• Education of Primary School Mathematics
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• v.23 no.3
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• pp.117-134
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• 2020

Based on the current curriculum, students learn the concept of fraction in the 3rd grade for the first time. At that time, fraction is introduced as whole-part relationship. But as the idea of fraction expands to improper fraction and so on, fraction as measurement would be naturally appeared. In that situation where fraction as whole-part relationship and fraction as measurement are dealt together, it is necessary for students to get experiences of understanding and exploring unit and whole adequately in order to fully understand the concept of fractions. Therefore, the purpose of this study is to analyze how to deal with unit fractions, how to implement activities to find the standard of reference from the part, and what visual representations were used to help students to understand the concept of fractions in elementary mathematics textbooks from the 7th to the 2015 revised curriculum. And we analyzed 60 3rd graders' understanding of finding and drawing the whole by looking at the part. Several didactical implications for teaching the concept of fractions were derived from the discussion according to the analysis results.

• The Mathematical Education
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• v.56 no.2
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• pp.193-212
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• 2017

This study focuses on cuisenaire rods that can be used when teaching fractions to elementary school students. First of all, this study critically examines the use of cuisenaire rods in learning of fraction proposed by various researches. Then, based on this review, this study explores in detail the use of cuisenaire rods in teachers' manuals developed from the revised curriculum by 2009 and in lessons related to fraction. The results of this study show that there are subtle differences in how to use cuisenaire rods in learning fractions and these subtle differences have a significant impact on students' understanding of the fractions. Therefore, the teachers should be able to accurately grasp the differences and utilize appropriate methods for teaching purpose. The followings are some of the implications for teachers or textbook developers when using cuisenaire rods in fraction learning: First, we should use cuisenaire rods in ways that can fully exploit the interpretations of the fraction as a part-whole and the fraction as a ratio. Second, we should focus on quantitative reasoning with unit to determine what each cuisenaire rod refers to. Third, it is necessary to take a more careful and sensitive approach to the use of cuisenaire rods. Teachers and textbook developers should constantly explore ways to make good use of mathematical manipulatives to help students understand conceptually in fractional learning. Furthermore, when teaching various mathematical topics using different manipulatives, I expect that there will be sufficient discussions and specific studies on how to use each of these manipulatives.

• School Mathematics
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• v.12 no.3
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• pp.439-454
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• 2010

This study presents how two eighth grade students generated their own algorithms in the context of fraction measurement division situations by modifications of unit-segmenting schemes. Teaching experiment was adopted as a research methodology and part of data from a year-long teaching experiment were used for this report. The present study indicates that the two participating students' construction of reciprocal relationship between the referent whole [one] and the divisor by using their unit- segmenting schemes and its strategic use finally led the students to establish an algorithm for fraction measurement division problems, which was on par with the traditional invert-and-multi- ply algorithm for fraction division. The results of the study imply that teachers' instruction based on understanding student-generated algorithms needs to be accounted as one of the crucial characteristics of good mathematics teaching.

• School Mathematics
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• v.14 no.2
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• pp.191-212
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• 2012

In the field of arithmetic in mathematics education, there has been lack of fine-grained investigations addressing the relationship between students' construction of division knowledge with fractional quantities and their whole number division knowledge. This study, through the analysis of part of collected data from a year-long teaching experiment, presents a possible constructive itinerary as to how a student could modify her unit-segmenting scheme to deal with various fraction measurement division situations: 1) unit-segmenting scheme with a remainder, 2) fractional unit-segmenting scheme. Thus, this study provides a clue for curing a fragmentary approach to teaching whole number division and fraction division and preventing students' fragmentary understanding of the same arithmetical operation in different number systems.

• 한국해양학회지
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• v.29 no.2
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• pp.145-151
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• 1994

Investigations on distributions of bacterial abundance and production in the mideast part of the Yellow Sea were made in August and October, 1991 as a part of study of "The Exploitation Research of Marine Resources on the Yellow Sea". Here, we report spatial and temporal characteristics of distributions of bacteria in the mideast part of the Yellow Sea including data reported by Son (1989) for the same area. During the whole study period, bacterial abundance ranged from 0.5${\times}$10/SUP 8/ 1/SUP -1/ to 19${\times}$10/SUP 8/ 1/SUP -1/. Seasonal changes and the difference between two studies in bacterial abundance were less than 3.5 fold ar each station in the study area, except October, 1991. An interesting result was that bacterial abundances except October, 1991 were generally lower than those expected from the established relationship between chlorophyll and bacterial abundance in the oceans. For the bacterial abundance observed in October 1991, controlling factor(s) of bacteria might be different from the rest of study period. Bacterial production (0.1∼2.9ug C 1/SUP -1/ d/SUP -1/) comprised a small fraction (18${\pm}$11%) of primary production. Though data are limited, low bacterial abundances compared to chlorophyll concentration and low values of bacterial production to primary production seemed to occur in the mideast part of the Yellow Sea. Unravelling the causes of these phenomena would be necessary to understand the ecology of bacteria in the region.