• Journal of Elementary Mathematics Education in Korea
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• v.16 no.2
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• pp.253-267
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• 2012

In this paper, we primarily focus on the perspectives about creative process, which is how mathematical creativity emerged, as one aspect of mathematical creativity and then present a desirable task characteristic to measure and program characteristics to develop mathematical creativity. At first, we describe domain-generality perspective and domain-specificity perspective on creativity. The former regard divergent thinking skill as a key cognitive process embedded in creativity of various discipline domain involving language, science, mathematics, art and so on. In contrast the researchers supporting later perspective insist that the mechanism of creativity is different in each discipline. We understand that the issue on this two perspective effect on task and program to foster and measure creativity in mathematics education beyond theoretical discussion. And then, based on previous theoretical review, we draw a desirable characteristic on instruction program and task to facilitate and test mathematical creativity, and present an applicable task and instruction cases based on Geneplor model at the mathematics class in elementary school. In conclusion, divergent thinking is necessary but sufficient to develop mathematical creativity and need to consider various mathematical reasoning such as generalization, ion and mathematical knowledge.

• Research in Mathematical Education
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• v.27 no.1
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• pp.25-47
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• 2024

Mathematical modeling activities are gaining popularity in K-12 mathematics education curricula worldwide. These activities serve dual purposes by aiding students in making sense of real-world situations intertwined with social justice while acquiring mathematical knowledge. Despite efforts to prepare teacher candidates for instructing in mathematical modeling within a single country, little attention has been given to teacher candidates' approaches to mathematical modeling on a social justice issue from different countries. This article employs an in-depth, small-scale comparative study to examine the approaches of U.S. and Korean teacher candidates in solving a justice-oriented mathematics task. Our findings reveal that, although both U.S. and Korean teacher candidates identified certain variables as key when constructing a mathematical model, Korean teacher candidates formulated a more nuanced model than U.S. candidates by considering diverse variables. However, U.S. teacher candidates exhibited a heightened engagement in linking the task to social justice issues, whereas Korean teacher candidates barely perceived real-world problems in relation to social justice concerns. This study serves as a valuable tool to inform the roles and limitations of teacher education programs, shaped within specific educational contexts.

• East Asian mathematical journal
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• v.16 no.2
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• pp.251-266
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• 2000

The problem of solution uniqueness to the task of determining unknown parameters of mathematical models from input-output observations is studied. This problem is known as structural identifiability problem. We offer a new approach for testing structural identifiability of linear state space models. The approach compares favorably with numerous methods proposed by other authors for two main reasons. First, it is formulated in obvious mathematical form. Secondly, the method does not involve unfeasible symbolic computations and thus allows to test identifiability of large-scale models. In case of non-identifiability, when there is a set of solutions to the task, we offer a method of computing functions of the unknown parameters which can be determined uniquely from input-output observations and later used as new parameters of the model. Such functions are called parametric functions capable of estimation. To develop the method of computation of these functions we use Lie group transformation theory. Illustrative example is given to demonstrate applicability of presented methods.

• Communications of Mathematical Education
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• v.29 no.3
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• pp.281-300
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• 2015

The purpose of this research is to analyze cognitive demands, answer types, and storytelling types on the basis of mathematical tasks in five different mathematics textbooks based on 2009 revised curriculum in order to suggest directions for the development and use of storytelling mathematics textbooks in school. Results show that first, PNC (Procedures without Connections) task was the largest category in cognitive demands of all mathematical tasks, Low-Level task was larger than others in cognitive demands of mathematical content tasks, and High-Level task was larger than others in cognitive demands of mathematical activity tasks. Second, a short-answer type was the largest category in answer types of all mathematical tasks, the majority of mathematical content tasks were a short-answer type, and the majority of mathematical activity tasks were both short-answer and explanation-answer types. Finally, storytelling connected to real-life was the largest category in storytelling types, and the number of mathematical activity tasks was less than that of mathematical content tasks. However, in the tasks reflected on storytelling, the percentage of mathematical activity tasks was higher than that of mathematical content tasks. Based on the results, while developing storytelling mathematics textbooks and using storytelling textbooks in school, it suggests to consider the need for balance and diversity in cognitive demands, answer types, and storytelling types according to mathematical tasks.

• The Mathematical Education
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• v.57 no.4
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• pp.353-369
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• 2018

This study started with the following questions. Suppose that students do not accept various forms of geometric series tasks as the same task. Also, let's say that the approach was different for each task. Then, when they realize that they are the same task, how will students connect the different approaches? This study is a process of pro-actively confirming whether or not such a question can be made. For this purpose, three students in the second grade of high school participated in the teaching experiment. The results of this study are as follows. It also confirmed how the students think about the various types of tasks in the geometric series. For example, students have stated that the value is 1 in a series type of task. However, in the case of the 0.999... type of task, the value is expressed as less than 1. At this time, we examined only mathematical expressions of students approaching each task. The problem of reachability was not encountered because the task represented by the series symbol approaches the problem solved by procedural calculation. However, in the 0.999... type of task, a variety of expressions were observed that revealed problems with reachability. The analysis of students' expressions related to geometric series can provide important information for infinite concepts and limit conceptual research. The problems of this study may be discussed through related studies. Perhaps more advanced research may be based on the results of this study. Through these discussions, I expect that the contents of infinity in the school field will not be forced unilaterally because there is no mathematical error, but it will be an opportunity for students to think about the learning method in a natural way.

