• Communications of Mathematical Education
• /
• v.2
• /
• pp.181-191
• /
• 1997

The purpose of this study is to provide the primary sources to improve the problem solving performance by analyzing the errors and the strategies selection of the high school students when solving given algebraic problems. To attain the purpose of this study, the questions for investigation in this study are : 1. What are the differences / similarities in the patterns of errors committed by successful and unsuccessful problem-solvers when solving particular algebraic problems ? 2. What are the error types chosen by unsuccessful problem-solvers when solving particular algebraic problems? 3. Do students utilize checking, either locally or globally, when solving particular algebraic problems? Twenty students were drawn out of 10th grade students in J girls' high school in Yengi -gun, Chung-Nam, for this study. The problem-solving test was used as a test instrument. From the data, the verbal protocols and the written protocols were analyzed by the patterns. The conclusions drawn from the results obtained in the present study are as follows: First, in solving particular algebraic problems, when the problems were solved with one strategy, most students didn't give any consideration to other strategies. So mathematics teachers should teach them to use the various strategies, and should develop the problems to be used the various strategies. Second, in solving particular algebraic problems, errors on notions or transformations of equations were found. Thus, the basic knowledges related to equation should be taught. In addition, most unsuccessful students seleted the strategies inadequately to solve the problems because of misunderstanding the problems. So, to improve the problem solving performance the processes of 'understanding problem' should be emphasized to students. Third, although the unsuccesful students used the 'checking' processes when solving the problems, most of them did not find the errors because of misconceptions related to the problems, carelessness, and unskillfulness of checking. Thus, students must be taught more carefully and encouraged to use the checking.

• Korean Journal of Human Ecology
• /
• v.19 no.2
• /
• pp.257-270
• /
• 2010

This study investigated preschoolers' happiness, behavior problems, and interpersonal problem solving strategies according to their sex and age, and the relationships among them. The subjects were 185 preschoolers (97 boys and 88 girls; 83 four-year-olds and 102 five-year-olds). Results showed that boys were higher in behavior problems (aggression) and forceful problem solving strategies than girls, while girls were higher in happiness (characteristics of self) than boys. Also, 4-year-old children were higher in forceful problem solving strategies than 5-year-olds. Children's happiness was negatively related to their internalizing and externalizing behavior problems. Behavior problems and interpersonal problem solving strategies of children were influenced by their happiness. These findings provide preliminary evidence that children's happiness may predict their behavior problems and interpersonal problem solving strategies.

• The Mathematical Education
• /
• v.31 no.2
• /
• pp.109-119
• /
• 1992

The primary purpose of the present study is to provide the sources to improve the mathematical problem solving performance by analyzing the effects of the belief systems and the misconceptions of the middle school students in solving the problems. To attain the purpose of this study, the reserch is designed to find out the belief systems of the middle school students in solving the mathematical problems, to analyze the effects of the belief systems and the attitude on the process of the problem solving, and to identify the misconceptions which are observed in the problem solving. The sample of 295 students (boys 145, girls 150) was drawn out of 9th grade students from three middle schools selected in the Kangdong district of Seoul. Three kinds of tests were administered in the present study: the tests to investigate (1) the belief systems, (2) the mathematical problem solving performance, and (3) the attitude in solving mathematical problems. The frequencies of each of the test items on belief systems and attitude, and the scores on the problem solving performance test were collected for statistical analyses. The protocals written by all subjects on the paper sheets to investigate the misconceptions were analyzed. The statistical analysis has been tabulated on the scale of 100. On the analysis of written protocals, misconception patterns has been identified. The conclusions drawn from the results obtained in the present study are as follows; First, the belief systems in solving problems is splited almost equally, 52.95% students with the belief vs 47.05% students with lack of the belief in their efforts to tackle the problems. Almost half of them lose their belief in solving the problems as soon as they given. Therefore, it is suggested that they should be motivated with the mathematical problems derived from the daily life which drew their interests, and the individual difference should be taken into account in teaching mathematical problem solving. Second. the students who readily approach the problems are full of confidence. About 56% students of all subjects told that they enjoyed them and studied hard, while about 26% students answered that they studied bard because of the importance of the mathematics. In total, 81.5% students built their confidence by studying hard. Meanwhile, the students who are poor in mathematics are lack of belief. Among are the students accounting for 59.4% who didn't remember how to solve the problems and 21.4% lost their interest in mathematics because of lack of belief. Consequently, the internal factor accounts for 80.8%. Thus, this suggests both of the cognitive and the affective objectives should be emphasized to help them build the belief on mathematical problem solving. Third, the effects of the belief systems in problem solving ability show that the students with high belief demonstrate higher ability despite the lack of the memory of the problem solving than the students who depend upon their memory. This suggests that we develop the mathematical problems which require the diverse problem solving strategies rather than depend upon the simple memory. Fourth, the analysis of the misconceptions shows that the students tend to depend upon the formula or technical computation rather than to approach the problems with efforts to fully understand them This tendency was generally observed in the processes of the problem solving. In conclusion, the students should be taught to clearly understand the mathematical concepts and the problems requiring the diverse strategies should be developed to improve the mathematical abilities.

