• Research in Mathematical Education
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• v.9 no.4 s.24
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• pp.317-328
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• 2005

The aim of this study is to investigate future teachers' skills that can make problem solving methods concrete for 7-11 year old students. For the students in the concrete operations level, solutions of word problems should also be taught by concreting. But most of teacher candidates can not solve the problems without algebra because they got used to solve the word problems with algebra during their high school and university education. In this study, whether the teacher candidates have the skills of solving the primary school level problems without using algebra or not are being observed. At the end of this observation it is determinated that primary level teacher candidates generally prefer using algebra operations because of their former habits. The results show that in the education of the primary level teacher candidates, there is the need of developing the solving skills using figures and diagrams without algebra rather than algebraic solutions in word problems.

• 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.

• 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.

• Research in Mathematical Education
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• v.15 no.4
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• pp.311-325
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• 2011

In this paper I propose that teaching students the most efficient method of problem solving may curtail students' creativity. Instead it is important to arm students with a variety of problem solving heuristics. It is the students' responsibility to decide which heuristic will solve the problem. The chosen heuristic is the one which is meaningful to the students.

• The Journal of the Korea Contents Association
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• v.14 no.12
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• pp.1083-1099
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• 2014

The purpose of this study is to analyze that The arithmetic and algebraic word problem solving skill, strategy preference, and assessment ability of elementary preservice teachers is investigated using a statistical methodology. The research findings are as follows. First, elementary preservice teachers demonstrated logical and delicate problem solving behaviors in arithmetic and algebraic word problem solving. And elementary preservice teachers prefer to create a formula and table strategy in problem solving of the arithmetic question. Second, there was meaningful difference in the math and english elementary preservice teachers' appreciations with significant level of 0.05. And there was not meaningful difference in the 1 and 4 grade elementary preservice teachers' appreciations with significant level of ${\alpha}=0.05$. Results of the study suggest that teachers education course need to improve elementary preservice teachers' word problem solving skill, strategy preference, and assessment ability in the arithmetic and algebraic.

• Journal of Educational Research in Mathematics
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• v.17 no.1
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• pp.67-90
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• 2007

The purpose of this study is to understand students' thinking process in the algebra problem solving, on the base of the works of Vinner(1997a, 1997b). Thus, two middle school students were evaluated in this case study to examine how they think to solve algebra word problems. The following question was considered to analyze the thinking process from the similarity-based perspective by focusing on the process of solving algebra word problems; What is the relationship between similarity and the characteristics of thinking process at the time of successful and unsuccessful problem solving? The following results were obtained by analyzing the success or failure in problem solving based on the characteristics of thinking process and similarity composition. Successful problem solving can be based on pseudo-analytical thought and analytical thought. The former is the rule applied in the process of applying closed formulas that is constructed structural similarity not related with the situations described in the text. The latter means that control and correction occurred in all stages of problem solution. The knowledge needed for solutions was applied with the formulation of open-end formulas that is constructed structural similarity in which memory and modification with the related principles or concepts. In conclusion, the student's perception on the principles involved in a solution is very important in solving algebraic word problems.

• Communications of Mathematical Education
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• v.35 no.3
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• pp.323-340
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• 2021

The purpose of this case study is to explore the similarities revealed in the process of solving and generalizing word problems related to systems of linear equations in two variables according to covariational reasoning. As a result, student S, who reasoned with coordination of value level, had a static image of the quantities given in the situation. student D, who reasoned with smooth continuous covariation level, had a dynamic image of the quantities in the problem situation and constructed an invariant relationship between the quantities. The results of this study suggest that the activity that constructs the relationship between the quantities in solving word problems helps to strengthen the mathematical problem solving ability, and that teaching methods should be prepared to strengthen students' covariational reasoning in algebra learning.

• Education of Primary School Mathematics
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• v.27 no.3
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• pp.281-301
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• 2024

Many students have experienced difficulties due to the discontinuity in instruction between arithmetic and algebra, and in the field of elementary education, algebra is often treated somewhat implicitly. However, algebra must be learned as algebraic thinking in accordance with the developmental stage at the elementary level through the expansion of numerical systems, principles, and thinking. In this study, algebraic thinking-based classes were developed and conducted for 6th graders in elementary school, and the effect on the ability to solve word-problems in fraction division was analyzed. During the 11 instructional sessions, the students generalized the solution by exploring the relationship between the dividend and the divisor, and further explored generalized representations applicable to all cases. The results of the study confirmed that algebraic thinking-based classes have positive effects on their ability to solve fractional division word-problems. In the problem-solving process, algebraic thinking elements such as symbolization, generalization, reasoning, and justification appeared, with students discovering various mathematical ideas and structures, and using them to solve problems Based on the research results, we induced some implications for early algebraic guidance in elementary school mathematics.

• The Mathematical Education
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• v.42 no.3
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• pp.353-368
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• 2003

Analogy, based on a similarity, is to infer the properties of the similar object from properties of an object. It can be a very useful thinking tool for learning mathematical patterns and laws, noticing on relational properties among various situations. The purpose of this study, when manipulating hint condition, figure and table conditions and the amount of original learning by using algebra word problems, is to verify the effects of analogical transfer in solving equivalent, isomorphic and similar problems according to the similarity of source problems and target ones. Five study questions were set up for the above purpose. It was 354 first grade students of S and G middle schools in Seoul that were experimented for this study. The data was processed by MANOVA analysis of statistical program, SPSS 10.0. The results of this studies would indicate that most of the students would be poor at solving isomorphic and similar problems in the performance of analogical transfer according to the similarity of source and target problems. Hints, figure and table conditions did not facilitate the analogical transfer. Merely, on the condition that amount of teaming was increased, analogical transfer of the students was facilitated. Therefore, it is necessary to have students do much more analogical problem-solving experience to improve their analogical reasoning ability through the instruction program development in the educational fields.