• Journal of Elementary Mathematics Education in Korea
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• v.13 no.2
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• pp.247-268
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• 2009

The purpose of this study was to examine the mathematical components of word problems and the structure of the components, to examine the characteristics of the understanding of mathematics high achievers about word problems, and ultimately to devise a teaching method geared toward facilitating learner understanding of the word problems. Given the findings of the study, the following conclusion was reached: First, word problems could be categorized according to their mathematical components, namely the mathematical structure of multiple variables provided to learners for their problem solving. And learner's reaction might hinge on the type of word problems. Second, the mathematics high achievers relied on diverse strategies to understand the mathematical components of word problems to solve the problems. The use of diverse strategies made it possible for them to succeed in problem solving. Third, identifying the characteristics of the understanding of the mathematics high achievers about word problems made it possible to layout successful lesson plans that stressed understanding of the mathematical structure of word problems. And the teaching plans enabled the learners to get a better understanding of the given word problems.

• Education of Primary School Mathematics
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• v.25 no.4
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• pp.297-312
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• 2022

Word problems can lead learners to more meaningfully learn mathematics by providing learners with various problem-solving experiences and guiding them to apply mathematical knowledge to the context. This study attempted to provide implications for the textbook writing and teaching and learning process by examining the word problem of elementary mathematics textbooks from the perspective of practical context. The word problem of elementary mathematics textbooks was examined, and elementary mathematics textbooks in the United States and Finland were referenced to find specific alternatives. As a result, when setting an unnatural context or subject to the word problem in elementary mathematics textbooks, artificial numbers were inserted or verbal expressions and illustrations were presented unclearly. In this case, it may be difficult for learners to recognize the context of the word problem as separate from real life or to solve the problem by understanding the content required by the word problem. In the future, it is necessary to organize various types of word problems in practical contexts, such as setting up situations in consideration of learners in textbooks, actively using illustrations and diagrams, and organizing verbal expressions and illustrations more clearly.

• Communications of Mathematical Education
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• v.8
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• pp.209-229
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• 1999

보통 문장제(거리 ${\cdot}$ 속도 문제, 시계 문제, 농도 문제, 개수 세기, 측도 영역)는 초등학교부터 반복하면서 대학수학능력 시험에서는 외적 문제해결력을 측정하는 문장으로 나타난다. 문장제를 해결하는데는 사고가 여러 단계로 이루어져야 한다. 따라서 일반적으로 문장제는 난해하므로 조직적이고 전문적인 학습지도가 이루어져야 한다. 하지만 입시위주의 교육 등 여러 여건상 잘 이루어지지 않고 있는 것이 현실이다. 수학을 잘하는 학생이라도 문장제를 해결하지 못하는 경우가 많다. 본 연구에서는 문장제의 해결의 저해 요인을 완화시킬 수 있는 지도 방안으로서 Polya의 문제해결 전략을 이용하며, 실험반과 비교반의 학습 효과를 비교 분석하여 이를 통하여 효율적인 문장제 지도방안을 연구한다.

• School Mathematics
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• v.6 no.2
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• pp.135-151
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• 2004

This study investigated children's realistic response on problematic word problems focused on number operations. Even though word problems and problem solving should be considered in terms of realistic context, results indicates that children's responses didn't show realistic consideration in solving problems. Also, children showed their tendency of mindless or mechanical operation in solving problems and modeling problems

• Annual Conference on Human and Language Technology
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• 2018.10a
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• pp.310-315
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• 2018

본 논문에서는 한국어 수학 문장제 문제 자동 풀이를 위한 방법을 소개한다. 수학 문장제 문제란 수학적 관계가 언어와 숫자로 주어질 때, 문제에서 요구하는 정보를 도출하는 수학 문제로, 언어 의미 분석과 수학적 관계 추출이 요구된다. 본 논문에서는 이원 일차 연립 방정식을 포함한 514 문제의 영어 데이터셋을 번역해 한국어 문제를 확보하였다. 또한 한국어의 수학적 관계 표현과 언어 유형적 특성을 고려한 자질 추출을 제안하고, 템플릿 기반 Log-linear 모델이 정답 방정식을 분류하도록 학습하였다. 5겹 교차 검증을 실시한 결과, 영어 문제를 풀이한 선행 연구의 정답률 79.7% 대비 1%p 낮은 78.6%의 정답률을 보였다.

• Education of Primary School Mathematics
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• v.25 no.4
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• pp.395-410
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• 2022

Nominalization is one of the grammatical metaphors, and it is the representation of verbal meaning through noun equivalent phrases. In mathematical word problems, texts using nominalization have both the advantage of clarifying the object to be noted in the mathematization stage, and the disadvantage of complicating sentence structure, making it difficult to understand the sentences and hindering the experience of the full steps in mathematical modelling. The purpose of this study is to analyze word problems in the textbooks from the perspective of nominalization, a linguistic element, and to derive implications in relation to students' difficulties during solving the word problems. To this end, the types of nominalization of 341 word problems from the content domain of 'Numbers and Operations' of elementary math textbooks according to the 2015 revised national curriculum were analyzed in four aspects: grade-band group, main class and unit assessment, specialized class, and mathematical expression required word problems. Based on the analysis results, didactical implications related to the linguistic expression of the mathematical word problems were derived.