• Journal of The Korean Association For Science Education
• /
• v.8 no.1
• /
• pp.43-55
• /
• 1988

This study intended to find the differences between expert's and novice's thinking processes when they solve physics problems. Five physics professors and twenty sophomore students in a physics department were participated in the study. The researcher investigated their thinking processes in solving three physics problems on NEWTON's law of motion. The researcher accepted so called "Thinking Aloud" method. The thinking processes were recorded and transfered into protocols. The protocols were analysised by problem solving process coding system which was developed by the researcher on the basis of Larkin's problem solving process model. The results were as follows: (1) There was no difference of time required in solving physics problem of low difficulty between expert and novices; but, it takes 1.5 times longer for novices than experts in solving physics problems which difficulties are high and average. (2) Novices used working forward strategy and working backward strategy at the similiar rate in solving physics problems which difficulties were average and low. while Novices mo mostly used working backward strategy in solving physic problems which difficulty was high. Experts mostly used working forward strategy in solving physics problems whose difficulties was average and low, however experts used working forward strategy and working backward strategy at the similiar rate in solving physics problem which difficulty was high. (3) Novices usually wrote only a few information on the diagram of figure they drawn, on the other hand experts usually wrote almost all the information which are necessary for solving the problems. (4) Experts spent much time in understand the problem and evaluation stage than novices did, however experts spent less time in plan stage than novices did. (5) Physics problems are solved in sequence of understanding the problem, plan, carrying out the plan, and evaluation steps regardless of problem difficulty.

• The Mathematical Education
• /
• v.26 no.2
• /
• pp.9-13
• /
• 1988

Mathematics education is generally to cultivate mathematical thought. Most meaningful thought is to solve a certain given situation, that is, a problem. The aim of mathematies education could be identified with the cultivation of mathematical problem-solving ability. To cultivate mathematical problem-solving ability, it is necessary to study the nature of mathematical ability and its aspects pertaining to problem-solving ability. The purpose of this study is to investigate the relation between problem-solving ability and classficational viewpoint of mathematical verbal problems, and bet ween the detailed abilities of problem-solving procedure and classificational viewpoint of mathematical verbal problems. With the intention of doing this work, two tests were given to the third-year students of middle school, one is problem-solving test and the other classificational viewpoint test. The results of these two tests are follow ing. 1. The detailed abilities of problem-solving procedure are correlated with each other: such as ability of understanding, execution and looking-back. 2. From the viewpoint of structure and context, students classified mathematical verbal problems. 3. The students who are proficient at problem-solving, understanding, execution, and looking-back have a tendency to classify mathematical verbal problems from a structural viewpoint, while the students who are not proficient at the above four abilities have a tendency to classify mathematical verbal problems from a contextual viewpoint. As the above results, following conclusions can be made. 1. The students have recognized at least two fundamental dimensions of structure and context when they classified mathematical verbal problems. 2. The abilities of understanding, execution, and looking- back effect problem-solving ability correlating with each other. 3. The instruction emphasizing the importance of the structure of mathematical problems could be one of the methods cultivating student's problem-solving ability.

• Research in Mathematical Education
• /
• v.11 no.4
• /
• pp.247-263
• /
• 2007

Problem solving takes place not only in mathematics classes but also in real-world. For this reason, a problem and the structure of problem solving, and the enhancing of success in problem solving is a subject which has been studied by any educators. In this direction, the aim of this study is that the strategy used by students in Turkey when solving oral problems and their achievements of choosing operations when solving oral problems has been researched. In the research, the students have been asked three types of questions made up groups of 5. In the first category, S-problems (standard problems not requiring to determine any strategy but can be easily solved with only the applications of arithmetical operations), in the second category, AS-SA problems (problems that can be solved with the key word of additive operation despite to its being a subtractive operation, and containing the key word of subtractive operation despite to its being an additive operation), and in the third category P-problems (problematic problem) take place. It is seen that students did not have so much difficulty in S-problems, mistakes were made in determining operations for problem solving because of memorizing certain essential concepts, and the succession rate of students is very low in P-problems. The reasons of these mistakes as a summary are given below: $\cdot$ Because of memorizing some certain key concepts about operations mistakes have been done in choosing operations. $\cdot$ Not giving place to problems which has no solution and with incomplete information in mathematics. $\cdot$ Thinking of students that every problem has a solution since they don't encounter every type of problems in mathematics classes and course books.

