• Research in Mathematical Education
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• v.6 no.2
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• pp.171-182
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• 2002

Students approach mathematical problem solving in fundamentally different ways, particularly problems requiring conceptual understanding and complicated strategies such as mathematical word problems. The main objective of this study is to compare students' performance with different cognitive styles (Field-dependent vs. Field-independent) on mathematics problem solving, particularly, in word problems. A sample of 180 school girls (13-years-old) were tested on the Witkin's cognitive style (Group Embedded Figures Test) and two mathematics exams. Results obtained support the hypothesis that students with field-independent cognitive style achieved much better results than Field-dependent ones in word problems. The implications of these results on teaching and setting problems emphasizes that word problems and cognitive predictor variables (Field-dependent/Field- independent) could be challenging and rather distinctive factors on the part of school learners.

• Journal of the Korean School Mathematics Society
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• v.12 no.4
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• pp.433-452
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• 2009

This study investigated the teaching strategies of two exemplary American teachers regarding word problems and their impact on students' ability to both understanding and solving word problems. The teachers commonly explained the background details of the background of the word problems. The explanation motivated the students' mathematical problem solving, helped students understand the word problems clearly, and helped students use various solving strategies. Emphasizing communication, the teachers also provided comfortable atmosphere for students to discuss mathematical ideas with another. The teachers' continuous questions became the energy for students to plan various problem solving strategies and reflect the solutions. Also, this research suggested a complementary model for Polya's problem solving strategies.

• Korean Journal of Child Studies
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• v.12 no.1
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• pp.52-67
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• 1991

The purpose of the present study was to investigate children's interpersonal problem solving strategies. Specifically, the number and categories of interpersonal problem solving strategies were examined by age, sex, and source of problem (friends or mother). The subjects were eighty 4,-and 6-year-old boys and girls. The instrument was based on Shure and Spivack's (1974) Preschool Interpersonal Problem Solving (PIPS) test. The test was administered to the children individually in the preschool setting. The data were analyzed by two-way ANOVA, frequency, percentage, and Kendall's Tau. The results showed that the older children had higher PIPS scores; that is, the 6-year-olds suggested more alternative problem solving strategies than 4-year-olds. Children suggested more alternate strategies and different strategies for solving problems with friends compared to solving problems with mothers.

• Journal of The Korean Association For Science Education
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• v.15 no.1
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• pp.80-91
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• 1995

This study aims to identify the differences in chemical problem solving process of college students when the amount of information, problem context and the reasoning level were varied. Four students were participated and each student solved the problem by think-aloud method and then interviewed individually. Problem solving stage, ratio of time for each solving stage, solving strategy, misconceptions, and errors were identified and discussed related to the characteristics of problems. And, the relationships of students' belief system about chemistry & chemistry problem solving and problem solving characteristics were also identified.

• Education of Primary School Mathematics
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• v.24 no.4
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• pp.175-187
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• 2021

The purpose of this study is to investigate the effects of solving multi-strategic mathematics problems on mathematical creativity and attitudes of the 6th grade students. For this study, the researchers conducted a survey of forty nine (26 students in experimental group and 23 students in comparative group) 6th graders of S elementary school in Seoul with 19 lessons. The experimental group solved the multi-strategic mathematics problems after learning mathematics through mathematical strategies, whereas the group of comparative students were taught general mathematics problem solving. The researchers conducted pre- and post- isomorphic mathematical creativity and mathematical attitudes of students. They examined the t-test between the pre- and post- scores of sub-elements of fluency, flexibility and creativity and attitudes of the students by the i-STATistics. The researchers obtained the following conclusions. First, solving multi-strategic mathematics problems has a positive impact on mathematical creativity of the students. After learning solving the multi-strategic mathematics problems, the scores of mathematical creativity of the 6th grade elementary students were increased. Second, learning solving the multi-strategy mathematics problems impact the interest, value, will and efficacy factors in the mathematical attitudes of the students. However, no significant effect was found in the areas of desire for recognition and motivation. The researchers suggested that, by expanding the academic year and the number of people in the study, it is necessary to verify how mathematics learning through multi-strategic mathematics problem-solving affects mathematical creativity and mathematical attitudes, and to verify the effectiveness through long-term research, including qualitative research methods such as in-depth interviews and observations of students' solving problems.

