its general social structure. The notion also allows us to see a teacher as promoting sociomathematical norms to the extent that she or he attends to concordance between the social processes of the classroom, and the characteristically mathematical ways of engaging. In this way, the construct of sociomathematical norms include, but in no ways needs to be limited to, teacher's mediation of mathematics discussions.

• Journal of The Korean Association For Science Education
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• v.15 no.3
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• pp.332-348
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• 1995

The use of attitude as a psychological concepts dates back to 1918(Thomas and Znaniecki). Assessment of attitudes has been conducted by a number of researchers since then in a wide range of contexts: religion, government, industry, community interrelations, and education; and sociology and psychology. In science, the number of research summaries and meta-analyses points to the significance of the concept of attitude toward science. However, in spite of the wide spread use of attitude assessment in science, many of the existing instruments have severe limitations. Those limitations serve as the rationale for the construction of a new instrument to assess attitudes toward science The term "attitude" and "science" are somewhat ambiguous, taking on different meanings for different people in different contexts. Very often an assessment includes several dimensions of attitude and, therefore, provides no clear idea of what was really measured. As a result there is no consistency with respect to the construct among attitude instruments. To clarify this issue, Gauld(1982), Munby(1983a, 1983b), Blosser(1984) and Haladyna and Shaughnessy(1982) offer some guiding descriptions. Attitude as it relates to science is divided into two areas-scientific attitude and attitude toward science. Scientific attitude refers to a particular approach a person assumes for solving problems, for assessing ideas and information, and for making decisions. It includes such scientific methods and predispositions as objectivity, suspended judgement, critical evaluation, and skepticism. Munby(1983a, 1983b) characterized scientific attitude as thinking as scientists do, that is, acting on evidence in a disciplined way. Attitude toward science. on the other hand, may address scientific attitudes, scientists, scientific careers, methods of teaching science, scientific interests, parts of curriculum, or the subject of science in the classroom (Blosser,1984). It may refer to belief about processes, theoretical products, technological products, or the science-technology relationship (Munby, 1983).

• Journal of The Korean Association For Science Education
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• v.28 no.1
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• pp.1-14
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• 2008

The image of science is one of the recurrent topics in science education research. In particular, we believe that students' images of Doing-Science-Well could be used for identifying not only students' perceived goals of science learning, but also practical guidelines of effective science teaching. In this study, the students' images of Doing-Science-Well were investigated with the following two research questions: (i) what are student's images of Doing-Science-Well?; (ii) in what contexts do students perceive that someone is doing science well? Thirty seven students in a high school in Seoul, Korea were asked to write their personal experiences by which they realized that someone was doing science well. The main results of the study are the following: Firstly, the images of Doing-Science-Well could be categorized into 'Einstein type', 'Socrates type', 'MacGyver type' and six more types. Secondly, with regard to contexts, students tended to realize that somebody is doing science well in terms of two kinds of contexts: 4 physical contexts and 6 psychological contexts. The findings led us to develop a frame of judging Doing-Science-Well, which combines the types and two kinds of contexts. The frame illustrates the multiplicity of the images of Doing-Science-Well.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.4
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• pp.385-403
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• 2018

Fraction division can be categorized as partitive division, measurement division, and the inverse of a Cartesian product. In the contexts of quotitive division and the inverse of a Cartesian product, the multiply-by-the-reciprocal algorithm is drawn well out. In this study, I analyze the potential and significance of the method of using $1{\div}$(divisor) as an alternative way of developing the multiply-by-the-reciprocal algorithm in the context of quotitive division. The method of using $1{\div}$(divisor) in quotitive division has the following advantages. First, by this method we can draw the multiply-by-the-reciprocal algorithm keeping connection with the context of quotitive division. Second, as in other contexts, this method focuses on the multiplicative relationship between the divisor and 1. Third, as in other contexts, this method investigates the multiplicative relationship between the divisor and 1 by two kinds of reasoning that use either ${\frac{1}{the\;denominator\;of\;the\;divisor}}$ or the numerator of the divisor as a stepping stone. These advantages indicates the potential of this method in understanding the multiply-by-the-reciprocal algorithm as the common structure of fraction division. This method is based on the dual meaning of a fraction as a quantity and the composition of times which the current elementary mathematics textbook does not focus on. It is necessary to pay attention to how to form this basis when developing teaching materials for fraction division.

• School Mathematics
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• v.19 no.1
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• pp.209-228
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• 2017

Understanding decimal numbers is important in mathematics as well as real-life contexts. However, lots of students focus on procedures or algorithms of decimal numbers without understanding its meanings. This study analyzed teaching method related to decimal numbers in a series of mathematics textbooks of Korea, Japan, Singapore and the US. The results showed that three countries except Japan introduced the decimal numbers as another name of fraction, which highlights the relation between the concept of decimal numbers and fractions. And limited meanings of decimal numbers were shown such as 'equal parts of a whole' and 'measurement'. Especially in the korean textbooks, relationships between the decimals were dealt instrumentally and small number of models such as number lines or $10{\times}10$ grids were used repeatedly. Based these results, this study provides implications on what and how to deal with decimal numbers in teaching and learning decimal numbers with textbooks.