• Education of Primary School Mathematics
• /
• v.10 no.2
• /
• pp.141-149
• /
• 2007

It is undeniably important to bring up a solution capability of arithmetic word problems in the elementary mathematical education. The goal of this study is to acquire the implication for remedial instruction on arithmetic word problems solving through surveying elementary school students' difficulties in the solving of arithmetic word problems. In order to do it, this study was intended to analyze the following two aspects. First, it was analyzed that they generally felt more difficulties in which field among addition, subtraction, multiplication and division word problems. Second, with the result of the first analysis, it was examined that they solved it by imagining as which sphere of the other word problems. Also, the cause of their error on the word problem solving was analyzed by the interview. From the foregoing analyses, the following implications for remedial instruction on arithmetic word problems solving are acquired. First, the accumulation of learning deficiency must be diminished through the remedial instruction. Second, it must help students to understand the given problem and to make of what the goal of problem is. Third, it must help students to form a good habit for reading the problem and to understand the context of problem. forth, the teacher must help students to review and reflect their problem-solving processes.

• Knowledge Management Research
• /
• v.15 no.4
• /
• pp.15-34
• /
• 2014

Creative problem solving has become an important issue in many fields. Among problems, dilemma need creative solutions. New creative and innovative problem solving strategies are required to handle the contradiction relations of the dilemma problems because most creative and innovative cases solved contradictions inherent in the dilemmas. Among various kinds of problem solving theories, TRIZ provides the concept of physical contradiction as a common problem solving principle in inventions and patents. In TRIZ, 4 separation principles solve the physical contradictions of given problems. The 4 separation principles are separation in time, separation in space, separation within a whole and its parts, and separation upon conditions. Despite this attention, an accurate definitions of the separation principles of TRIZ is missing from the literature. Thus, there have been several different interpretations about the separation principles of TRIZ. The different interpretations make problems more ambiguous to solve when the problem solvers apply the 4 separation principles. This research aims to fill the gap in several ways. First, this paper classify the types of contradiction relations and the contradiction solving dimensions based on the Butterfly model for contradiction solving. Second, this paper compares and analyzes each contradiction relation type with the Butterfly diagram. The contributions of this paper lies in reducing the problem space by recognizing the structures and the types of contradiction problems exactly.

• Research in Mathematical Education
• /
• v.9 no.1 s.21
• /
• pp.11-24
• /
• 2005

Problem solving is an important aspect of learning mathematics and has been extensively researched into by mathematics educators. In this paper we analyze the difficulties students encounter in various steps involved in solving problems involving physical and geometrical applications of mathematical concepts. Our research shows that, generally students, in spite of possessing adequate theoretical knowledge, have difficulties in identifying the hidden data present in the problems which are crucial links to their successful resolutions. Our research also shows that students have difficulties in solving problems involving constructions and use of symmetry.

• School Mathematics
• /
• v.1 no.2
• /
• pp.617-636
• /
• 1999

This study was executed with the intention of guiding ‘open education’ toward a desirable school innovation. The basic two directions of curriculum reconstruction essential for implementing ‘open education’ are one toward intra-subject (within a subject) and inter-subject (among subjects). This study showed an example of intra-subject curriculum reconstruction with a problem solving area included in elementary mathematics curriculum. In the curriculum, diverse strategies to enhance ability to solve problems are included at each grade level. In every elementary math textbook, those strategies are suggested in two chapters called ‘diverse problem solving’, in which problems only dealing with several strategies are introduced. Through this method, students begin to learn problem solving strategies not as something related to mathematical knowledge or contents but only as a skill or method for solving problems. Therefore, problems of ‘diverse problem solving’ chapter should not be dealt with separatedly but while students are learning the mathematical contents connected to those problems. Namely, students must have a chance to solve those problems while learning the contents related to the problem content(subject). By this reasoning, in the name of curriculum reconstruction toward intra-subject, this study showed such case with two ‘diverse problem solving’ chapters of the 4th grade second semester's math textbook.