• Communications of Mathematical Education
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• v.11
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• pp.201-233
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• 2001

보통 문장제(일량, 거리, 속도 문제, 시계 문제, 농도 문제, 개수 세기, 측도 영역)는 초등학교부터 반복하며 나오며 대학 수학 능력 시험에서는 외적 문제 해결능력으로 측정되기도 한다. 문장제를 해결하는데는 사고가 여러 단계로 이루어져야 한다. 따라서 일반적으로 문장제는 난해하므로, 조직적이고 전문적인 학습지도가 이루어져야 한다. 하지만 입시위주의 교육 등 여러 여건상 잘 이루어지지 않고 있는 것이 현실이다. 본 연구에서는 문장제의 문제 해결에 필요한 해결요소를 발견하고 저해 요인을 없앨 수 있는 지도 방안으로서 소집단 토의학습에 문제해결 전략을 이용하여, 효율적인 문장제 지도 방안을 연구하고 상이한 문제에 접근하는 방법, 문제를 이용하는 방법 등을 토의학습을 통하여 다양한 풀이방법을 해결하면서 이를 통하여 사고력을 신장할 수 있도록 연구한다.

• Communications of Mathematical Education
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• v.38 no.1
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• pp.49-67
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• 2024

Recent interest in the diverse applications of artificial intelligence (AI) language models has highlighted the need to explore didactical uses in mathematics education. AI language models, capable of natural language processing, show promise in solving mathematical word problems. This study tested the capability of ChatGPT, an AI language model, to solve word problems from elementary school textbooks, and analyzed both the solutions and errors made. The results showed that the AI language model achieved an accuracy rate of 81.08%, with errors in problem comprehension, equation formulation, and calculation. Based on this analysis of solution processes and error types, the study suggests implications for the didactical application of AI language models in education.

• Proceedings of the Korea Information Processing Society Conference
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• 2021.05a
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• pp.362-365
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• 2021

이 논문에서는 자연어로 구성된 수학 문장제 문제를 자동으로 풀이하기 위한 Transformer 기반의 생성 모델인 KoEPT를 제안한다. 수학 문장제 문제는 일상 상황을 수학적 형식으로 표현한 자연어 문제로, 문장제 문제 풀이 기술은 실생활에 응용 가능성이 많아 국내외에서 다양하게 연구된 바 있다. 한국어의 경우 지금까지의 연구는 문제를 유형으로 분류하여 풀이하는 기법들이 주로 시도되었으나, 이러한 기법은 다양한 수식을 포괄하여 분류 난도가 높은 데이터셋에 적용하기 어렵다는 한계가 있다. 본 논문은 이를 해결하기 위해 우선 현존하는 한국어 수학 문장제 문제 데이터셋인 CC, IL, ALG514의 분류 난도를 측정한 후 5겹 교차 검증 기법을 사용하여 KoEPT의 성능을 평가하였다. 평가에 사용된 한국어 데이터셋들에 대하여, KoEPT는 CC에서는 기존 최고 성능과 대등한 99.1%, IL과 ALG514에서 각각 89.3%, 80.5%로 새로운 최고 성능을 얻었다. 뿐만 아니라 평가 결과 KoEPT는 분류 난도가 높은 데이터셋에 대해 상대적으로 개선된 성능을 보였다.

• Education of Primary School Mathematics
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• v.15 no.2
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• pp.107-134
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• 2012

The purpose of this study is to investigate the effectiveness of two teaching methods of word problems, one based on mathematical modeling learning(ML) and the other on traditional learning(TL). Additionally, the influence of mathematical modeling learning in word problem solving behavior, application ability of real world experiences in word problem solving and the beliefs of word problem solving will be examined. The results of this study were as follows: First, as to word problem solving behavior, there was a significant difference between the two groups. This mean that the ML was effective for word problem solving behavior. Second, all of the students in the ML group and the TL group had a strong tendency to exclude real world knowledge and sense-making when solving word problems during the pre-test. but A significant difference appeared between the two groups during post-test. classroom culture improvement efforts. Third, mathematical modeling learning(ML) was effective for improvement of traditional beliefs about word problems. Fourth, mathematical modeling learning(ML) exerted more influence on mathematically strong and average students and a positive effect to mathematically weak students. High and average-level students tended to benefit from mathematical modeling learning(ML) more than their low-level peers. This difference was caused by less involvement from low-level students in group assignments and whole-class discussions. While using the mathematical modeling learning method, elementary students were able to build various models about problem situations, justify, and elaborate models by discussions and comparisons from each other. This proves that elementary students could participate in mathematical modeling activities via word problems, it results form the use of more authentic tasks, small group activities and whole-class discussions, exclusion of teacher's direct intervention, and classroom culture improvement efforts. The conclusions drawn from the results obtained in this study are as follows: First, mathematical modeling learning(ML) can become an effective method, guiding word problem solving behavior from the direct translation approach(DTA) based on numbers and key words without understanding about problem situations to the meaningful based approach(MBA) building rich models for problem situations. Second, mathematical modeling learning(ML) will contribute attitudes considering real world situations in solving word problems. Mathematical modeling activities for word problems can help elementary students to understand relations between word problems and the real world. It will be also help them to develop the ability to look at the real world mathematically. Third, mathematical modeling learning(ML) will contribute to the development of positive beliefs for mathematics and word problem solving. Word problem teaching focused on just mathematical operations can't develop proper beliefs for mathematics and word problem solving. Mathematical modeling learning(ML) for word problems provide elementary students the opportunity to understand the real world mathematically, and it increases students' modeling abilities. Futhermore, it is a very useful method of reforming the current problems of word problem teaching and learning. Therefore, word problems in school mathematics should be replaced by more authentic ones and modeling activities should be introduced early in elementary school eduction, which would help change the perceptions about word problem teaching.