• The Mathematical Education
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• v.48 no.4
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• pp.419-442
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• 2009

This study was to find the difficulties students faced in their mathematical learning and to identify the instructional dimensions a teacher provided for the students from multi-cultural background. Since the study was focused on the process of students' learning, the qualitative method was chosen through clinical interviews with 2 students in a total of 11 units which played a role of compensating their learning of mathematics as an extra curriculum. The students solved the computational problems relying on formal procedure without understanding of concepts and principles and solved the word problems based on own interpretation of certain words without semantic comprehension out of math sentences. As the instructional dimensions of teaching mathematics, tasks, a tool and classroom norm were found in the activities they performed. For the tasks, situated tasks, challenging tasks, tasks with lack of conditions, and open-ended exploratory tasks were used. As the tool, pictorial representations were very useful to describe their ideas. Finally, as the classroom norm, consider equity for everyone, and cooperate and encourage each other were found.

• Journal of the Korean School Mathematics Society
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• v.2 no.1
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• pp.93-104
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• 1999

The subject of this study was the graph of relation of direct inverse proportion, linear function and quadratic function in the 1st, 2nd and 3rd grade of current middle school mathematics curriculum. GSP materials were developed to simplify the principle, trait and characteristics of graphs and make them easier to understand. The overall aim of the materials is to improve the effectiveness of teaching and learning through the utilization of enhanced students' practice. Additionally, the use of the GSP will be useful in the development of mere effective materials. The effectiveness of the GSP materials will be as followings. 1. The step by step approach of GSP materials through computer interaction will enhance students motivation and interest in mathematics. 2. By presenting the subject matter simply and in a variety of ways, difficult concepts can be understood without the use of complex mathematical calculation. 3. The GSP program is different from CAI and other software programs. It should be used only after learning how to input and output data.

• East Asian mathematical journal
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• v.26 no.4
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• pp.581-597
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• 2010

In this paper, the author focuses on the teaching-level and learning-level of the completeness axiom and its applications on [0,1] and $\mathbb{R}$, $\mathbb{R}{\times}\mathbb{R}$, $\mathbb{R}{\times}\mathbb{R}{\times}\mathbb{R}$ by (expected) teachers in the school mathematics, which is usually introduced in the class of real analysis of university mathematics. Firstly the author considers the properties of the completeness axiom and its 19 equivalent theorems, next he deals with its importances in the school mathematics and finally he suggests the teaching and learning of the concepts on the completeness axiom and its applications on [0,1] and $\mathbb{R}$, $\mathbb{R}{\times}\mathbb{R}$, $\mathbb{R}{\times}\mathbb{R}{\times}\mathbb{R}$ by (expected) teachers in the school mathematics.

• Journal of the Korean School Mathematics Society
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• v.4 no.1
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• pp.103-114
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• 2001

The purpose of this study is to develop learning materials for functional concept on variable and to verify the effect of how well students could learn functional concept after they studied with those materials. To accomplish the purpose of this study, I developed learning materials and after teaching students with them. I have concluded the followings : First, there was little effect in teaching functional concept on variable between two experimental groups, whereas teaching functional concept had greater effect on forming functional concept in high level groups in those two experimental groups. Second, teaching functional concept on variable had little effect on students' understanding of functional concept and perfecting tables in Black box, graph, and mathematical problems, whereas there was much effect in students' understanding functional concept and solving relation formula, image, and range problems related to everyday life or general things. On the basis of the problems which appeared in the process of this study, the following can be suggested : First, we should develop learning materials fit for low level students so that they could understand functional concept. Second, we should continue to teach the basic problems like solving relation formula, image, and range, and understanding functional concept in graph until students are able to understand them exactly. Third, since the goals of Unit Function in a middle school textbook is to solve problems related to everyday life through functional thinking, there should be change in constructing systematic contents of Unit Function in a middle school textbook.

• Journal of the Korea Society of Computer and Information
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• v.13 no.1
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• pp.213-218
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• 2008

Through the development of computer and multimedia, many different kinds of theories about instructional method are presented. Especially, many lectures in associated with E-learning are done. In mathematics teaching, mathematica-algebra system lecturing, computer and Maple Matlab lecturing etc, are accomplished. There are many controversies among educators in problems originated by computer teaching. In this paper, we going to make a research about problems which are caused by mathematics computer-based education and present a desirable way of computer based education through studying comprehension rate and application ability among learner who uses omputer learning and other learner who uses exiting blackboard-based learning with statistical analysis after sampling test

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.93-114
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• 2015

The "flipped" or "inverted" classroom, in which students study lecture-type material at home and do their "homework" in the classroom, has been the subject of research, particularly in the area of student achievement. Yet Bishop and Verleger (2013) state the need for an underlying theory to the practice. The purpose of this paper is to explore "multidimensional teaching," the authors' extension of the two-dimensional "flipped" classroom concept in light of Cambourne's (1995) Conditions for Learning. One author's math class for pre-service teachers was taught in two styles, a more traditional lecture format and in the \inverted" format. Students in the "flipped" format achieved at a higher level. Moreover, students' open-ended comments reveal that Cambourne's Conditions for Learning were implicit to the teaching practice. The authors suggest that practitioners of this style of teaching should deliberately develop student-centered practices, such as those mentioned by Cambourne, in order to retain the power that this teaching style currently has.

