• Research in Mathematical Education
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• v.11 no.2
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• pp.127-141
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• 2007

This paper compares and analyzes mathematics teachers' understanding of students' mathematical comprehension after experiences with the Cognitively Guided Instruction (CGI) or the Development of Mathematical Ideas (DMI) teaching strategies. This report sheds light on current issues confronted by the educational system in the context of mathematics teaching and learning. In particular, the declining rate of mathematical literacy among adolescents is discussed. Moreover, examples of CGI and DMI teaching strategies are presented to focus on the impact of these teaching styles on student-centered instruction, teachers' belief, and students' mathematical achievement, conceptual understanding and word problem solving skills. Hence, with a gradual enhancement of reformed ways of teaching mathematics in schools and the reported increase in student achievement as a result of professional development with new teaching strategies, teacher professional development programs that emphasize teachers' understanding of students' mathematical comprehension is needed rather than the currently dominant traditional pedagogy of direct instruction with a focus on teaching problem solving strategies.

• Journal of the Korean School Mathematics Society
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• v.20 no.2
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• pp.141-161
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• 2017

As it's important to understand the order of operation in the mixed calculation of natural number and perform it, mathematics curriculums and textbooks focused that students can calculate with understanding the order of operation and its principles. For attaining the implications of teaching about the mixed calculations, this study analyzed the problem solving abilities and error types of 67 elementary students and 57 pre-service teachers using questionnaire which was developed in this study and composed of numeric expressions and word problems. The conclusions drawn from this study were as follows: Students were revealed the correct rates(86.2% and 73.5%) in numeric expressions and word problems, but they were showed the paradigmatic error types-the errors of the order of operation and the composition of numeric expression from word problems. Even though the correct rates of the preservice teachers were extremely high, the result of problem solving processes required that it's needed to be interested in teaching the principles of the order of operation in the mixed calculations. In addition, subjects were revealed the problems about using parentheses and equal sign.

• 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.

• Journal of Educational Research in Mathematics
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• v.25 no.3
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• pp.281-302
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• 2015

In the current study, answer sheets from 8007 students in 236 Korean schools were selected and analyzed to examine errors that emerge in the process of solving descriptive questions of the National Educational Achievement Assessment in mathematics. Questions used in the analysis were response assessment covering middle school mathematics topics: "mathematical symbols and equations" and "functions." The behavioral domain of the questions was that of "problem solving and computation," which requires establishing an equation for a word problem and allows the calculation of an answer that meets a certain condition. The analysis results revealed various errors in each stage of each question, from understanding to solving; the study attempts to conjecture causes for these errors and draw pedagogical implications.

• The Mathematical Education
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• v.53 no.3
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• pp.329-355
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• 2014

The purpose of this study is to understand the difference of cognitive structure depending on the level of the 6th graders' problem-solving abilities about the division of fraction and to propose a method for improving the 6th graders' understanding about the division of fraction through the word association test. The following is the findings from this study. 1)The lower level students' is, the lower the step that the chunk appeared in cognitive structure is. 2)The basic level students' association frequency between any two concepts was less than the excellent level students and the ordinary level students' it. 3)The basic level students' connection number between concepts was far less than the excellent level students and the ordinary level students' it. 4)The connection between natural number and unit fractions, subtraction of fraction and division of fraction, division of fraction and reduction to common denominator, and division of fraction and common multiple that expected in this study did not appear in the three groups.

• East Asian mathematical journal
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• v.32 no.4
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• pp.565-587
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• 2016

The purpose of this study was to analyze the understanding of the meaning of fraction division and fraction division algorithm of elementary mathematical gifted students through the process of problem posing and solving activities. For this goal, students were asked to pose more than two real-world problems with respect to the fraction division of ${\frac{3}{4}}{\div}{\frac{2}{3}}$, and to explain the validity of the operation ${\frac{3}{4}}{\div}{\frac{2}{3}}={\frac{3}{4}}{\times}{\frac{3}{2}}$ in the process of solving the posed problems. As the results, although the gifted students posed more word problems in the 'inverse of multiplication' and 'inverse of a cartesian product' situations compared to the general students and pre-service elementary teachers in the previous researches, most of them also preferred to understanding the meaning of fractional division in the 'measurement division' situation. Handling the fractional division by converting it into the division of natural numbers through reduction to a common denominator in the 'measurement division', they showed the poor understanding of the meaning of multiplication by the reciprocal of divisor in the fraction division algorithm. So we suggest following: First, instruction on fraction division based on various problem situations is necessary. Second, eliciting fractional division algorithm in partitive division situation is strongly recommended for helping students understand the meaning of the reciprocal of divisor. Third, it is necessary to incorporate real-world problem posing tasks into elementary mathematics classroom for fostering mathematical creativity as well as problem solving ability.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.131-164
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• 2024

