• The Mathematical Education
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• v.58 no.3
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• pp.443-458
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• 2019

Mathematical modeling has been a crucial topic in mathematics education as students' problem solving competency are regarded as a core skill for future society. Despite of the importance of mathematical modeling in school mathematics, there have been very limited studies relating pre-service teachers' knowledge and perceptions on mathematical modeling. In this vein, this study aimed to investigate pe-service mathematics teachers' perceptions on mathematical model, mathematical modeling and educational use of mathematical modeling, and their relationships. The current study utilized a survey consisted of 18 items. The responses of 210 pre-service mathematics teachers to the survey items were quantitatively analyzed using descriptive statistics, analysis of variance, exploratory and confirmatory factor analysis, the structural equation model, and multi group analysis. The results of analysis of variance revealed that pre-service teachers in difference groups (majors, grades, and experiences with mathematical modeling) showed statistically significant differences in mean values. Moreover, according to the results from the structural equation modeling analysis, pre-service mathematics teachers' perceptions on mathematical model and modeling affected their perceptions on educational use of mathematical modeling. In addition, depending on their pre-experiences with mathematical modeling, pre-service teachers represented a different relationship between perceptions on mathematical modeling and educational use of mathematical modeling. Implications for future studies and mathematics classrooms were discussed.

• Communications of Mathematical Education
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• v.31 no.3
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• pp.257-277
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• 2017

The purpose of this research is divide into two kinds. First, develop the mathematical modeling program for mathematically gifted students focused on Voronoi diagram and Delaunay triangulation, and then gifted teachers can use it in the class. Voronoi diagram and Delaunay triangulation are Spatial partition theory use in engineering and geography field and improve gifted student's mathematical connections, problem solving competency and reasoning ability. Second, after applying the developed program to the class, I analyze gifted student's core competency. Applying the mathematical modeling program, the following findings were given. First, Voronoi diagram and Delaunay triangulation are received attention recently and suitable subject for mathematics gifted education. Second,, in third enrichment course(Student's Centered Mathematical Modeling Activity), gifted students conduct the problem presentation, division of roles, select and collect the information, draw conclusions by discussion. In process of achievement, high level mathematical competency and intellectual capacity are needed so synthetic thinking ability, problem solving, creativity and self-directed learning ability are appeared to gifted students. Third, in third enrichment course(Student's Centered Mathematical Modeling Activity), problem solving, mathematical connections, information processing competency are appeared.

• School Mathematics
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• v.14 no.4
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• pp.409-429
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• 2012

This paper reports the process two 11th grade students went through in reinventing derivatives on their own via a context problem involving the concept of velocity. In the reinvention process, one of the students conceived a tangent line as the limit of a secant line, and then the other student explained to a peer that the slope of a tangent line was the geometric mean of derivative. The students also used technology to concentrate on essential thinking to search for mathematical concepts and help visually understand them. The purpose of this study was to provide meaningful implications to school practices by describing students' process of reinvention of derivatives. This study revealed certain characteristics of the students' reinvention process of derivatives and changes in the students' thinking process.

• Journal of Educational Research in Mathematics
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• v.14 no.4
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• pp.403-419
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• 2004

The perspective on this study assumes that the mathematical modeling activity provides students with the environment which promotes metacognitive thinking. The purposes of this paper are to investigate metacognitive thinking on the mathematical modeling with the result of case study. The study revealed that development of students' model was accompanied with the control and monitoring of modeling activities. Also students refined the model by self-assessment and peer-assessment in small group modeling activities and developed generalizable model.

• Journal of the Korean School Mathematics Society
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• v.24 no.3
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• pp.283-308
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• 2021

This study aims to analyze statistical tasks in Korean and Singaporean textbooks with the mathematical modeling perspective and compare the learning contents and experiences of students from both countries. I analyzed mathematical modeling tasks in the textbooks based on five aspects: (1) the mathematical modeling process, (2) the data type, (3) the expression type, (4) the context, and (5) the mathematical activity. The results of this study show that Korean and Singaporean textbooks provide the highest percentage of the "working-with-mathematics" task, the highest percentage of the "matching task," and the highest percentage of the "picture" task. The real-world context and mathematical activities used in Korean and Singaporean textbooks differed in percentage. This study provides implications for the development of textbook tasks to support future mathematical modeling activities. This includes providing a balanced experience in mathematical modeling processes and presenting tasks in various forms of expression to raise students' cognitive level and expand the opportunity to experience meaningful mathematizing. In addition, it is necessary to present a contextually realistic task for students' interest in mathematical modeling activities or motivation for learning.

