• School Mathematics
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• v.18 no.2
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• pp.257-275
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• 2016

The purpose of this study was to investigate the impact of multiple representations on students' understanding of fractions, decimals, and percent. The instructional approach integrating multiple representations was compared to traditional algorithmic instruction, a form of direct instruction. To examine and compare the impact of multiple representations instruction with traditional algorithmic instruction, pre and post tests consisting of five similar items were administered with 87 middle school students. Students' scores in these two tests and their problem solving processes were analyzed quantitatively and qualitatively. The quantitative results indicated that students taught by traditional algorithmic instruction showed higher scores on the post-test than students in the multiple representations group. Furthermore, findings suggest that instruction using multiple representations does not guarantee a positive impact on students' understanding of mathematical concepts. Qualitative results suggest that the limited use of multiple representations during a class may have hindered students from applying their use in novel problem situations. Therefore, when using multiple representations, teachers should employ more diverse examples and practice with multiple representations to help students to use them without error.

• School Mathematics
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• v.14 no.1
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• pp.29-43
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• 2012

This paper investigated the conceptual schemes in which four children constructed a strategy representing the situation as a figure and partitioning it related to the work which they quantify the result of partitioning to various types of fractions when an equal sharing situation was given to them in contextual or an abstract symbolic form of division. Also, the paper researched how the relationship of factors and multiples between the numerator and denominator, or between the divisor and dividend affected the construction. The children's partitioning strategies were developed such as: repeated halving stage ${\rightarrow}$ consuming all quantity stage ${\rightarrow}$ whole number objects leftover stage ${\rightarrow}$ singleton object analysis/multiple objects analysis ${\rightarrow}$ direct mapping stage. When children connected the singleton object analysis with multiple object analysis, they finally became able to conceptualize division as fractions and fractions as division.

• Annual Conference on Human and Language Technology
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• 2023.10a
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• pp.203-208
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• 2023

본 논문에서는 대규모 언어 모델의 인컨텍스트 러닝과 프롬프팅을 활용하여 수치 추론 태스크 데이터셋을 효과적으로 증강시킬 수 있는 방법론을 제안한다. 또한 모델로 하여금 수치 추론 데이터의 이해를 도울 수 있는 전처리와 요구사항을 만족하지 못하는 결과물을 필터링 하는 검증 단계를 추가하여 생성되는 데이터의 퀄리티를 보장하고자 하였다. 이렇게 얻어진 증강 절차를 거쳐 증강을 진행한 뒤 추론용 모델 학습을 통해 다른 증강 방법론보다 우리의 방법론으로 증강된 데이터셋으로 학습된 모델이 더 높은 성능을 낼 수 있음을 보였다. 실험 결과 우리의 증강 데이터로 학습된 모델은 원본 데이터로 학습된 모델보다 모든 지표에서 2%p 이상의 성능 향상을 보였으며 다양한 케이스를 통해 우리의 모델이 수치 추론 학습 데이터의 다양성을 크게 향상시킬 수 있음을 확인하였다.

• Journal of the Korean School Mathematics Society
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• v.3 no.1
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• pp.189-200
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• 2000

The purpose of this thesis is that the students understand the sentence stated math problems closely related to the real life and adapted the right solving strategies try to find the solution to a problem. The following research problem were proposed. 1. How repeated thinking lessons develop the understanding of problems and influence the usage of correct problem solving strategies and extensions of problem solving. 2. There are how much differences of achievement for each type of sentence stated problems by using comparative analysis of upper class, intermediate class, and lower class for each level between the experimental and comparative classes. In order to conduct this research the classes were divided into three different level - upper class, intermediate class and lower class. Each level include an experimental class and a comparative class. The two classes (experimental class and comparative class) of the same level were tested on the basis of class division record with the experimental class repeated learning papers for two weeks were used to guide the fixed thinking algorism for each sentence stated math problems. Eight common problems were chosen from a variety of textbooks : number calculation problems, velocity-distance-time problems, the density of a mixture, benefit problems, distribution problems, problems about working, ratio problems, the length of a figure problems. After conducting this research experiment The differences in achievement level between the experimental class and comparative class, were compared and analyzed through achievement tests made from the achievement test papers with seven problems, which were worth seventy points (total score). The conclusions of this thesis are as follows: Firstly, leaning activities through the usage of repeated learning papers for each level class produce an even development of achievement level especially in the case of the upper class learners, they have particular differences (between experimental class and comparative class) compared to the intermediate level and lower classes. Secondly, according to the analysis about achievement development each problems, learners easily accept the strategies of solution through the formula setting up to the problem of velocity -distance-time, and to the density of the mixture they adapted the picture drawing strategies interestingly, However each situation requires a variety of appropriate solution strategies. Teachers will have to employ other interesting solution strategies which relate to real life.