In this research, we study a modified relaxed Tseng method with a single projection approach for solving common solution to a fixed point problem involving finite family of τ-demimetric operators and a quasi-monotone variational inequalities in real Hilbert spaces with alternating inertial extrapolation steps and adaptive non-monotonic step sizes. Under some appropriate conditions that are imposed on the parameters, the weak and linear convergence results of the proposed iterative scheme are established. Furthermore, we present some numerical examples and application of our proposed methods in comparison with other existing iterative methods. In order to show the practical applicability of our method to real word problems, we show that our algorithm has better restoration efficiency than many well known methods in image restoration problem. Our proposed iterative method generalizes and extends many existing methods in the literature.

• The Mathematical Education
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• v.59 no.2
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• pp.101-112
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• 2020

The purpose of this study is to analyze the structures of teacher's discourse according to the pattern of interaction between teachers and students in the understanding mathematical word problem. The structures of teacher's discourse could be conceptualized as a process in which the teacher starts, develops and organizes the discourse based on prior research. For this purpose, the fourth class(example, a problem of the same type as the example, formative assessment, and final assessment) was extracted from one semester of experienced teachers who have been practicing teaching methods to facilitate student participation for many years. A methodology used to develop a theory based on data collected through classroom observations. Because the purpose of the study is to identify the structures of teacher's discourse to help the problem understanding, observe the teacher's discourse and collect data based on student engagement. Results show that the structure of teacher's discourse, which consults on important aspects of interaction between teachers-students and creates mathematical meanings, helped students understand the mathematics word problem by promoting their engagement in class. Based on the structures of teacher's discourse to understand problems based on the interaction patterns between teachers and students, it can be said that teachers provided specific methodologies on how to communicate with students in order to understand problems in the future.

• Journal of Korea Technology Innovation Society
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• v.16 no.2
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• pp.408-423
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• 2013

As the word 'creation and innovation' has been the keyword in success, there has been an increasing interest in TRIZ (Theory of inventive problem solving). So far, TRIZ has been applied to electronics and mechanics as the prime mover of product innovation. This study is to explore the applicability of TRIZ to the biotechnology sector, a future emerging technologies, especially to problem solving and innovative research and development. This study was focused on red ginseng processing. Problem causes and contradictions were identified with regard to processing-related problems, and 'the 40 principles of invention' were applied to problem solving. Steamed fresh ginseng is called 'Red ginseng'. Cracks in red ginseng cause the loss of active ingredients and also are not of merchantable quality. In the 40 principles of invention, applicable ones were finally selected through contradiction matrix and brainstorming, the tools of TRIZ. With experiments, effective methods were suggested to prevent red ginseng from cracking in a steaming process.

• Journal for History of Mathematics
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• v.16 no.1
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• pp.45-62
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• 2003

The goals of a major reform effort are to enable us to educate informed citizens who are better able to function in our increasingly technological society. Discrete mathematics is an exciting and appropriate vehicle for working toward and achieving these goals. it is an excellent tool for improving reasoning and problem solving skills. Discrete mathematics has many practical applications that are useful for solving some of the problems of our society and that are meaningful to our students. Its problems make mathematics come alive for students, and help them see the relevance of mathematics th the real word. To build up the role of Discrete mathematics in the school, this study is to investigate various theories and curricula related to discrete mathematics, and to collect a great deal of valuable material that will help teachers introduce discrete mathematics in their classrooms. In conclusion. mathematics teachers will find the need and importance of why and how discrete mathematics can be introduced into their curricula by this study.