• The Mathematical Education
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• v.49 no.4
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• pp.411-421
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• 2010

Teacher reflection as a form of professional development has been an enduring interest in education that can be traced back to Dewey. Information about how teachers interpret and analyze their students' learning would help us understand difficulties in teaching and learning. Moreover, it can be useful for teacher education by improving teaching methods. The purpose of this research was to understand how mathematics teachers reflected on their students' understanding. For the purpose of this study, I investigated four U.S.A. mathematics teachers in a middle school. In particular, I discussed Assess instances among the teachers' reflections on their students' thinking and changes of the reflections as time went by. The results showed two different types of Assess instances and shifts by time.

• Journal of the Korean School Mathematics Society
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• v.11 no.3
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• pp.439-466
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• 2008

In this paper, we aim to draw up an alternative instruction scheme by designing a web based instruction model on mathematics. Some learning materials are developed according to the scheme, and its educational effects are examined when it is committed to through regular curriculum. The study is composed of three major parts; setting of the theoretical foundation on cultivating Web based educational materials, design and composition of Web based teaching-learning model, and its experiments in the regular class. First of all, we are concerned with the core principles on WBI including the learning theories, developing learner oriented instruction model, design as well as build-up process for education materials, and strategy in instruction. Next, we propose an alternative instruction model for mathematics, in which programs to embody mathematics education and instruction on the Web are constructed, on the while, the study is proceeded through the Web Site. Finally, we design and produce a WBI instruction model on the subject of the plane quadratic curves. This model is examined in the regular class to estimate its educational effects compared with traditional teaching standpoints. Concomitantly, we explore essential elements and the direction of future growth associated with the Web oriented education.

• Communications of Mathematical Education
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• v.19 no.4 s.24
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• pp.733-767
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• 2005

During the past decades, there has been a fundamental change in the objectives and nature of mathematics education, as well as a shift in research paradigms. The changes in mathematics education emphasize learning mathematics from realistic situations, students' invention or construction solution procedures, and interaction with other students of the teacher. This shifted perspective has many similarities with the theoretical . perspective of Realistic Mathematics Education (RME) developed by Freudental. The RME theory focused the guide reinvention through mathematizing and takes into account students' informal solution strategies and interpretation through experientially real context problems. The heart of this reinvention process involves mathematizing activities in problem situations that are experientially real to students. It is important to note that reinvention in a collective, as well as individual activity, in which whole-class discussions centering on conjecture, explanation, and justification play a crucial role. The overall purpose of this study is to examine the developmental research efforts to adpat the instructional design perspective of RME to the teaching and learning of differential equation is collegiate mathematics education. Informed by the instructional design theory of RME and capitalizes on the potential technology to incorporate qualitative and numerical approaches, this study offers as approach for conceptualizing the learning and teaching of differential equation that is different from the traditional approach. Data were collected through participatory observation in a differential equations course at a university through a fall semester in 2003. All class sessions were video recorded and transcribed for later detailed analysis. Interviews were conducted systematically to probe the students' conceptual understanding and problem solving of differential equations. All the interviews were video recorded. In addition, students' works such as exams, journals and worksheets were collected for supplement the analysis of data from class observation and interview. Informed by the instructional design theory of RME, theoretical perspectives on emerging analyses of student thinking, this paper outlines an approach for conceptualizing inquiry-oriented differential equations that is different from traditional approaches and current reform efforts. One way of the wars in which thus approach complements current reform-oriented approaches 10 differential equations centers on a particular principled approach to mathematization. The findings of this research will provide insights into the role of the mathematics teacher, instructional materials, and technology, which will provide mathematics educators and instructional designers with new ways of thinking about their educational practice and new ways to foster students' mathematical justifications and ultimately improvement of educational practice in mathematics classes.

• Research in Mathematical Education
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• v.14 no.3
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• pp.249-262
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• 2010

Large Midwest university faculty members proposed the Science and Technology Enhancement Program Project (STEP) to improve students' learning in the secondary mathematics classroom using modules of inquiry-based teaching. The purpose of this study was to determine the impact of the STEP Project on students' attitude toward mathematics. Hierarchical linear models (HLM) were used to evaluate the impact of the STEP Project. The sample group for the study was 130 ninth grade students enrolled in Integrated Algebra I in a large urban school district. The school was one of eight secondary schools that participated in the STEP Project. The classes in the treatment group were three of five classes ordered in terms of the highest, middle, and lowest mean GPA. The control group consisted of two other middle GPA classes. The classes had an average of 25 students. Teachers who previously had been involved in the STEP Project taught all treatment and control classes. The inquiry-based teaching activities provided by the project were confined to the treatment classes. The survey measuring students' attitudes toward mathematics were obtained for both groups of students. The inquiry-based teaching affected students' attitudes toward mathematics (p < 0.07, ES = 3.07). Especially, students who had preexisting low attitudes toward mathematics were significantly affected by treatment (p < 0.02, ES = 0.02), while the treatment positively affected African American students overall at p < 0.08 (ES = 0.58).