• The Mathematical Education
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• v.40 no.2
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• pp.253-263
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• 2001

Developing mathematical thinking skills is one of the most important goals of school mathematics. In particular, recent performance based on assessment has focused on the teaching and learning environment in school, emphasizing student's self construction of their learning and its process. Because of this reason, people related to mathematics education including math teachers are taught to recognize the fact that the degree of students'acquisition of mathematical thinking skills and strategies(for example, inductive and deductive thinking, critical thinking, creative thinking) should be estimated formally in math class. However, due to the lack of an evaluation tool for estimating the degree of their thinking skills, efforts at evaluating student's degree of mathematics thinking skills and strategy acquisition failed. Therefore, in this paper, mathematical thinking was studied, and using the results of study as the fundamental basis, mathematical thinking process model was developed according to three types of mathematical thinking - fundamental thinking skill, developing thinking skill, and advanced thinking strategies. Finally, based on the model, evaluation factors related to essential thinking skills such as analogy, deductive thinking, generalization, creative thinking requested in the situation of solving mathematical problems were developed.

• Research in Mathematical Education
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• v.1 no.1
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• pp.75-85
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• 1997

One of the main objectives of school mathematics education is to develop a student' intuition and logical thinking [11]. But two -valued logical thinking, in fact, is not sufficient to express the concepts of a student's mind since intuition is fuzzy. Hence fuzzy -valued logical thinking may be a more natural way to develop a student's mathematical thinking.

• The Mathematical Education
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• v.60 no.1
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• pp.77-110
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• 2021

In this study, a student participation-centered class based on student mathematical thinking as a the meaningful subject was called a student thinking-based math class. And as a way to support these classes, I paid attention to lesson design. For student thinking-based mathematics classes, it is necessary not only to anticipate student thinking and teacher feedback, but also to plan in advance how to properly arrange and connect expected student responses. The student thinking-based lesson design template proposed in this study is a modified three-step(introduction, main topic, summary) lesson design template. The reason for revising the existing design template is that it has limitation that it cannot focus on mathematical thinking. Using the conceptual framework of student thinking-based mathematics lesson as a lens, the difference between the three-step lesson design prepared by pre-service teachers and the students' thinking-based lesson design prepared by the same pre-service teachers was analyzed. As a result of planning lessons using the student thinking-based lesson design, more attention was paid to the cognitive and social engagement of students. In addition, emphasis was placed in the role of teachers as formative facilitator. This study is of significant in that it recognizes the importance of classes focusing on students' mathematical thinking and provides tools to plan math classes based on students' thinking.

• East Asian mathematical journal
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• v.27 no.4
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• pp.381-389
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• 2011

The flexible mathematical thinking - the ability to generate and connect various representations of concepts - is useful in understanding mathematical structure and variation in problem solving. In particular, the flexible mathematical thinking with the inventive mathematical thinking, the original mathematical problem solving ability and the mathematical invention is a core concept, which must be emphasized in all branches of mathematical education. In this paper, the author considered a case of flexible mathematical thinking with an inventive problem solving ability shown by his student via real analysis courses. The case is on the proofs of the equivalences of three different definitions on the concept of limit superior shown in three different real analysis books. Proving the equivalences of the three definitions, the student tried to keep the flexible mathematical thinking steadily.

• Journal of the Korean School Mathematics Society
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• v.11 no.2
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• pp.201-219
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• 2008

The purpose of this study was to provide useful information for teachers by analyzing various levels of teacher-student communication in elementary mathematics classes and students' mathematical thinking. This study explored mathematical communication of 3 classrooms with regard to questioning, explaining, and the source of mathematical ideas. This study then probed the characteristics of students' mathematical thinking in different standards of communication. The results showed that the higher levels of teacher-student mathematical communication were found with increased frequency of students' mathematical thinking and type. The classroom that had a higher level of Leacher-student mathematical communication was exhibited a higher level of students' mathematical thinking. This highlights the importance of mathematical communication in mathematics c1asses and the necessity of further developing skills of mathematical communication.

