• Research in Mathematical Education
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• v.9 no.2 s.22
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• pp.125-133
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• 2005

This paper investigates student conceptual understanding and application on algebra using problem-based curricula. Seven principles which National Research Council announced were considered because these seven principles all involved in the development of a deep conceptual understanding. A problem-based curriculum itself provides a significant contribution to improving student learning. A problem-based curriculum encourages students to obtain a more conceptual understanding in algebra. From the results the national curriculum developers in Korea consider the problem-based curriculum.

• East Asian mathematical journal
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• v.29 no.2
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• pp.207-239
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• 2013

This research is a study on student's understanding fundamental concepts of mathematical curriculum, especially in geometry domain. The goal of researching is to analyze student's concepts about that domain and get the mathematical teaching methods. We developed various questions of descriptive assessment. Then we set up the term, procedure of research for the understanding student's knowledge of geometric figures. And we analyze the student's understanding extent through investigating questions of descriptive assessment. In this research, we concluded that most of students are having difficulty with defining the fundamental concepts of mathematics, especially in geometry. Almost all the students defined the fundamental conceptions of mathematics obscurely and sometimes even missed indispensable properties. And they can't distinguish between concept definition and concept image. Prior to this study, we couldn't identify this problem. Here are some suggestions. First, take time to reflect on your previous mathematics method. And then compile some well-selected questions of descriptive assessment that tell us more about student's understanding in geometric concepts.

• Journal of the Korean Chemical Society
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• v.67 no.4
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• pp.253-270
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• 2023

The purpose of this study was to examine the effect of student-led assessment on achievement emotions and science concept understanding in middle school science classes. For this purpose, 4 of the 7 classes in the third grade of mid- dle school in small and medium-sized cities were selected as the experimental group and conducted student-led assessment, while the comparative group (3 classes) conducted teacher-led assessment. The student-led assessment consisted of 4 stages in which learners took initiative to set learning goals and develop assessment criteria, conduct self assessment and peer assess- ment, and carry out seven assessment activities. Student-led assessment was effective in improving positive achievement emotions and relieving negative achievement emotions and increasing students' science concept understanding in middle school students. Students perform student-led assessment, grasp their reach, and repeatedly go through reflective thinking to compensate for deficiencies in the learning process. Therefore, student-led assessment can be used as a tool to increase science concept understanding by continuously checking the level of science concept understanding.

• School Mathematics
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• v.1 no.2
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• pp.637-660
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• 1999

Although ‘to understand mathematics’ is an important educational purpose, most student do not have a relational understanding of the basic concept of mathematics but have a instrumental understanding. This paper will investigate the possibility of using computers for enhancing relational understanding. In the ‘Qualitative case study’, three students who are in the first grade at E-High school took part in 7 activities during four weeks, and were later interviewed and engaged in informal discussion and were observed. This is the result of this study. 1. The three students were passive participants in mathematics problem solving situation at school. Therefore, student B just applied formulas which she had memorized, and student C would forgot the formulas occasionally. These common students needed to participate actively in doing mathematics. 2. The activities utilized two software healing with connection between graphs and function, giving the students the opportunity to plan, practice, and test by themselves. As a result, they understood the mathematical formulas and rules more deeply through their own trial and error, and then they gained thinking abilities necessary for doing mathematics. In addition, the activities boosted their confidence. 3. The understanding type of students was slightly different. Student A who received a high score, understood the most relationally, but student B who received a very high score, understood instrumentally and so couldn't app1y her knowledge to solving problems related to function concept. Student C who received a middle score lacked knowledge of mathematics but thought more creatively. The result is that students need an opportunity to think rotationally regardless of score. Therefore, this study concludes that using computer software will provide a positive effect for relational understanding in loaming function concept.

• School Mathematics
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• v.4 no.1
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• pp.79-95
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• 2002

This paper is to make strides toward an enriched understanding of student learning and performance in mathematics that acknowledges the roles social and cultural contexts play in what students learn as well as what we are able to team about student learning. A student's mathematical practice over a year and a half is presented in detail in order to explore the relationships between classroom contexts and student performance. This study was situated at a K-4 urban elementary school in the United States. The data used for this study included classroom observations, interviews with the teachers and the student, and document collection. The data were analyzed by characterizing each classroom context and exploring the student's practice both in the classrooms and in the interviews. Despite the student's ongoing status as a struggling student, there were tremendous changes in his level of engagement in and persistence with mathematical tasks. The student was substantially more engaged in and enthusiastic about the daily mathematics lessons in third grade than he had been in second. However, we found little improvement in his mathematical understanding and performance during class or in the interviews. This highlights that increased engagement in the mathematical tasks does not necessarily signal increased learning. This paper discusses several issues of learning and performance raised by the student, looking at the relationship between classroom context and student performance. This paper also considers implications for how students' performances are interpreted and how learning is assessed.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.422-425
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• 2004

Many believe that electronic distance teaming education transform higher education, saving money and improving learning qualify So, the open University, which teaches around 280,000 students at a distance, is examining the adaption of its distance teaching methods for the internet. But, there are only one type of distance learning education of one way direction. To understand all of a student which selected some of e teaming course, teacher must check that how many student to understand and what is the difficult problems. Without checking this condition, It will be a very difficult and boring distance learning course. In this paper, we introduce of intelligent learning contents of full duplex direction that teach understanding student and not understanding student. The computer simulation results confirms that full duplex e learning system has been proven to be much more efficient than one way direction which not considering about understanding problems.

