• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.789-806
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• 2010

As calls for more attention toward social minority group increases in our society recently, in the field of mathematics education more attention toward an issue about mathematics underachievers is being amplified. Thus, the present study is to examine the effects of teaching method considering students' cognitive characteristics on mathematical underachievers' problem solving and mathematical disposition. For this study, 10 fifth graders identified as mathematical underachievers based on the results of the national level diagnosis assessment and school based assessment were voluntarily selected from an elementary school in Seoul. The results of this study found out the fact that students participating in this program improved in terms of an ability both to solve problems in various ways and to explain an process of problem solving using spoken or written language and drawings. In addition, learning environment respecting students' own mathematical ideas seems to positively influence students' attitudes toward mathematics learning and mathematical dispositions. Furthermore, this study pointed out that mathematical underachievers tend to have difficulty in expressing their own mathematical thinking by reason of linguistic limitation. Finally, the findings of this study imply that for effective teaching of mathematics underachievers, these students' own informal experience and knowledge about mathematics as well as their characteristics regarding learning difficulties should be strongly considered.

• School Mathematics
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• v.3 no.2
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• pp.295-324
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• 2001

Until now, There have been few studies to investigate a degree of abilities or interesting about mathematical problem-posing of first and second grades in elementary school. This is due to the fact that this students(1st and 2nd grades) have a limited amount of study time and their minds are not fully developed, and are lacking in their representation of ability to use the national language. This being the case, it is difficult to investigate their Mathematical problem-posing in a practical manner. However, our 7th elementary school Mathematics curriculum emphasizes the teaching and learning of Mathematical problem-posing from a basic level of first and second grade with emphasis on activity in teaming Mathematics. Through this study, having analysed the problems those children posed, I have found out they improved in numbers and correctness of their posed problems. And I too could found out showing to their much interesting and confidence to mathematical problem-posing and could confirmed for the children to admit themselves its merits through analyzing some questions to ask their opinions to it. I expect that this study can help to develop the teaching and learning materials for mathematical problem-posing and also to improve its methods of elementary school mathematics. The next study task is, I think, that it is necessary to accumulate the studies to investigate and analyse the practical learning activities of children for problem-posing contents of mathematics text books.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.3
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• pp.347-370
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• 2015

The purpose of this study is to examine the effects of mathematical modeling activities on mathematical problem solving abilities and mathematical dispositions in elementary school students. For this study, we administered mathematical modeling activities to fifth graders, which consisted of 8 topics taught over 16 classes. In the results of this study, mathematical modeling activities were statistically proven to be more effective in improving mathematical problem solving abilities and mathematical dispositions compared to traditional textbook-centered lessons. Also, it was found that mathematical modeling activities promoted student's mathematical thinking such as communication, reasoning, reflective thinking and critical thinking. It is a way to raise the formation of desirable mathematical dispositions by actively participating in modeling activities. It is proved that mathematical modeling activities quantitatively and qualitatively affect elementary school students's mathematical learning. Therefore, Educators may recognize the applicability of mathematical modeling on elementary school, and consider changing elementary teaching-learning methods and environment.

• Education of Primary School Mathematics
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• v.18 no.2
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• pp.123-139
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• 2015

The purpose of this study was to investigate the effects of the experiences of productive failures on students' mathematical problem solving abilities and mathematical dispositions. The experiment was conducted with two groups. The treatment group was applied with the productive mathematics failure program, and the comparative group was taught with traditional mathematics lessons. In this study, for quantitative analysis, the students were tested their understanding of mathematical concepts, mathematical reasoning abilities, students' various strategies and mathematical dispositions before and after using the program. For qualitative analysis, the researchers analyzed the discussion processes of the students, students's activity worksheets, and conducted interviews with selected students. The results showed the followings. First, use of productive failures showed students' enhancement in problem solving abilities. Second, the students who experienced productive failures positively affected the changes in students' mathematical dispositions. Along with the more detailed research on productive mathematical failures, the research results should be included in the development of mathematics textbooks and teaching and learning mathematics.

• The Mathematical Education
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• v.49 no.3
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• pp.299-311
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• 2010

The purpose of this study was to examine the effects of abstraction offer of basic concept principle and feedback of self-efficacy attributional and mathematical study ability of math underachievers in high school based on the attribution theory and self-efficacy theory. The hypothesis were posed as below : Hypothesis 1: The experimental group that takes the abstraction offer of concept principle and attributional feedback training would be better at most self-efficacy than the control group that doesn't. Hypothesis 2: The experimental group that takes the abstraction offer of concept principle and attributional feedback training would have better math achievement than the control group that doesn't. They were divided into an experimental group and a control group, and the attribution disposition, self-efficacy and academic achievement of the children were measured by pretest and posttest. For data analysis, SPSS/PC+ program was employed and t-test was conducted. The main findings of this study were as below : First, the abstraction offer of concept principle and attributional feedback training was effective for enhancing the math self-efficacy in high school underachievers. Second, the abstraction offer of concept principle and attributional feedback training was effective for increasing the math achievement in high school underachievers.

