• Communications of Mathematical Education
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• v.25 no.1
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• pp.63-78
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• 2011

The purpose of this study is to explore a teaching method of limits of functions with more intuitive and visual of CAS graphing calculators rather than with the rigorous ${\epsilon}-{\delta}$ method. Texas Instruments Voyage200 CAS graphing calculators are used for studying the possibility of the use of technology in calculus course. For this, various related theoretical constructs are reviewed: concept image, concept definition, cognitive conflict, the use of visualization of technology for calculus concepts, the theory of APOS, and local straightness. Based on such theoretical constructs this study suggests a teaching method of limits of functions with embodied visualization of CAS graphing calculators.

• Communications of Mathematical Education
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• v.25 no.2
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• pp.403-430
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• 2011

The purpose of the study was to investigate how the use of graphing calculators influence on forming students' mathematical concept of algebra, students' mathematical connection, and attitude toward mathematics. First, graphing calculators give instant feedback to students as they make students compare their written answers with the results, which helps students learn equations and linear inequalities for themselves. In respect of quadratic inequalities they help students to correct wrong concepts and understand fundamental concepts, and with regard to functions students can draw graphs more easily using graphing calculators, which means that the difficulty of drawing graphs can not be hindrance to student's learning functions. Moreover students could understand functions intuitively by using graphing calculators and explored math problems volunteerly. As a result, students were able to perceive faster the concepts of functions that they considered difficult and remain the concepts in their mind for a long time. Second, most of students could not think of connection among equations, equalities and functions. However, they could understand the connection among equations, equalities and functions more easily. Additionally students could focus on changing the real life into the algebraic expression by modeling without the fear of calculating, which made students relieve the burden of calculating and realize the usefulness of mathematics through the experience of solving the real-life problems. Third, we identified the change of six students' attitude through preliminary and an ex post facto attitude test. Five of six students came to have positive attitude toward mathematics, but only one student came to have negative attitude. However, all of the students showed positive attitude toward using graphing calculators in math class. That's because they could have more interest in mathematics by the strengthened and visualization of graphing calculators which helped them understand difficult algebraic concepts, which gave them a sense of achievement. Also, students could relieve the burden of calculating and have confidence. In a conclusion, using graphing calculators in algebra and function class has many advantages : formulating mathematics concepts, mathematical connection, and enhancing positive attitude toward mathematics. Therefore we need more research of the effect of using calculators, practical classroom materials, instruction models and assessment tools for graphing calculators. Lastly We need to make the classroom environment more adequate for using graphing calculators in math classes.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.611-626
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• 2010

The purpose of this study is to explore the composite properties of linear functions using CAS calculators. The meaning and processes in which technological tools such as CAS calculators generated to instrument are reviewed. Other theoretical topic is the design of an exploring model of observing-conjecturing-reasoning and proving using CAS on experimental mathematics. Based on these background, the researchers analyzed the properties of the family of composite functions of linear functions. From analysis, instrumental capacity of CAS such as graphing, table generation and symbolic manipulation is a meaningful tool for this exploration. The result of this study identified that CAS as a mediator of mathematical activity takes part of major role of changing new ways of teaching and learning school mathematics.

• School Mathematics
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• v.15 no.4
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• pp.975-994
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• 2013

In this paper, we analyzed the utilization trend of technology in the secondary mathematics textbooks based on the 6th, 7th and 2007 revised mathematics curriculums in Korea. We analyzed 30, 60 and 90 mathematics books based on the 6th, 7th and 2007 revised mathematics curriculums respectively. The analysis focused on three aspects of using technology, i.e., contents areas in which technology used, technological tools and programs used, and methods of using technology in teaching and learning mathematics. The results shows that the frequency of using technology in mathematics books has been increased as mathematics curriculum has been revised. In the mathematics books based on th 6th curriculum, only 25 scenes were found, but in 7th and 2007 revised curriculum 248 and 355 scenes were found. In the 6th curriculum, calculators and graphing calculators were used mainly, but in the 7th and 2007 revised curriculum many kinds of technological tools and softwares were used including CAS, dynamic geometry software, spreadsheets, programming language, and the Internet. Especially the internet was used frequently in the 7th curriculum. And the methods of using technology has been diversified as time passed. In the 6th curriculum, the technology mainly used for introducing technology and simple calculation, but in the 7th and 2007 revised curriculum the technologies and software were also used for understanding mathematical laws, principles and concepts and students-centered exploring the mathematical properties.