• Title/Summary/Keyword: 비와 비율

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A Comparative Analysis of Ratio and Rate in Elementary Mathematics Textbooks (비와 비율에 대한 초등 수학 교과서 비교 분석)

  • Chang, Hyewon;Lim, Miin;Yu, Migyoung;Park, Haemin;Kim, Jusuk;Lee, Hwayoung
    • Journal of Elementary Mathematics Education in Korea
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    • v.21 no.1
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    • pp.135-160
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    • 2017
  • Since mathematics textbooks for 6th graders based on the 2009 revised national curriculum were applied to the site, there has been a note pointing out that the unit of 'ratio and rate' causes some learning difficulties. This implies the necessity of search for desirable methods of organizing the unit of ratio and rate in mathematics textbooks. This study analyzed and compared Korean and foreign mathematics textbooks on ratio and rate longitudinally and horizontally, respectively. For longitudinal analysis, we selected the mathematics textbooks according to the national curriculum since the 5th one. For horizontal analysis, we took the mathematics textbooks of Japan, Singapore, Hong Kong, and Finland. In each textbook, the contents and the order in relation to ratio and rate, the definitions of terminology, and the methods for introducing related concepts are set as the analysis framework. The results of analysis revealed many characteristics and the differences in ways of dealing contents about ratio and rate. Based on these results, we suggested some implications for writing the unit of ratio and rate in elementary mathematics textbooks.

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An Analysis of Teachers' Pedagogical Content Knowledge about Teaching Ratio and Rate (비와 비율 지도에 대한 교사의 PCK 분석)

  • Park, Seulah;Oh, Youngyoul
    • Journal of Elementary Mathematics Education in Korea
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    • v.21 no.1
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    • pp.215-241
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    • 2017
  • This study analyzed teachers' Pedagogical Content Knowledge (PCK) regarding the pedagogical aspect of the instruction of ratio and rate in order to look into teachers' problems during the process of teaching ratio and rate. This study aims to clarify problems in teachers' PCK and promote the consideration of the materialization of an effective and practical class in teaching ratio and rate by identifying the improvements based on problems indicated in PCK. We subdivided teachers' PCK into four areas: mathematical content knowledge, teaching method and evaluation knowledge, understanding knowledge about students' learning, and class situation knowledge. The conclusion of this study based on analysis of the results is as follows. First, in the 'mathematical content knowledge' aspect of PCK, teachers need to understand the concept of ratio from the perspective of multiplicative comparison of two quantities, and the concept of rate based on understanding of two quantities that are related proportionally. Also, teachers need to introduce ratio and rate by providing students with real-life context, differentiate ratios from fractions, and teach the usefulness of percentage in real life. Second, in the 'teaching method and evaluation knowledge' aspect of PCK, teachers need to establish teaching goals about the students' comprehension of the concept of ratio and rate and need to operate performance evaluation of the students' understanding of ratio and rate. Also, teachers need to improve their teaching methods such as discovery learning, research study and activity oriented methods. Third, in the 'understanding knowledge about students' learning' aspect of PCK, teachers need to diversify their teaching methods for correcting errors by suggesting activities to explore students' own errors rather than using explanation oriented correction. Also, teachers need to reflect students' affective aspects in mathematics class. Fourth, in the 'class situation knowledge' aspect of PCK, teachers need to supplement textbook activities with independent consciousness and need to diversify the form of class groups according to the character of the activities.

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Teacher Knowledge Necessary to Address Student Errors and Difficulties about Ratio and Rate (비와 비율에 관한 학생의 오류와 어려움 해결을 위해 필요한 교사지식)

  • Kang, Hyangim;Choi, Eun Ah
    • School Mathematics
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    • v.17 no.4
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    • pp.613-632
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    • 2015
  • In this study, we hope to reveal teacher knowledge necessary to address student errors and difficulties about ratio and rate. The instruments and interview were administered to 3 in-service primary teachers with various education background and teaching experiments. The results of this study are as follows. Specialized content knowledge(SCK) consists of profound knowledge about ratio and rate beyond multiplicative comparison of two quantities and professional knowledge about the definitions of textbook. Knowledge of content and students(KCS) is the ability to recognize students' understanding the concept and the representation about ratio and rate. Knowledge of content and teaching(KCT) is made up of knowledge about various context and visual models for understanding ratio and rate.