• The Mathematical Education
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• v.44 no.1 s.108
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• pp.15-40
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• 2005

This study basically investigates the meaning and properties of performance task applicable to mathematics classroom and it finds out how to run effectively performance task activities included in the present mathematics textbooks. To accomplish this, this study deals with twelves kinds of mathematics textbooks for ninth graders and is proceeded on the basis of textbook analysis and teacher interview. Considering a situation that in future mathematics textbook would be developed, according to the analytic results of this study, common understanding of performance task and qualified performance task are needed, a variety of tasks classified by differentiated level are needed. In addition, each task should be dealt with the contents related to curious and interesting real-life situations. Furthermore, fairness of checking and recording should be established and teachers' positive attitudes to applying performance tasks to math class are needed.

• Research in Mathematical Education
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• v.26 no.3
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• pp.167-202
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• 2023

A central problem of mathematics teaching worldwide is probably the insufficient adaptive handling of tasks-especially in computational practice phases and modeling tasks. All students in a classroom must often work on the same tasks. In the process, the high-achieving students are often underchallenged, and the low-achieving ones are overchallenged. This publication uses different modeling of the tennis serve as an example to show a possible solution to the problem and develops and discusses one adaptive task each for middle school, high school, and college using three mathematical models of the tennis serve each time. From model to model within the task, the complexity of the modeling increases, the mathematical or physical demands on the students increase, and the new modeling leads to more realistic results. The proposed models offer the possibility to address heterogeneous learning groups by their arrangement in the surface structure of the so-called parallel adaptive task and to stimulate adaptive mathematics teaching on the instructional topic of mathematical modeling. Models A through C are suitable for middle school instruction, models C through E for high school, and models E through G for college. The models are classified in the specific modeling cycle and its extension by a digital tool model, and individual modeling steps are explained. The advantages of the presented models regarding teaching and learning mathematical modeling are elaborated. In addition, we report our first teaching experiences with the developed parallel adaptive tasks.

• The Mathematical Education
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• v.52 no.1
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• pp.111-128
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• 2013

The purpose of this study was to examine and analyze the cognitive demand of the mathematical tasks suggested in the middle school textbooks. In particular, it aimed to reveal the overall picture of the level of cognitive demand of the mathematical tasks in the strand of geometry in the textbooks. We adopted the framework for mathematical task analysis suggested by Stein & Smith(1998) and analyzed the mathematical tasks accordingly. The findings from the analysis showed that 95 percent of the mathematical tasks were at high level and the rest at low level in terms of cognitive demand. Most of the mathematical tasks in the textbooks were algorithmic and focused on producing correct answers by using procedures. In particular, the high level tasks were presented at the end of each chapter or unit for wrap up rather than as key resources.

• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.413-444
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• 2010

The purpose of the present study is to develop an instrument of mathematical learning motivation and causal attribution for students and to analyze the results of the instrument. Based on the literature review, mathematical learning motivation is the cumulative effects of self-assessment and self-regulation in mathematical learning and achievement experience. Three factors of mathematical learning motivation is identified as self-regulatory efficacy, task difficulty and mathematical anxiety with 17 self-regulatory efficacy items, 9 task difficulty items and 9 mathematical anxiety items. Three factors of causal attribution for success is identified as ability/effort, luck, and other person with 6 ability/effort items, 4 luck items and 3 other person items. Also, four factors of causal attribution for failure is identified as ability, effort, luck, and other person with 3 ability items, 7 effort items, 3 luck items and 4 other person items. The instrument of mathematical learning motivation and causal attribution for success and failure was administered to 919 middle school students from eight different middle middle schools in Seoul, Gyeonggi-Do, Busan, jeolla-Do area. The correlation of three factors of mathematical learning motivation was calculated. As a result, a positive correlation between self-regulatory efficacy and task difficulty was appeared but mathematical anxiety has a negative correlation with self-regulatory efficacy and task difficulty. This study also examined the differences about mathematical learning motivation's sub-factors shown by three groups of mathematics achievement level. Students of higher achievement level showed that the degree of self-regulatory efficacy and task difficulty was higher than that of lower level group. Students of lowest achievement level showed significantly higher mathematical anxiety degree than that of middle and high group. Students that have higher degree of self-regulatory efficacy and task difficulty preference were attributed into ability/effort cause toward success of mathematics achievement. Also, Male students preferred more difficult task and higher degree of self-regulatory efficacy in mathematics learning than female students. On the contrary, Female students showed higher mathematical anxiety level than male students.

• Communications of Mathematical Education
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• v.36 no.1
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• pp.59-72
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• 2022

The purpose of this study is to understand the characteristics of the mathematical modeling tasks and lesson designs developed by pre-service teachers based on the inherent awareness of mathematical modeling, considering the importance of creating a task to perform mathematical modeling activity and designing a lesson. As a result, the mathematical modeling tasks developed by pre-service teachers mainly presents an appropriate amount of information using real life contexts for the purpose of learning using concepts, and it showed a tendency to develop to the level of cognitive demand that required procedures with connections to understanding, meaning, or concepts. And most of the developed modeling task-based lessons showed a tendency to design warm-up activity, model-eliciting activity, and model-exploration activity. This result is due to the lack of experience of pre-service teachers in creating mathematical modeling tasks. Therefore, it is necessary to continuously provide opportunities for pre-service teachers to learn concepts or create mathematical modeling tasks intended for exploration according to various mathematical contents, thereby actively cultivating their ability to create modeling tasks in the course of training pre-service teachers. Furthermore, it is necessary to strengthen the expertise in mathematical modeling teaching and learning by providing opportunities to actually perform the mathematical modeling-based classes designed by pre-service teachers and to experience the process of reflecting on the lessons.