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

• Communications of Mathematical Education
• /
• v.8
• /
• pp.209-229
• /
• 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
• /
• v.6 no.2
• /
• pp.135-151
• /
• 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

• Education of Primary School Mathematics
• /
• v.25 no.4
• /
• pp.297-312
• /
• 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
• /
• v.11
• /
• pp.201-233
• /
• 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.

• School Mathematics
• /
• v.11 no.3
• /
• pp.479-496
• /
• 2009

Some children can construct a basic concept of addition and subtraction during the preschool years. Children start to experience mathematics via numbers and their of operations and contact with various contexts of addition and subtraction. In special, word problems reflect mathematics which is appliable to real life. In this paper, I analyse the types of word problems in text book and its students' responses. First, I analyse the types of addition word problems which consist of change add-into situations and part-part-whole situations. Second, I analyse the types of subtraction word problems which consist of change take-away situations, compare situations and equalize situations. Third, I analyse the students' responses by the types of word problems in addition and subtraction. And 115 2nd grade elementary school students participated in this survey. The following results have been drawn from this study. First, the proposition of word problems of part-part-whole situations is higher than that of change add-into situations and the proposition of word problems of take-away situations is higher than that of compare situations and equalize situations. According to the analysis about students' responses, It is no difference between change add-into situations and part-part-whole situations. But the proposition of word problems of take-away situations is higher than that of compare situations and equalize situations. This results from word problems which contain unnecessary information in problem. So, we have to present the various word problems to students.

• Journal of the Korean School Mathematics Society
• /
• v.10 no.3
• /
• pp.353-367
• /
• 2007

The purpose of this study was to examine what errors students made in solving word problems with figures and to compare the problem-solving abilities of boys and girls for each type of word problems with figures. It's basically meant to provide information on effective teaching-learning methods about world problems with figures that were given the greatest weight among different sorts of word problems. The findings of the study were as fellows: First, there was no difference between the boys and girls in the types of error they made. Both groups made the most errors due to a poor understanding of sentences, and they made the least errors of making the wrong expression. And the students who gave no answers outnumbered those who made errors. Second, as for problem-solving ability, the boys outperformed the girls in problem solving except variable problems. There was the greatest gap between the two in solving combining problems. Third, they made the average or higher achievement in solving the types of problems that were included much in the textbooks, and made the least achievement in relation to the types of problems that were handled least often in the textbooks.

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

• Education of Primary School Mathematics
• /
• v.25 no.4
• /
• pp.395-410
• /
• 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
• /
• v.23 no.3
• /
• pp.761-783
• /
• 2009

Problem solving ability can be fostered by dealing with many different types of problems. We investigated how $5^{th}$ and $6^{th}$ graders who did not learn traditional algebraic methods might approach the word problems of simultaneous equations. This result reveals that the strategy of guess-and-check serves as a basis for elementary school students in solving simultaneous equations. A noticeable remark is that students used the guess-and-check strategy in various ways. Whereas some students changed a variable given in the problem step by step, others did in a sophisticated way focusing on the relation between two variables. Moreover, some students were able to write an equation which was not typical but meaningful and correct. This paper emphasizes the need of connections between pre-algebraic and algebraic solutions.