• Communications of Mathematical Education
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• v.35 no.1
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• pp.37-74
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• 2021

In this study, the student participation-centered class, which takes students' mathematical thinking as an important issues of the class, is named as student thinking-based math class. The main characteristics of student thinking-based mathematics classes were examined in terms of tasks, students engagement, and the role of teachers. According to the results of analysis of class cases practiced by five secondary mathematics teachers, student thinking-based mathematics classes were conducted in the intersection of the rich mathematics tasks, students' cognitive and social engagement, and the role of teachers' formative facilitator. The results of this study showed that the student's thinking is more important than the activity itself. And it is meaningful in that it examines the influence of the dynamic interaction of the three components of the mathematics class on the direction and outcome of the class.

• The Mathematical Education
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• v.54 no.3
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• pp.223-240
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• 2015

This study qualitatively investigates the nature of the challenges that a student who is highly successful in mathematics faces in learning college-level elementary statistics. The study draws on the constructs of eagerness, flexibility and willingness to characterize the necessary disposition for critical thinking that is essential in learning statistics. The case study is based on data collected through a survey assessment and a follow-up interview with a mathematics major enrolled in an elementary college statistics course at the time of the study. The qualitative analysis relies on the student's verbal descriptions of the challenges he was experiencing in the course. The findings suggest that while his strong inclination towards inquisitive learning and strong understanding of mathematical concepts supported this student's mathematics learning, the same characteristics might have been causing him difficulties in learning college-level elementary statistics.

• Education of Primary School Mathematics
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• v.12 no.1
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• pp.1-20
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• 2009

The purposes of this study are to analyze elementary school student's intuitive thinking in the process of mathematical problem solving and to analyze elementary school student's errors of intuitive thinking in the process of mathematical problem solving. According to these purposes, the research questions can be set up as followings. (1) How is the state of illumination of the elementary school student's intuitive thinking in the process of mathematical problem solving? (2) What are origins of errors by elementary school student's intuitive thinking in the process of mathematical problem solving? In this study, Bogdan & Biklen's qualitative research method were used. The subjects in this study were 4 students who were attending the elementary school. The data in this study were 'Intuitine Thinking Test', records of observation and interview. In the interview, the discourses were recorded by sound and video recording. These were later transcribed and analyzed in detail. The findings of this study were as follows: First, If Elementary school student Knows the algorithm of problem, they rely on solving by algorithm rather than solving by intuitive thinking. Second, their problem solving ability by intuitive model are low. What is more they solve the problem by Intuitive model, their Self- Evidence is low. Third, in the process of solving the problem, intuitive thinking can complement logical thinking. Last, in the concept of probability and problem of probability, they are led into cognitive conflict cause of subjective interpretation.

• Research in Mathematical Education
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• v.25 no.1
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• pp.91-97
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• 2022

Competent mathematics teachers need to implement the responsive teaching strategy to use student thinking to make instructional decisions. However, the responsive teaching strategy is difficult to implement, and limited research has been conducted in traditional classroom settings. Therefore, we need a better understanding of responsive teaching practices to support mathematics teachers adopting and implementing them in their classrooms. Responsive teaching strategy is connected with teachers' noticing practice because mathematics teachers' ability to notice classroom events and student thinking is connected with their interaction with students. In this regard, this review introduced and examined a study of the relationship between mathematics teachers' noticing and responsive teaching: In the context of teaching for all students' mathematical thinking conducted by Kim et al. (2017).

• Research in Mathematical Education
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• v.24 no.3
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• pp.201-228
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• 2021

Teacher noticing has been termed consequential to teaching because what you see and do not see impacts decisions made within the classroom. Further, how a teacher responds to student thinking depends on what a teacher sees in student thinking. Within this study we sought to understand what teachers noticed within an engineering lesson and the decisions made as a result of that noticing. Findings indicate that student teachers and cooperating teachers drew on their pedagogical knowledge for decisions, rather than taking up the integrated content of student thinking and understanding. These findings serve as a guide for the experiences needed to engage in the complex work of teaching or, more specifically, implementing engineering into instruction through a responsive teaching frame.