A Comparative Analysis on Units about Ratio and Rate between Korean Mathematics Textbook and MIC Textbook (우리나라 교과서와 미국 MIC 교과서의 비와 비율 관련 단원 비교.분석)

  • Park, Hee-Ja;Jeong, Eun-Sil
    • Journal of Elementary Mathematics Education in Korea
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    • v.14 no.3
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    • pp.769-788
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    • 2010
  • This study analyzed the characteristics of units about ratio and rate between Korean mathematics textbooks and MIC of America. With bases to this, I would find the problems and suggested point of curriculums about ratio and rate in order to propose the basic materials of developing mathematic curriculum and textbook and improving the mathematic teaching method. With bases to this, Korean mathematics textbooks should be supplemented as follows. A. Develop the various problems with meaningful situation rather than the problems which can be solved with algorithms and rules. B. Develop the students' rational judgement competence with the situation that can induce the active communication. C. Develop the problem situation that need the student's activity. D. Let the students easily take the situation about ratio and rate with suggesting much visual mode and sustain their interest and positive learning attitude.

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Teaching the Concept of Rate and Ratio - Focused on Using the Reconstructed Textbook - (비와 비율 지도에 대한 연구 -교과서 재구성을 중심으로-)

  • Kim, Su-Hyun;Na, Gwi-Soo
    • Journal of Educational Research in Mathematics
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    • v.18 no.3
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    • pp.309-333
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    • 2008
  • In this research, we reconstructed the textbook on the concept of rate and ratio, which is based on the review on the previous researches and the analysis on the elementary textbook of the 7th mathematics curriculum. We conducted the teaching experiment using the reconstructed textbook, which is to identify the students' conception of rate and ratio and the appropriateness and limit of the reconstructed textbook. As the results of this study, we identify that the changed sequence of instruction (that is, ratio ${\rightarrow}$ percent and value of rate ${\rightarrow}$ rate) was very proper to help students understand the concept of rate and ratio. The relative comparison and absolute comparison and the additive thinking and multiplicative thinking included in the reconstructed textbook were identified very helpful to students' understanding. Meanwhile some contexts given in the reconstructed textbook were identified to cause the students' cognitive confusions.

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A Discussion on the Terms Related to ratio and rate from the Revised 2007 Curriculum textbook (초등학교 2007 개정 교과서 비와 비율 관련 용어에 대한 고찰)

  • Hong, Gap Ju
    • Journal of Educational Research in Mathematics
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    • v.23 no.2
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    • pp.285-295
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    • 2013
  • In this study I examine the definitions of terms related to ratio and rate from 5, 6, 7th revised elementary school math textbooks to discuss the improvements and the remained problems in 2007 curriculum textbook. Next, I make the alternative definitions of the terms, 'biyoul', the value of 'bi', and 'baekboonyul' by re-establishing the relations between them. Finally, I point out that those problems are intrinsic to the attempt of the textbook to introduce the terms related to ratio with little consideration for the mathematical meaning of ratio as a equivalence class.

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An Analysis on the Epistemological Obstacles of Elementary Students in the Learning of Ratio and Rate (비와 비율 학습에서 나타나는 초등학교 학생들의 인식론적 장애 분석)