• The Mathematical Education
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• v.57 no.4
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• pp.453-475
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• 2018

This study examines how elementary students understand fractions with operations conceptually and how they perform procedures in the division of fractions. We attempted to look into students' understanding about fractions with divisions in regard to mathematical proficiency suggested by National Research Council (2001). Mathematical proficiency is identified as an intertwined and interconnected composition of 5 strands- conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. We developed an instrument to identify students' understanding of fractions with multiplication and division and conducted the survey in which 149 6th-graders participated. The findings from the data analysis suggested that overall, the 6th-graders seemed not to understand fractions conceptually; in particular, their understanding is limited to a particular model of part-whole fraction. The students showed a tendency to use memorized procedure-invert and multiply in a given problem without connecting the procedure to the concept of the division of fractions. The findings also proposed that on a given problem-solving task that suggested a pathway in order for the students to apply or follow the procedures in a new situation, they performed the computation very fluently when dividing two fractions by multiplying by a reciprocal. In doing so, however, they appeared to unable to connect the procedures with the concepts of fractions with division.

• Journal of Elementary Mathematics Education in Korea
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• v.12 no.2
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• pp.165-183
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• 2008

This study is to help to understand the influence of exchange writing activity in the elementary mathematics on students' mathematical communication skill. Various technical activities had been implemented during the classes and the ideas from those activities had been interpreted into writings in the final stage of the classes. Those writings, then, were distributed to other students or teachers in order to devise a teaching model for exchange writing, which is to be applied to the 3rd grade classes and to identify the influence on the in mathematical communication skill. From this study, we could get such conclusions as follows: First, there was considerable difference between experimental group practicing exchange writing and control group engaging in normal learning activities in the progress of their mathematical communication skill (group discussion), writing skill and expressivity when examining their average communication skill using t-method. Similar trend had been witnessed when self-evaluating their mathematical communication skill. Second, when it comes to the mathematical tendency, experimental group showed a higher tendency in positiveness compared to the control group. Therefore, we might conclude that the exchange writing has a positive influence on the students' mathematical tendency, especially on their curiosity or interest in teaming, willingness to study and their comprehension of its importance.

• Journal of the Korean School Mathematics Society
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• v.9 no.1
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• pp.1-17
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• 2006

This thesis analyzed the effects of cooperative learning blended with TAI(Team Assisted Individualization) and STAD(Student Team Achievement Division) models on the students' ability of problem solving in mathematics in order to discover what kind of effects would give to their ability of that, and would promote their disposition and attitude to learn mathematics. The results of this study were as follows : First, the learning method blended with TAI and STAD models was more effective in the students' ability of problem solving in mathematics than traditional learning method because of the blended model's characteristics; positive interdependence, individual accountability, team recognition, curriculum materials. Second, the learning method blended with TAI and STAD models was more effective in sub-elements - self-confidence, adaptability, will, curiosity and value - of mathematical disposition than traditional learning method. And the learning method blended with TAI and STAD models was more effective in sub-elements - self-consciousness of mathematics and interests - of mathematical attitude than traditional learning method. In conclusion, the learning method blended with TAI and STAD models could affect to not only the students' ability of problem solving in mathematics but also the students' several affective factors.

• School Mathematics
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• v.4 no.3
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• pp.415-433
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• 2002

The mathematics education community is seeking to change a teacher-centered class-room culture to a student-centered culture. However, the real transition is not easy, even for teachers who are eager and willing to teach differently. The challenge for teachers is to use the social structure of the classrooms to nurture students' development toward mathematical ways of thinking and communicating as well as their under-standing of mathematical concepts and processes. By introducing an elementary teacher's teaching practice and professional develop-ment along with her classroom episodes, this paper is to make strides toward an enriched understanding of the culture of the elementary mathematics classrooms in which students may have a lot of opportunities to develop conceptual under standing and math-ematical disposition. This paper first provides a detailed description of the classroom flow in terms of general social norms and sociomathematical norms in order to explore how the teacher and the students have established such a student-centered math-ematics microculture. This paper then analyzes the teacher's teaching approach and professional development.

• East Asian mathematical journal
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• v.36 no.1
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• pp.81-90
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• 2020

Many compartment models assume a kinetically homogeneous amount of materials that have well-stirred compartments. However, based on observations from such processes, they have been heuristically fitted by exponential or gamma distributions even though biological media are inhomogeneous in real environments. Fractional differential equations using a specific kernel in Pharmacokinetic/Pharmacodynamic (PKPD) model are recently introduced to account for abnormal drug disposition. We discuss a tumor growth inhibition (TGI) model using fractional-order derivative from it. This represents a tumor growth delay by cytotoxic agents and additionally show variations in the equilibrium points by the change of fractional order. The result indicates that the equilibrium depends on the tumor size as well as a change of the fractional order. We find that the smaller the fractional order, the smaller the equilibrium value. However, a difference of them is the number of concavities and this indicates that TGI over time profile for fitting or prediction should be determined properly either fractional order or tumor sizes according to the number of concavities shown in experimental data.