• Journal of Korean Elementary Science Education
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• v.19 no.2
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• pp.57-74
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• 2000

Students' concepts of scientific phenomena have become a point of focus in science education research. This study investigated into developmental process and mechanism of the students' respiration concept through a cross-age study. This study utilized the 1st, 3rd, 6th grade elementary students to find out changes in student's understanding of the concept of respiration. The 1st and 3rd grade level students were interviewed what the respiration mean and whether each of living things respires, etc. The 6th grade students were interviewed and tested. Respiration is a word that students come across often in everyday life. It was found that they were more likely to associate respiration with its more common concept of breathing or gas exchange as opposed to its more scientific definition as the process in which nutrients are oxidized to provide energy. This trend didn't improve as they advanced grade. This is an indication that the knowledge system of student is split into a generic knowledge system and scientific knowledge system. Understanding of concept increased and differentiated across grade levels but that understanding was limited. They overcome their tendency to base their understanding of respiration on their understanding of human phenomena and learn to integrate their understanding of biological phenomena through a one organ - one role type of logic. They also intuitively explain everything based on their own experience.

• Education of Primary School Mathematics
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• v.3 no.1
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• pp.1-36
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• 1999

The case of four classrooms analyzed in this study point to many commonalities in the challenges of reforming mathematics teaching in Korea and the U. S. In both national contexts we have seen the need fur a clear distinction between implementing new student-centered social practices in the classroom, and providing significant new loaming opportunities for students. In particular, there is an important need to distinguish between attending to the social practices of the classroom and attending to students conceptual development within those social practices. In both countries, teachers in the less successful student-centered classes tended to abdicate responsibility fur sense making to the students. They were more inclined to attend to the literal statements of their students without analyzing their conceptual understanding (Episodes KA5 and UP 2). This is easy to do when the rhetoric of reform emphasizes student-centered social practices without sufficient attention to psychological correlates of those social practices. The more successful teachers tended to monitor the understanding of the students and to take proactive measures to ensure the development of that understanding (Episodes KO5 and UN3). This suggests the usefulness of constructivism as a model (or successful student-centered instruction. As Simon(1995) observed, constructivist teachers envision a hypothetical learning trajectory that constitutes their plan and expectation for students learning from the particular if the trajectory is being followed. If not, the teacher adjusts or supplements the task to obtain a more satisfactory result, or reconsider her or his assumptions concerning the hypothetical learning trajectory. In this way, the teacher acts proactively to try to ensure that students are progressing in their understanding in particular ways. Thus the more successful student-centered teacher of this study can be seen as constructivist in their orientation to student conceptual development, in comparison to the less successful student-centered teachers. It is encumbant on the authors of reform in Korea and the U. S. to make sure that reform is not trivialized, or evaluated only on the surface of classroom practices. The commonalities of the two reform endeavores suggest that Korea and the U. S. have much to share with each other in the challenges of reforming mathematics teaching for the new millennium.

• The Mathematical Education
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• v.51 no.4
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• pp.377-393
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• 2012

The understanding demands the different degree of the understanding according to student's learning situation. In this paper, we investigate what is the foundation for the complete understanding for the generalization in the generalization-process and justification of some concepts or some theories, through a case. We discovered that the completeness of the understanding in the generalization-process and justification requires 'the meaningful-mental object' which can give the meaning about the concept or theory to students. Students can do the generalization-process through the construction of 'the meaningful-mental object' and confirm the validity of generalization through 'the meaningful-mental object' which is constructed by them. And we can judge the whether students construct the completeness of the understanding or not, by 'the meaningful-mental object' of the student. Hence 'the meaningful-mental object' are vital condition for the generalization-process and justification.

• The Mathematical Education
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• v.62 no.3
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• pp.341-362
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• 2023

This study analyzed student noticing in a lesson that emphasized relational understanding of equal signs for first graders from four aspects: centers of focus, focusing interactions, mathematical tasks, and nature of the mathematical activity. Specifically, the instructional factors that emphasize the relational understanding of equal signs derived from previous research were applied to a first-grade addition and subtraction unit, and then lessons emphasizing the relational understanding of equal signs were conducted. Students' noticing in this lesson was comprehensively analyzed using the focusing framework proposed in the previous study. The results showed that in real classroom contexts centers of focus is affected by the structure of the equation and the form of the task, teacher-student interactions, and normed practices. In particular, we found specific teacher-student interactions, such as emphasizing the meaning of the equals sign or using examples, that helped students recognize the equals sign relationally. We also found that students' noticing of the equation affects reasoning about equation, such as being able to reason about the equation relationally if they focuse on two quantities of the same size or the relationship between both sides. These findings have implications for teaching methods of equal sign.