• Journal of Science Education
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• v.46 no.1
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• pp.109-120
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• 2022

Fraction division is the content that is important but difficult to learn because it includes the process of finding a numerical expression in the real-world context, the process of making a context that matches a numerical expression, how to solve division, and the justification of standard algorithm. This study analyzes the word problems and problem solving methods about fraction division which elementary pre-service teachers represented. Pre-service teachers have more difficulty in making word problem where the dividend is less than the divisor and they also show typical errors in making the word problems. There were differences in the methods presented according to the contexts of division in problem solving. Through this study, it is necessary to rethink the teaching methods for fraction division instruction in the curriculum for pre-service teachers and analyze the formation process of 'knowledge for content and teaching' because of the differences in responses between grades.

• Journal of the Korean School Mathematics Society
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• v.8 no.3
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• pp.367-382
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• 2005

In this paper, we deal with various contents relating to the group concept in school mathematics and teaching of algebraic structures indirectly by combining these contents. First, we consider structure of knowledge based on Bruner, and apply these discussions to the teaching of algebraic structure in school algebra. As a result of these analysis, we can verify that the essence of algebraic structure is group concept. So we investigate the previous researches about group concept: Piaget, Freudenthal, Dubinsky. In our school, the contents relating to the group concept have been taught from elementary level indirectly. Tn elementary school, the commutative law and associative law is implicitly taught in the number contexts. And in middle school, various linear equations are taught by the properties of equality which include group concept. But these algebraic contents is not related to the high school. Though we deal with identity and inverse in the binary operations in high school mathematics, we don't relate this algebraic topics with the previous learned contents. In this paper, we discussed algebraic structure focusing to the group concept to obtain a connectivity among school algebra. In conclusion, the group concept can take role in relating these algebraic contents and teaching the algebraic structures in school algebra.

• Journal of the Korean earth science society
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• v.42 no.6
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• pp.734-751
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• 2021

The purpose of this study is to prepare basic data to reflect polar literacy education in the school curriculum. The perception about the polar regions, teaching experience, and polar-related cognitive and affective characteristics of teachers were investigated. The survey was conducted among 56 elementary, middle, and high school teachers from schools from 10 major cities and surrounding regions, based on their perceptions of the polar region, current teaching status, polar knowledge, and beliefs and attitudes toward polar region and climate change. Results showed that although teachers' polar information efficacy was low, they positively evaluated the status of educators in resolving polar and climate change problems, and prioritized global citizenship values over practical purposes. The experience of teaching polar region and climate change issues at schools varied across subjects and non-subjects, but showed a passive aspect in teaching development, such as wanting to be provided with consolidated learning materials. On the cognitive aspect, teachers revealed an ambiguous understanding of the mechanisms and processes by which polar change and climate influence each other. On the affective aspect, most teachers showed strong beliefs and attitudes for polar-related issues beyond the school level, but their behavior choices were relatively lower. Based on the results, we propose the following as recommendations: providing opportunities and materials to promote polar knowledge, discovering educational materials in various contexts to form values and attitudes, developing educational materials from polar research materials, identifying misconceptions about polar knowledge among students and teachers, strengthening elementary school teachers' polar literacy, and cultivating positive attitudes and values toward polar issues.

• English Language & Literature Teaching
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• v.12 no.3
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• pp.267-286
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• 2006

The purpose of the study was to investigate what kinds of learning strategies EFL learners use to learn English grammar and what is benefit from structured grammar input processing. Students of the study consisted of 48 college students who took Practical English Grammar at a university in Kyung-Gi area and were divided into two groups based on grammar scores. The students were asked to take two grammar tasks and grammar tests and complete a survey including questions on grammar strategy and input processing. The results of the study are as follows. First, learners' grammar level has an effect on use of grammar attack strategy including asking teachers, using grammar books and given contexts whereas there was no significant difference between groups in the planning strategies, Among memory strategies, using grammar exercise and linking with already known structure demonstrated a significant difference between groups. Second, with regard to input processing, high level students got higher score on how much they understood the structured grammar input compared with low level students. Third, explicit implicit instruction added to input processing seems more comprehensible and more available than structured input only, Finally, it showed that there is positive relationship between perception and score of input processing tasks and grammar tests. Especially, learners' perception of input processing correlated more with final tests and tasks. Therefore, it suggests that the more input processing task need to develop and utilize in order to facilitate learners' intake.