• 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.

• 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.

• 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.

• 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.

• 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.

• Journal of the Korean School Mathematics Society
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• v.15 no.4
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• pp.719-745
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• 2012

This research is a study on student's understanding fundamental conception of mathematical curriculum, especially in geometry domain. The goal of researching is to analyze student's wrong conception about that domain and get the mathematical teaching method. We developed various questions of descriptive assessment. Then we set up the term, procedure of research for the understanding student's knowledge of geometry. And we figured out the student's understanding extent through analysing questions of descriptive assessment in geometry. In this research, we concluded that most of students are having difficulty with defining the fundamental conception of mathematics, especially in geometry. Almost all the students defined the fundamental conceptions of mathematics obscurely and sometimes even missed indispensable properties. 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 geometry.

• Journal of The Korean Association For Science Education
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• v.25 no.1
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• pp.41-56
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• 2005

Assessing students' knowledge can be a challenging endeavor, as researchers attempt to capture the full complexity and potential development of children's ideas. In this study, the Dynamic Science Assessment (DSA) method (Magnusson, Templin, and Boyle, 1997) was employed to investigate 9-12 year old students' understandings of light, while engaging in multiple tasks with a flashlight with various reflectors and mirrors. The results showed that DSA was effective in providing an opportunity to establish a Zone of Proximal Development, in addition to diagnosing a student's prior understanding. Throughout the interview, a student showed a conceptual model of light as being a solid single entity whose shape can be determined by the shape of the casing of a flashlight. However, as DSA provided phenomena that could not be explained by his unitary model, the student began to re-examine his original conceptual model, and attempted to revise it. This study addressed how Dynamic Science Assessment can help us better understand, not only students' current state of understanding, but also a potential development of understanding in their ZPD. In that sense, this study argues that we should pay more attention to the instructive role of classroom assessment that can promote and support further development of students' deeper understandings.

• Research in Mathematical Education
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• v.24 no.3
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• pp.255-278
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• 2021

Proof serves a critical role in mathematical practices as well as in fostering student's mathematical understanding. However, the research literature accumulates results that there are not many opportunities available for students to engage with proving-related activities and that students' understanding about proof is not promising. This unpromising state of instruction of proof calls for a novel approach to address the aforementioned issues. This study investigated an instruction of proof to explore a pedagogy to teach how to prove. The teacher utilized the way of problem posing to make proving a routine part of everyday lesson and changed the classroom culture to support student proving. The study identified the teacher's support for student proving, the key pedagogical changes that embraced proving as part of everyday lesson, and what changes the teacher made to cultivate the classroom culture to be better suited for establishing a supportive community for student proving. The results indicate that problem posing has a potential to embrace proof into everyday lesson.

• The Mathematical Education
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• v.42 no.3
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• pp.303-325
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• 2003

This study sought to provide an explanation of university students' concept understanding on the infinity and infinite process and utilized a psychological constructivist perspective to examine the differences in transitions that students make from static concept of limit to actualized infinity stage in context of problems. Open-ended questions were used to gather data that were used to develop an explanation concerning student understanding. 47 university students answered individually and were asked to solve 16 tasks developed by Petty(1996). Microgenetic method with two cases from the expert-novice perspective were used to develop and substantiate an explanation regarding students' transitions from static concept of limit to actualized infinity stage. The protocols were analyzed to document student conceptions. Cifarelli(1988)'s levels of reflective abstraction and Robert(1982) and Sierpinska(1985)'s three-stage concept development model of infinity and infinite process provided a framework for this explanation. Students who completed a transition to actualized infinity operated higher levels of reflective abstraction than students who was unable to complete such a transition. Developing this ability was found to be critical in achieving about understanding the concept of infinity and infinite process.

• Journal of Korea Multimedia Society
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• v.21 no.11
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• pp.1353-1361
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• 2018

With the availability of real-time educational data collection and analysis techniques, the education paradigm is shifting from educator-centric to data-driven lectures. However, most offline and online education frameworks collect students' feedback from question-answering data that can summarize their understanding but requires instructor's attention when students need additional help during lectures. This paper proposes a content restructure recommendation framework based on collected student feedback. We list the types of student feedback and implement a web-based framework that collects both implicit and explicit feedback for content restructuring. With a case study of four-week lectures with 50 students, we analyze the pattern of student feedback and quantitatively validate the effect of the proposed content restructuring measured by the level of student engagement.