• The Mathematical Education
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• v.46 no.4
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• pp.483-492
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• 2007

The purpose of this study was to investigate the relation between the cognitive processes and the mathematical achievement of the 4th grade students. And according to the several studies, there were significant relation between cognitive processes and achievement. Based on the PASS(Planning-Attention-Simultaneous-Successive Processes) Model presented by Das and Naglieri, four cognitive process variables were selected. The results of this study as follows. First, there was not significant relation between attention and mathematical achievement. Second, there was significant relation between planning and mathematical achievement. Third, there was significant relation between simultaneous/successive processes and mathematical achievement. Fourth, the students who got higher scores in the two types (simultaneous/successive)of information processing had more mathematical achievement. Specially, the students who got higher scores in the type of simultaneous information processing had higher scores in mathematical achievement. These results indicated that planning and simultaneous information processing had influence on the mathematical achievement.

• The Mathematical Education
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• v.47 no.2
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• pp.169-180
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• 2008

The purpose of this study was to analyze the elementary students' mathematical thinking, which is found during mathematical problem solving processes based on mathematical knowledge, heuristics, control, and mathematical disposition. The participants were 8 fifth grade elementary students in Seoul. A qualitative case study was used for investigating the students' mathematical thinking. The data were coded according to the four components of the students' mathematical thinking. The results of the analyses concerning mathematical thinking of the elementary students were as follows: First, in terms of mathematical knowledge, the elementary students frequently used conceptual knowledge, procedural knowledge and informal knowledge during problem solving processes. Second, students tended not to find new heuristics or apply new one, but they only used the heuristics acquired from the experiences of the class and prior experiences. Third, control was found while students were solving problems. Last, mathematical disposition influenced on the mathematical problem solving processes. Teachers need to in-depth observations on the problem solving processes of students, which leads to teachers'effective assistance on facilitating students' problem solving skills.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.1
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• pp.19-37
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• 2013

2009 revised national curriculum for mathematics emphasizes the mathematical processes which consist of mathematical problem solving, mathematical reasoning, and mathematical communication. This study focused on applying these processes to an elementary school class for mathematics. Even though they say that it is desirable that the mathematical processes are realized in every mathematics class, any vague intention for their application without specific plans is apt to be apart from meaningful practice. Therefore this study proposed a lesson plan about the characteristics and the comparison of bar graphs and line graphs for 4th grade students based on the mathematical processes. And we applied it to 27 subjects. By observing and analyzing their activities and communications, we discussed about the guidelines of applying the mathematical processes to elementary school classes for mathematics.

• School Mathematics
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• v.7 no.1
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• pp.55-75
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• 2005

Mathematical symbolizing is an important part of mathematics learning. But many students have difficulties m symbolizing mathematical ideas formally. If students had experiences inventing their own mathematical symbols and developing them to conventional ones natural way, i.e. learning mathematical symbols via expressive approaches, they could understand and use formal mathematical symbols meaningfully. These experiences are especially valuable for students who meet mathematical symbols for the first time. Hence, there are needs to investigate how early elementary school students can and should experience meaningful mathematical symbolizing. The purpose of this study was to analyze students' mathematical symbolizing processes and characteristics of theses. We carried out teaching experiments that promoted meaningful mathematical symbolizing among eight first graders. And then we analyzed students' symbolizing processes and characteristics of expressive approaches to mathematical symbols in early elementary students. As a result, we could places mathematical symbolizing processes developed in the teaching experiments under five categories. And we extracted and discussed several characteristics of early elementary students' meaningful mathematical symbolizing processes.

• East Asian mathematical journal
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• v.24 no.2
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• pp.151-159
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• 2008

An error analysis introduced in [1], [2] is utilized in combination with nondiscrete mathematical induction to provide a finer than before [3]-[7], [11] semilocal convergence analysis for a certain class of modified Newton processes.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.545-562
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• 2009

This study is trying to analyze characteristics of mathematical thinking processes of the mathematical gifted students in an objective and a systematic way, by using "Protocol Analysis Method"and "Problem Behavior Graph" which is suggested by Newell and Simon as a qualitative analysis. In this study, four middle school students with high achievement in math were selected as subjects-two students for mathematical gifted group and the other two for control group also with high scores in math. The thinking characteristics of the four subjects, shown in the course of solving problems, were elicited, analyzed and compared, through the use of the creative test questionnaires which were supposed to clearly reveal the characteristics of mathematical gifted students' thinking processes. The results showed that there were several differences between the two groups-the mathematical gifted student group and their control group in their mathematical talents. From these case studies, we could say that it is significant to find out the characteristics of mathematical thinking processes of the mathematical gifted students in a more scientific way, in the sense that this result can be very useful to provide them with the chances to get more proper education by making clear the nature of thinking processes of the mathematical gifted students.

• The Mathematical Education
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• v.44 no.1 s.108
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• pp.87-101
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• 2005

The purpose of this paper is to propose a teaching method which is focused on the mathematical thinking skills such as the use of induction, counter example, analogy, and so on mathematicians use when they explore their research fields. Many have indicated that students have learned mathematics exploring to use very different methods mathematicians have done and suggested students explore as they do. In the first part of the paper, the plausible whole processes from the beginning time they get a rough idea to a refined mathematical truth. In the second part, an example with Euler characteristic of 1. In the third, explaining the same processes with ${\pi}$, a model modified from the processes is designed. It is hoped that the suggested model, focused on a variety of mathematical thinking, helps students learn mathematics with understanding and with the association of exploring entertainment.

• Korean Journal of Child Studies
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• v.28 no.4
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• pp.319-331
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• 2007

This review of literature establishes a contemporary meaning of mathematical problem solving including young children's mathematical problem solving processes/assessments and teaching strategies. The contemporary meaning of mathematical problem solving involves complicated higher thinking processes. Explanations of the mathematical problem solving processes of young children include the four steps suggested by $P{\acute{o}}lya$(1957) : understand the problem, devise a plan, carry out the plan, and review/extend the plan. Assessments of children's mathematical problem solving include both the process and the product of problem solving. Teaching strategies to support children's mathematical problem solving include mathematical problems built upon children's daily activities, interests, and questions and helping children to generate new approaches to solve problems.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.319-332
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• 1996

Many authors have studied multiple stochastic integrals in pursuit of the existence of product processes in terms of multiple integrals. But there has not been much research into the structure of the product processes themselves. In this direction, a study which gives emphasis on sample path continuity and boundedness properties was initiated in Pyke[9]. For details of problem set-ups and necessary notations, see [9]. Recently the weak limits of U-processes are shown to be chaos processes, which is product of the same Brownian measures, see [2] and [7].

• Communications of Mathematical Education
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• v.28 no.4
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• pp.553-571
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• 2014

Mathematical process is an issue in current mathematics education. In this paper discuss how to assess the mathematical process using essay type questions. For this we first suggest the concept of Mathematical Process Oriented Question which is an essay type question and possible to assess mathematical processes, that is, the mathematical communication, reasoning, and problem solving as well as mathematics knowledge. And we develop a framework for developing the mathematical process oriented question and rubric, examples of assessment standards and those questions containing rubric for assessing mathematical processes. The results of this paper can serve as basic data and examples for follow up research about mathematical process assessment.