• Journal of the Korean School Mathematics Society
• /
• v.17 no.4
• /
• pp.697-716
• /
• 2014

The purpose of this paper is to investigate high school students' learning characteristics which revealed in their learning process of limit using GeoGebra. And we are going to analyze effects of teaching of limit using GeoGebra to high school students' interesting and attitudes for mathematics learning. To do this, we selected three high school students as participants and ask them performing limit learning using GeoGebra. We recorded their problem solving process. Through analyzing their problem solving process relate to their solution, we found the followings: First, students did not logically approach based on mathematical properties or given materials, rather showing tendency decide with self-conscious and intuition. Second, it is possible that former reasoning strategies disturb following reasoning in the process of high school students' mathematics learning. Third, learning process of limit using GeoGebra help high school students to identify and correct their errors relate to limit learning. Forth, learning process of limit using GeoGebra positively effects to high school students' interesting and attitudes for mathematics learning.

• Journal of Gifted/Talented Education
• /
• v.24 no.6
• /
• pp.897-916
• /
• 2014

In this study, we presented a teaching-learning method that can apply process-focused assessment for mathematical creativity of problem solving process of the gifted student, By necessity of appropriate teaching-learning program development to the level and ability of students who belong to high school gifted classes and courses evaluation for students who participated in education programs for the gifted. In the construction implementation process of students utilizing a kind of teaching-learning software, GeoGebra. We analyzed process of a variety of creative constructing figures using interfaces of GeoGebra and algebraic calculation. Utilizing 'Construction Protocol' and 'Navigation Bar' of GeoGebra, We identified computer languages, construction order, run times used in construction process of individual student and found mathematical creativity of students in the process. Comparing this result with prerequisite learning degree of individual student, We verified that this teaching-learning method can apply at the high school gifted classes as well as institutes for the gifted education in the city office.

• Education of Primary School Mathematics
• /
• v.16 no.2
• /
• pp.123-145
• /
• 2013

This study was expected to yield the meaningful conclusions from the experimental group who took lessons based on inductive activities using GeoGebra at the beginning of proof learning and the comparison one who took traditional expository lessons based on deductive activities. The purpose of this study is to give some helpful suggestions for teaching proof to mathematically gifted elementary students. To attain the purpose, two research questions are established as follows. 1. Is there a significant difference in proof abilities between the experimental group who took inductive lessons using GeoGebra and comparison one who took traditional expository lessons? 2. Is there a significant difference in proof attitudes between the experimental group who took inductive lessons using GeoGebra and comparison one who took traditional expository lessons? To solve the above two research questions, they were divided into two groups, an experimental group of 10 students and a comparison group of 10 students, considering the results of gift and aptitude test, and the computer literacy among 20 elementary students that took lessons at some education institute for the gifted students located in K province after being selected in the mathematics. Special lesson based on the researcher's own lesson plan was treated to the experimental group while explanation-centered class based on the usual 8th grader's textbook was put into the comparison one. Four kinds of tests were used such as previous proof ability test, previous proof attitude test, subsequent proof ability test, and subsequent proof attitude test. One questionnaire survey was used only for experimental group. In the case of attitude toward proof test, the score of questions was calculated by 5-point Likert scale, and in the case of proof ability test was calculated by proper rating standard. The analysis of materials were performed with t-test using the SPSS V.18 statistical program. The following results have been drawn. First, experimental group who took proof lessons of inductive activities using GeoGebra as precedent activity before proving had better achievement in proof ability than the comparison group who took traditional proof lessons. Second, experimental group who took proof lessons of inductive activities using GeoGebra as precedent activity before proving had better achievement in the belief and attitude toward proof than the comparison group who took traditional proof lessons. Third, the survey about 'the effect of inductive activities using GeoGebra on the proof' shows that 100% of the students said that the activities were helpful for proof learning and that 60% of the reasons were 'because GeoGebra can help verify processes visually'. That means it gives positive effects on proof learning that students research constant character and make proposition by themselves justifying assumption and conclusion by changing figures through the function of estimation and drag in investigative software GeoGebra. In conclusion, this study may provide helpful suggestions in improving geometry education, through leading students to learn positive and active proof, connecting the learning processes such as induction based on activity using GeoGebra, simple deduction from induction(i.e. creating a proposition to distinguish between assumptions and conclusions), and formal deduction(i.e. proving).

• Journal for History of Mathematics
• /
• v.25 no.1
• /
• pp.71-88
• /
• 2012

The purpose of this study is to find the way to build the concept image about natural logarithm and the method is using definite integral in calculus under GeoGebra environment. When the students approach to natural logarithm, need to use dynamic program about the definite integral in calculus. Visible reasoning process through using dynamic program(GeoGebra) is the most important part that make the concept image to students. Also, for understand mathematical concept to students, using GeoGebra environment in dynamic program is not only useful but helpful method of teaching and studying. In this article, about graph of natural logarithm using the definite integral, to explore process of understand and to find special feature under GeoGebra environment. And it was obtained from a survey of undergraduate students of mathmatics. Also, relate to this process, examine an aspect of students, how understand about connection between natural logarithm and the definite integral, definition of natural logarithm and mathematical link of e. As a result, we found that undergraduate students of mathmatics can understand clearly more about the graph of natural logarithm using the definite integral when using GeoGebra environment. Futhermore, in process of handling the dynamic program that provide opportunity that to observe and analysis about process for problem solving and real concept of mathematics.