• The Mathematical Education
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• v.57 no.3
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• pp.197-213
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• 2018

Descriptive problems can be used to grow student's ability of thinking logically and creatively, because it shows if the students had a reasonable way of thinking. Rate of descriptive problems is increasing in middle and high school exams. However, students in middle and high schools are generally used to answering multiple-choice or short-answer questions rather than describing the solving process. The purpose of this paper is to gain a theoretic ground to increase the rate of descriptive problems. In this study, students were to solve some multiple-choice problems, and after a few weeks, to solve the problems of same contents in the form of descriptive problems which requires the students to write the solving process. The difference of the scores were measured for each problems to each students, and students were asked what they think the reason for rise or fall of the score is. The result is as follows: First, average scores of 7 of 8 problems used in this study had fallen when it was in descriptive form, and for 5 of them in the rate of 11.2%~16.8%. Second, the main reason of falling is that the students have actual troubles of describing the solving process. Third, in the case of rising, the main reason was that partial scores were given in the descriptive problems. Last, there seems a possibility gender difference in the reason of falling. From these results, followings are suggested to advance the learning, teaching and evaluation in mathematics education: First, it has to be emphasized enough to describe the solving process when solving a problem. Second, increasing the rate of descriptive problems can be supported as a way to advance the evaluation. Third, descriptive problems have to be easier to solve than multiple-choice ones and it is convenient for the students to describe the solving process. Last, multiple-choice problems have to be carefully reviewed that the possibility of students' choosing incorrect answer with a small mistake is minimal.

• 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.

• Education of Primary School Mathematics
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• v.11 no.2
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• pp.121-139
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• 2008

This study analyzed problem presenting and solving activities in elementary school mathematics class to enhance insights of teachers in class for providing real meaning of learning. Following research problems were selected to provide basic information for improving to sound student oriented lesson rather than teacher oriented lessons. Protocols were made based on video information of 5th grade elementary school 'Na' level figure and measurement area 3. Congruence of figures, 4. Symmetry of figures, and 6. Areas and weight. Protocols were analyzed with numbering, comment, coding and categorizing processes. This study is an qualitative exploratory research held toward three teachers of 5th grade for problem solving activities analysis in problem presenting method, opportunity to providing method to solve problems and teachers' behavior in problem solving activities. Following conclusions were obtained through this study. First, problem presenting method, opportunity providing method to solve problems and teachers' behavior in problem solving activities were categorized in various types. Second, Effective problem presenting methods for understanding in mathematics problem solving activities are making problem solving method questions or explaining contents of problems. Then the students clearly recognize problems to solve and they can conduct searches and exploratory to solve problems. At this point, the students understood fully what their assignments were and were also able to search for methods to solve the problem. Third, actual opportunity providing method for problem solving is to provide opportunity to present activities results. Then students can experience expressing what they have explored and understood during problem solving activities as well as communications with others. At this point, the students independently completed their assignments, expressed their findings and understandings in the process, and communicated with others. Fourth, in order to direct the teachers' changes in behaviors towards a positive direction, the teacher must be able to firmly establish himself or herself as a teaching figure in order to promote students' independent actions.

• Journal of The Korean Association For Science Education
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• v.13 no.1
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• pp.31-47
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• 1993

This study was intended to find the characteristics of the middle school students' thinking processes and problem spaces when they solved the physics problems. Ten ninth grade students in Chon-Buk Do, Korea were participated in this study. The researcher investigated their thinking processes in solving 5 physics problems on electric circuit. "Thinking aloud" method was used as a research method. The students' thinking processes were recorded using an audio tape recorder and transfered into protocols. The protocols were analyzed by problem solving process coding system which was developed by Lee(1987) on the basis of Larkin's problem solving process model. The results are as follows : (1) On the average 2.85 items were solved among 5 test items, and only one person could solve all of the items correctly. (2) Problems were solved in sequence of understanding the problem, planning, carrying out the plan, and evaluating steps regardless of the problem difficulty. (3) In regard to the thinking process steps, there was no difference between the good solvers and the poor ones. But in the detail performance of problem solving, the former was different from the latter in respect with using the design of general solving procedure. (4) The basic problem spaces by the item analysis were divided into two classes. One was the problem space by using Qualitative approach in problem solving, and the other was one by using Quantitative approach. As novices in physics problem solving, most of the students used the problem space by using the Quantitative approach.

• The Mathematical Education
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• v.60 no.2
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• pp.133-157
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• 2021

Ill-structured problems have drawn attention in that they can enhance problem-solving skills, which are essential in future societies. The purpose of this study is to analyze and evaluate students' spatial reasoning(Intrinsic-Static, Intrinsic-Dynamic, Extrinsic-Static, and Extrinsic-Dynamic reasoning) and problem solving abilities(understanding problems and exploring strategies, executing plans and reflecting, collaborative problem-solving, mathematical modeling) that appear in ill-structured problem-solving. To solve the research questions, two ill-structured problems based on the geometry domain were created and 11 lessons were given. The results are as follows. First, spatial reasoning ability of sixth-graders was mainly distributed at the mid-upper level. Students solved the extrinsic reasoning activities more easily than the intrinsic reasoning activities. Also, more analytical and higher level of spatial reasoning are shown when students applied functions of other mathematical domains, such as computation and measurement. This shows that geometric learning with high connectivity is valuable. Second, the 'problem-solving ability' was mainly distributed at the median level. A number of errors were found in the strategy exploration and the reflection processes. Also, students exchanged there opinion well, but the decision making was not. There were differences in participation and quality of interaction depending on the face-to-face and web-based environment. Furthermore, mathematical modeling element was generally performed successfully.