• Journal of the Korean School Mathematics Society
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• v.24 no.2
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• pp.217-241
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• 2021

The purpose of this study is to qualitatively examine the effects of graphics representation of trigonometry modelling concerning question generating and idea sharing. The experimental setting(Experiment Group) was one class (N=26) at a public high school. The modelling process was designed as a process-oriented conceptualization divided into three steps i.e., (1) game with idea sharing and question generating, (2) graphic representation, and (3) symbolization in the mathematical applied tasks related to trigonometry function. The result indicates that Graphic Representation with Game Activity increases the opportunity of question generating and idea sharing during experimental work. Also, the results show that the introduction of computer graphics enhances the teaching of mathematical quantity in highschool classrooms.

• Journal of the Korean School Mathematics Society
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• v.12 no.3
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• pp.189-209
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• 2009

One of the characteristics in math -abstract concept- makes the students find difficulties in understanding general ideas about math. This study is about how much do the modeling lessons using the technical instruments which is based on the realistic mathematical theory influence on understanding the mathematical concept. This study is based on one of the contents the first grade of middle school students study, the function, especially the meaning of it. Some brilliant students being the objects of this study, mathematically experimental modeling lesson was planned, conducted. Survey on the students' attitudes about math before and after the modeling classes and Questionnaire survey on the effectiveness about the modeling class were conducted and their attitudes were recorded also. This study tells that students show very meaningful changes before and after the modeling class and scientific knowledge seems to be very helpful for the students to understand the mathematical concept and solve the problems. When scientific research and development get together with mathematics, students will be more motivated and be able to form the right mathematical concept easily.

• Journal of the Korean School Mathematics Society
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• v.14 no.4
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• pp.423-442
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• 2011

The purpose of this study was to examine the effects of tasks setting for mathematical modelling in the complex real situations. The tasks setting(MMa, MeA) in mathematical modelling was so important that we can't ignore its effects to develop meaning and integrate mathematical ideas. The experimental setting were two groups ($N_1=103$, $N_2=103$) at public high school and non-experimental setting was one group($N_3=103$). In mathematical achievement, we found meaningful improvement for MeA group on modelling tasks, but no meaningful effect on information processing tasks. The statistical method used was ACONOVA analysis. Beside their achievement, we were much concerned about their modelling approach that TSG21 had suggested in Category "Educational & cognitive Midelling". Subjects who involved in experimental works showed very interesting approach as Exploration, analysis in some situation ${\Rightarrow}$ Math. questions ${\Rightarrow}$ Setting models ${\Rightarrow}$ Problem solution ${\Rightarrow}$ Extension, generalization, but MeA group spent a lot of time on step: Exploration, analysis and MMa group on step, Setting models. Both groups integrated actively many heuristics that schoenfeld defined. Specially, Drawing and Modified Simple Strategy were the most powerful on approach step 1,2,3. It was very encouraging that those experimental setting was improved positively more than the non-experimental setting on mathematical belief and interest. In our school system, teaching math. modelling could be a answer about what kind of educational action or environment we should provide for them. That is, mathematical learning.

• Communications of Mathematical Education
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• v.30 no.3
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• pp.263-280
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• 2016

This study aims to examine the impact of RUBRIC writing on students' mathematical modeling. By analyzing 23 tenth grade students' responses to seven problems related to mathematical modeling, we found that the students who used RUBRIC writing could not only get more correct answers but also could use more various representations and mathematical models than the students who did not use it. The students with RUBRIC writing also could translate between reality and mathematics more appropriately, and better explain the process to solve the problem than the counterpart. It implies that RUBRIC writing can help improve students' mathematical modeling and problem solving as an alternative instruction and assessment.

• Journal of the Korean School Mathematics Society
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• v.17 no.4
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• pp.657-677
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• 2014

The present qualitative case study explored the ways in which three middle school students constructed and refined their mathematical models and modeling processes, and factors that had influenced such refinement. The results suggest that students' modeling processes are non-sequential in that the participant students reformulated their initial problem from the real-world problem situation and revised the model when they could not get a satisfactory solution or the acquired solution did not make sense. Moreover, the students' model refinement processes were affected by the following four elements: the types of real-word problem situations, students' metacognitive thinking, communications between teachers and peers, and the role of teachers.