• Communications of Mathematical Education
• /
• v.29 no.1
• /
• pp.73-90
• /
• 2015

When teachers make up assessment questions regarding the content area that contains shapes and graphs, they should present the pictures so that their role might be represented properly. We exhibited the process of constructing shapes and graphs utilizing GeoGebra, and simultaneously analyzed the process of developing and revising questions using this and awareness changes in teachers who participate in the teacher's training focused on improving professionalism for making up questions such as CSAT(College Scholastic Ability Test). Through the survey they mentioned that making questions utilizing algebraic construction overcame the limitations of making up questions and played an instrumental role in developing creative questions. Based on the results, We suggested effectiveness of making up questions utilizing algebraic construction. Our intention was to improve the skills of teachers for making up questions such as CSAT and to suggest implications about it.

• School Mathematics
• /
• v.16 no.2
• /
• pp.317-334
• /
• 2014

The purpose of this study is to grasp pre-service secondary teachers' understanding-realities for Taylor series convergence conceptions and to examine a teaching way using GeoGebra based on the understanding-realities. In this study, most pre-service teachers have abilities to calculate the Taylor series and radius of convergence, but they are vulnerable to conceptual problems which give meaning of the equality between a given function and its Taylor series at any point. Also they have some weakness in determining the change of radius of convergence according to the change of Taylor series' center. To improve their weakness, we explore a teaching way using dynamic and CAS functionality of GeoGebra. This study is expected to improve the pedagogical content knowledge of pre-service secondary mathematics teachers for infinite series treated in high school mathematics.

• Journal for History of Mathematics
• /
• v.29 no.2
• /
• pp.73-88
• /
• 2016

To introduce materials related to our traditional mathematics and to reinterpret modernly them could be a good tool to find the cultural values of them. We analyzed the degree for utilization of the history of mathematics in the middle school textbooks developed depending on the 2009 revised mathematics curriculum. Through this, we suggest the need for research on concrete and practical teaching and learning materials development utilizing the history of mathematics. We reinterpret, in modern style based on the curriculum, two subjects dealt with in 'GakDeungByeonHyeongSeupYu', the first theme of 'SanSulGwanGyeon' written by Lee Sang Hyuk. We expansively reconstruct the original samples up to regular decagon so that students might figure out the situation of all regular polygon using a kind of mathematics software GeoGebra. Also this process is constructed on the basis of the curriculum for an implementation the secondary school classes.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.15 no.3
• /
• pp.1015-1029
• /
• 2021

Modern technology offers many ways to enhance teaching and learning that in turn promote the development of tools for educational activities both inside and outside the classroom. Many educational programs using the augmented reality (AR) technology are being widely used to provide supplementary learning materials for students. This paper describes the potential and challenges of using GeoGebra AR in mathematical studies, whereby students can view 3D geometric objects for a better understanding of their structure, and verifies the feasibility of its use based on experimental results. The GeoGebra software can be used to draw geometric objects, and 3D geometric objects can be viewed using AR software or AR applications on mobile phones or computer tablets. These could provide some of the required materials for mathematical education at high schools or universities. The use of the GeoGebra application for education in Laos will be particularly discussed in this paper.

• East Asian mathematical journal
• /
• v.37 no.2
• /
• pp.265-288
• /
• 2021

In the 2015 revised mathematics curriculum, the system of equations is first introduced in 'Variables and Expressions' of [Middle School Grades 1-3]. Then, It is constructed that after learning the linear function in 'Functions', the relationship between the graphs of two linear functions and the systems of linear equations are learned so that students could improve the geometric representation of the systems of equations. However, in of Elective-Centered Curriculum Common Courses, Instruction is limited to algebraic manipulation when teaching and learning systems of quadratic equations. This paper presented the teaching and learning method that can improve students' mathematical connection through various representations by providing geometric representations in parallel using GeoGebra, a mathematics learning software, with algebraic solutions in the teaching and learning situation of simultaneous quadratic equations.

• Communications of Mathematical Education
• /
• v.28 no.4
• /
• pp.457-474
• /
• 2014

Recently, with the development of technology, intuitive understanding of abstract mathematical concepts through visualizations is growing in popularity within college mathematics. In this study, we introduce free visualization tools developed for better understanding of topics which students learn in Calculus. We visualize important concepts of Calculus as much as we can according to the order of most Calculus textbooks. In this process, we utilized a well-known, free mathematical software called GeoGebra. Finally, we discuss our experience with visualizations in Calculus using GeoGebra in our class and discuss how it can be effectively adopted to other university math classes and high school math education.