• 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.

• Journal of Educational Research in Mathematics
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• v.14 no.3
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• pp.267-281
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• 2004

Many students feel the word problems are very difficult. This study analyzes the linguistic and cognitive factors that affect word problem solving so that we help students bring through the difficulty. There are a text base, a situation model, and a real world in the linguistic aspects. Students have a difficulty at the transition from text base to situation model(equation), and make lots of errors at the situation model. In the cognitive aspects, I investigated problem solving schemes, strategies, and complexity level. Students are likely to choose strategy by the contents which teacher instructed, but not by low complexity level, and mix up the amount of sugar and sugar water, and concentration. We can recognize how complex the types of word problems are to solve, which strategies students choose largely, and what errors that students make in the problem solving are.

• Journal of the Korean School Mathematics Society
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• v.16 no.1
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• pp.113-139
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• 2013

The purpose of this study is to provide informations about cause of failures when students solve word problems by analyzing what errors students made in solving word problems and types of error and features of error according to problem solving strategy. The results of this study can be summarized as follows: First, $5^{th}$ grade students preferred the expressions, estimate and verify, finding rules in order when solving word problems. But the majority of students couldn't use simplifying. Second, the types of error encountered according to the problem solving strategy on problem based learning are as follows; In the case of 'expression', the most common error when using expression was the error of question understanding. The second most common was the error of concept principle, followed by the error of solving procedure. In 'estimate and verify' strategy, there was a low proportion of errors and students understood estimate and verify well. When students use 'drawing diagram', they made errors because they misunderstood the problems, made mistakes in calculations and in transforming key-words of data into expressions. In 'making table' strategy, there were a lot of errors in question understanding because students misunderstood the relationship between information. Finally, we suggest that problem solving ability can be developed through an analysis of error types according to the problem strategy and a correct teaching about these error types.

• Communications of Mathematical Education
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• v.27 no.4
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• pp.429-448
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• 2013

The aim of this study was to examine how analogical mapping articulation activity played a role in solving process in word problems. We analyzed the problem solving strategies and processes that the participating thirty-three 8th grade students employed when solving the problems through analogical mapping articulation activities, and also the characteristics of the thinking processes from the aspects of similarity. As a result, this study indicates that analogical mapping articulation activity could be helpful when the students solved similar word problems, although some of them gained correct answers through pseudo-analytic thinking. Not to have them use pseudo-analytic thinking, it might be necessary to help them recognize superficial similarity and difference among the problems and construct structural similarity to know the principle of solution associated with the problematic situations.

• 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.

• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.63-80
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• 2009

This paper has a purpose to find out the important points about linguistic factors suited to the assessment purpose and mathematics teaching/learning that a word-problem sentence has to possess. We also examine the degree of understanding of sentence and the perceptive/emotional reactions of students toward two different kinds of word-problem sentences that have same mathematical contents, but different linguistic structures. The objects of this thesis are 124 students from the third to sixth grade in an elementary school. We execute assessment of simple-sentence-word-problem and complex-sentence-word-problem that have same mathematical contexts, but different linguistic structures. Then we have compared and examined their own process of solving the two types word-problems and we make up questionnaire and have an interview with them. The conclusions are as followings: First, simple-sentence-word-problem is more successful to suggest an information for solving a problem than complex one. Second, it is hard to find the strategy for solving a problem in complex-sentence-word-problem than simple one. Third, students think that suggested information and mathematical knowledge are different according to the linguistic structure in the process of perceiving the information after reading a word-problem. Fourth, in spite of same sentence type, the negative mental reaction is showed greatly to complex-sentence-word-problem even before solving a problem.

• Communications of Mathematical Education
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• v.37 no.4
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• pp.569-590
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• 2023

The purpose of this case study is to compare and analyze the covariational reasoning levels of two middle school students revealed in the process of solving and generalizing algebra word problems. A class was conducted with two middle school students who had not learned quadratic equations in school mathematics. During the retrospective analysis after the class was over, a noticeable difference between the two students was revealed in solving algebra word problems, including situations where speed changes. Accordingly, this study compared and analyzed the level of covariational reasoning revealed in the process of solving or generalizing algebra word problems including situations where speed is constant or changing, based on the theoretical framework proposed by Thompson & Carlson(2017). As a result, this study confirmed that students' covariational reasoning levels may be different even if the problem-solving methods and results of algebra word problems are similar, and the similarity of problem-solving revealed in the process of solving and generalizing algebra word problems was analyzed from a covariation perspective. This study suggests that in the teaching and learning algebra word problems, rather than focusing on finding solutions by quickly converting problem situations into equations, activities of finding changing quantities and representing the relationships between them in various ways.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.599-624
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• 2009

The purpose of this study was to investigate the relationship between error types and Polya's problem solving process. For doing this, we selected 106 sophomore students in a middle school and gave them algebra word problem test. With this test, we analyzed the students' error types in solving algebra word problems. First, We analyzed students' errors in solving algebra word problems into the following six error types. The result showed that the rate of student's errors in each type is as follows: "misinterpreted language"(39.7%), "distorted theorem or solution"(38.2%), "technical error"(11.8%), "unverified solution"(7.4%), "misused data"(2.9%) and "logically invalid inference"(0%). Therefore, we found that the most of student's errors occur in "misinterpreted language" and "distorted theorem or solution" types. According to the analysis of the relationship between students' error types and Polya's problem-solving process, we found that students who made errors of "misinterpreted language" and "distorted theorem or solution" types had some problems in the stage of "understanding", "planning" and "looking back". Also those who made errors of "unverified solution" type showed some problems in "planing" and "looking back" steps. Finally, errors of "misused data" and "technical error" types were related in "carrying out" and "looking back" steps, respectively.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.4
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• pp.717-735
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• 2016

For teaching division-with-remainder(DWR) problems, it is necessary to know students' strategies and errors about DWR problems. The purpose of this study is to investigate and analyze students' strategies and errors of DWR problems and to make some meaningful suggestions for teaching various methods of solving DWR problems. We constructed a test which consists of fifteen DWR problems to investigate students' solving strategies and errors. These problems include mathematical as well as syntactic structures. To apply this test, we selected 177 students from eight elementary schools in various districts of Seoul. The results were analyzed both qualitatively and quantitatively. The sixth graders' strategies can be classified as follows : Single strategies, Multi strategies and Assistant strategies. They used Division(D) strategy, Multiplication(M) strategy, and Additive Approach(A) strategy as sub-strategies. We noticed that frequently used strategies do not coincide with strategies for their success. While students in middle group used Assistant strategies frequently, students in higher group used Single strategies frequently. The sixth graders' errors can be classified as follows : Formula error(F error), Calculation error(C error), Calculation Product error(P error) and Interpretation error(I error). In this study, there were 4 elements for syntaxes in problems : large number, location of divisor and dividend, divisor size, vocabularies. When students in lower group were solving the problems, F errors appeared most frequently. However, in case of higher group, I errors appeared most frequently. Based on these results, we made some didactical suggestions.

• School Mathematics
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• v.18 no.1
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• pp.43-59
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• 2016

The purpose of this qualitative case study is to investigate differences among two gifted middle school students emerging through the process of algebra word problem solving from the covariational perspective. We collected the data from four middle school students participating in the mentorship program for gifted students of mathematics and found out differences between Junghee and Donghee in solving problems involving varying rates of change. This study focuses on their actions to solve and to generalize the problems situations involving constant and varying rates of change. The results indicate that their covariational reasoning played a significant role in their algebra word problem solving.