  • Park, Hee-Ok;Park, Man-Goo
    • Education of Primary School Mathematics
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    • v.15 no.2
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    • pp.159-170
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    • 2012
  • Many obstacles have been found in the learning of ratio and rate. The types of epistemological obstacles concern 'terms', 'calculations' and 'symbols'. It is important to identify the epistemological obstacles that students must overcome to understand the learning of ratio and rate. In this respect, the present study attempts to figure out what types of epistemological obstacles emerge in the area of learning ratio and rate and where these obstacles are generated from and to search for the teaching implications to correct them. The research questions were to analyze this concepts as follow; A. How do elementary students show the epistemological obstacles in ratio and rate? B. What is the reason for epistemological obstacles of elementary students in the learning of ratio and rate? C. What are the teaching implications to correct epistemological obstacles of elementary students in the learning of ratio and rate? In order to analyze the epistemological obstacles of elementary students in the learning of ratio and rate, the present study was conducted in five different elementary schools in Seoul. The test was administered to 138 fifth grade students who learned ratio and rate. The test was performed three times during six weeks. In case of necessity, additional interviews were carried out for thorough examination. The final results of the study are summarized as follows. The epistemological obstacles in the learning of ratio and rate can be categorized into three types. The first type concerns 'terms'. The reason is that realistic context is not sufficient, a definition is too formal. The second type of epistemological obstacle concerns 'calculations'. This second obstacle is caused by the lack of multiplication thought in mathematical problems. As a result of this study, the following conclusions have been made. The epistemological obstacles cannot be helped. They are part of the natural learning process. It is necessary to understand the reasons and search for the teaching implications. Every teacher must try to develop the teaching method.

The Comparison and Analysis of Models on Ratio and Rate in Elementary Mathematics Textbooks : Centering on Multiplicative Perspectives on Proportional Relationships and the Structure of Proportion Situations (초등 수학 교과서 비와 비율 단원의 모델 비교 분석 -비례에 대한 곱셈적 사고 및 비례 상황의 구조를 중심으로)

  • Park, Sun Young;Lee, Kwangho
    • Education of Primary School Mathematics
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    • v.21 no.2
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    • pp.237-260
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    • 2018
  • This study investigated the models of four countries' elementary mathematics textbooks in Ratio and Rate and identified how multiplicative perspectives on proportional relationships and the structure of proportion situations are reflected in the textbooks. For this, textbooks of 5th and 6th grade textbooks in Korea Japan, Singapore and U.S. are compared and analyzed. As a result, we can find multiplicative perspectives on proportional relationships and the structure of proportion situations on pictorial models, ratio tables, double number lines and double tape diagrams. Also, the development of Japanese textbooks from multiple batches perspectives to variable parts perspectives and the examples of the use with two models together implied the connection and union of two multiplicative perspectives. Based on these results, careful verification and discussion for the next textbook is needed to develop students' proportional reasoning and teach some effective reasoning strategies. And this study will provide the implication for what kinds of and how visual models are presented in the next textbook.

An Analysis on the Proportional Reasoning Understanding of 6th Graders of Elementary School -focusing to 'comparison' situations- (초등학교 6학년 학생들의 비례 추론 능력 분석 -'비교' 상황을 중심으로-)

  • Park, Ji Yeon;Kim, Sung Joon
    • Journal of Elementary Mathematics Education in Korea
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    • v.20 no.1
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    • pp.105-129
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    • 2016
  • The elements of mathematical processes include mathematical reasoning, mathematical problem-solving, and mathematical communications. Proportion reasoning is a kind of mathematical reasoning which is closely related to the ratio and percent concepts. Proportion reasoning is the essence of primary mathematics, and a basic mathematical concept required for the following more-complicated concepts. Therefore, the study aims to analyze the proportion reasoning ability of sixth graders of primary school who have already learned the ratio and percent concepts. To allow teachers to quickly recognize and help students who have difficulty solving a proportion reasoning problem, this study analyzed the characteristics and patterns of proportion reasoning of sixth graders of primary school. The purpose of this study is to provide implications for learning and teaching of future proportion reasoning of higher levels. In order to solve these study tasks, proportion reasoning problems were developed, and a total of 22 sixth graders of primary school were asked to solve these questions for a total of twice, once before and after they learned the ratio and percent concepts included in the 2009 revised mathematical curricula. Students' strategies and levels of proportional reasoning were analyzed by setting up the four different sections and classifying and analyzing the patterns of correct and wrong answers to the questions of each section. The results are followings; First, the 6th graders of primary school were able to utilize various proportion reasoning strategies depending on the conditions and patterns of mathematical assignments given to them. Second, most of the sixth graders of primary school remained at three levels of multiplicative reasoning. The most frequently adopted strategies by these sixth graders were the fraction strategy, the between-comparison strategy, and the within-comparison strategy. Third, the sixth graders of primary school often showed difficulty doing relative comparison. Fourth, the sixth graders of primary school placed the greatest concentration on the numbers given in the mathematical questions.