• Journal of Educational Research in Mathematics
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• v.17 no.2
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• pp.91-109
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• 2007

This study deals with the problem of transition from arithmetic to algebra and the relationship between elementary and secondary school mathematics for systems of linear equations. In elementary school, activity for solving word problems related to systems of linear equations in two variables falls broadly into using two strategies: Guess and check and making a table. In secondary school, those problems are solved algebraically, for example, by solving systems of equations using the technique of elimination. The analysis of mathematics textbooks shows that there is no link between strategies of elementary school mathematics and secondary school mathematics. We devised an alternative way to reinforce link between elementary and secondary school mathematics for systems of linear equations. Drawing a diagram can be introduced as a strategy solving word problems related to systems of linear equations in two variables in elementary school. Moreover it is closely related to the idea of the technique of elimination of secondary school mathematics. It may be a critical juncture of elementary-secondary school mathematics in the case of systems of linear equations in two variables.

• School Mathematics
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• v.14 no.4
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• pp.445-468
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• 2012

This study is tried in order to link informal arithmetic reasoning to formal algebraic reasoning. In this study, we investigated elementary school student's non-formal algebraic reasoning used in algebraic problem solving. The result of we investigated algebraic reasoning of 839 students from grade 1 to 6 in two schools, Korea, we could recognize that they used various arithmetic reasoning and pre-formal algebraic reasoning which is the other than that is proposed in the text book in word problem solving related to the linear systems of equation. Reasoning strategies were diverse depending on structure of meaning and operational of problems. And we analyzed the cause of failure of reasoning in algebraic problem solving. Especially, 'quantitative reasoning', 'proportional reasoning' are turned into 'non-formal method of substitution' and 'non-formal method of addition and subtraction'. We discussed possibilities that we are able to connect these pre-formal algebraic reasoning to formal algebraic reasoning.

• School Mathematics
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• v.9 no.1
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• pp.141-160
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• 2007

The purpose of this paper was to evaluate how students apply prior knowledge or experience in solving algebra word problems from the chain of signification-based perspective. Three middle school students were evaluated in this case study. The results showed that the subjects formed similarities in the process of applying knowledge needed for solving a problem. The student A and C used semi-open-end formulas and closed formulas as solutions. They then formed concrete shape for each solution using the chain of signification that was applied for solution by forming procedural similarity. At this time, the chain of signification could be the combination of numbers, words, and pictures (such as diagrams or graphs) or just numbers or words. On the other hand, the student C who recognized closed formulas and her own rule as a solution method could not formulate completely procedural similarity due to many errors arising from number information. Nonetheless, all of the subjects showed something in common in the process of coming up with a algorithm that was semi-open-end formula or closed formula.

• The Mathematical Education
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• v.46 no.4
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• pp.371-388
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• 2007

This is a case study trying to understand from the view of affordance which certain three middle school students perceive an activation of previous knowledge in the course of problem solving when they solve algebra word problems with a previous knowledge. The results of this study showed that at first, every subjects perceived the text as affordance which explaining superficial similarities, that is, a working(painting)situation rather than problem structure and then activated the related solution knowledge on the ground of the experience of previous problem solving which is similar to current situation. The subject's applying process for solving knowledge could be arranged largely into two types. The first type is a numeral information connected with the described problem situation or a symbolic representation of mathematical meaning which are the transformed solution applied process with a suitable solution formula to the current problem. This process achieved by constructing a virtual mental model that indicating mathematical situation about the problem when the solver read the problem integrating symbolized information from the described text. The second type is a case that those subjects symbolizing a formal mathematical concept which is not connected with the problem situation about the described numeral information from the applied problem or the text of mathematical meaning, which process is the case to perceive superficial phrases or words that described from the problem as affordance and then applied previously used algorithmatical formula as it was. In conclusion, on the ground of the results of this case study, it is guessed that many students put only algorithmatical knowledge in their memories through previous experiences of problem solving, and the memories are connected with the particular phrases described from the problems. And it is also recognizable when the reflection process which is the last step of problem solving carried out in the process of understanding the problem and making a plan showed the most successful in problem solving.

• 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.

• Journal of the Korean School Mathematics Society
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• v.17 no.4
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• pp.507-539
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• 2014

The algebra is an important tool influencing on a mathematics in general. To make good use of the algebra, it is necessary to transfer from a given situation to a proper algebraic representation. But some research in related to algebraic word problems have reported the difficulty changing to a proper algebraic representation. Our study have focused on transformation and elaboration of algebraic representation. We investigated in detail the responses and perceptions of 29 Grade 7 students while transforming to algebraic representation, only concentrating on the literature expression form the problematic situations given. Most of students showed difficulties in transforming both descriptive and geometric problems to algebraic representation. 10% of them responded wrong answers except only a problem. Four of them were interviewed individually to show their thinking and find the factor influencing on a positive elaboration. As results, we could find some characteristics of their thinking including the misconception that regard the problem finding a functional formula because there are the variables x and y in the problematic situation. In addition, we could find the their fixation which student have to set up the equation. Furthermore we could check that making student explain own algebraic representation was able to become the factor influencing on a positive elaboration. From these, we also discussed about several didactical implications.