• Communications of Mathematical Education
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• v.31 no.4
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• pp.367-387
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• 2017

The educational environment in the digital age of the 21st century definitely affects teaching and learning methods to be changed. In addition, the perceptions and methods of mathematics education in the digital age have also been changing. This study proposes a university mathematics education model suitable for the digital age, which makes full use of the internet/digital environment and leads the students to participate in the learning processes. We apply the proposed model to Linear Algebra course, and present a concrete method of teaching and learning model including evaluation. This will be the first study on how to organize and operate digital courses in Korea in accordance with the mathematics education in the digital era which is rapidly spreading around the world.

• Communications of Mathematical Education
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• v.21 no.4
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• pp.621-646
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• 2007

In our new learning environment, we were asked to change our teaching method in our Linear Algebra class. In mathematics class, we could use several math-softwares such as MATHEMATICA, MATLAB, MAPLE, Drive etc.. MATLAB was quite well fit with our Linear Algebra class. In this paper we introduce an efficient way of delivery on important concepts in linear algebra by using well-known MATLAB/ATLAST M-files which we downloded from http://www.umassd.edu/specialprograms/atlast/.

• Journal of the Korean School Mathematics Society
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• v.22 no.2
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• pp.115-132
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• 2019

This study investigated results of bilingual learning of mathematics in teaching quadratic functions at an international high school in South Korea. Unlike a Korean traditional public school, this international school has provided bilingual learning. 10th grade students enrolled two math classes, Algebra II that was taught in English through CCSS and High School Mathematics I that was taught in Korean through the Korean National Math Curriculum. In order to collect information on students' behaviors and math achievement, we analyzed students' academic back grounds, mathematical abilities, results of interviews, observations, questionnaires and assessments. The results of this study include specific benefits. Bilingual learning of mathematics is effective as a method to improve Korean students' mathematical abilities and attitudes as well as positive influence on Korean mathematics education.

• Journal for History of Mathematics
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• v.21 no.1
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• pp.109-120
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• 2008

Today linear algebra is one of compulsory courses for university mathematics by virtue of its theoretical fundamentals and fruitful applications. However, a mechanical computation-oriented instruction or a formal concept-oriented instruction is difficult and dull for most students. In this context, how to teach mathematical concepts successfully is a very serious problem. As a solution for this problem, we suggest establishing original concepts in linear algebra from the students' point of view. Any original concept means not only a practical beginning for the historical order and theoretical system but also plays a role of seed which can build most of all the important concepts. Indeed, linear algebra has exactly two original concepts : geometry of planes, spaces and linear equations. The former was investigated in [2], the latter in the present paper.

• Communications of Mathematical Education
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• v.37 no.4
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• pp.569-590
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• 2023

The purpose of this case study is to compare and analyze the covariational reasoning levels of two middle school students revealed in the process of solving and generalizing algebra word problems. A class was conducted with two middle school students who had not learned quadratic equations in school mathematics. During the retrospective analysis after the class was over, a noticeable difference between the two students was revealed in solving algebra word problems, including situations where speed changes. Accordingly, this study compared and analyzed the level of covariational reasoning revealed in the process of solving or generalizing algebra word problems including situations where speed is constant or changing, based on the theoretical framework proposed by Thompson & Carlson(2017). As a result, this study confirmed that students' covariational reasoning levels may be different even if the problem-solving methods and results of algebra word problems are similar, and the similarity of problem-solving revealed in the process of solving and generalizing algebra word problems was analyzed from a covariation perspective. This study suggests that in the teaching and learning algebra word problems, rather than focusing on finding solutions by quickly converting problem situations into equations, activities of finding changing quantities and representing the relationships between them in various ways.

• Journal for History of Mathematics
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• v.22 no.1
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• pp.89-110
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• 2009

This paper observed the effect of CAS calculator usage while studying algebra on the achievement of low-achievement students. Participants were composed of 70 low-achievement tenth grade students from a high school located in a metropolitan city. That had never used a mathematics educational calculator before. Target participants were divided into two groups: an experiment group that studied activity papers with the aid of a CAS calculator, and a control group that studied the same activity papers using only paper-and-pencil. The content of the activity papers for the two groups was the same, but the structure differed. Content consisted of numbers and operations, equations and inequalities(character and expressions), and functions. Students in the experiment group exhibited matacognition learning using a CAS calculator. The two groups completed mathematics achievement tests both before and after the activity papers. Therefore, ANCOVA analysis results showed that compared to the pretest, results of the experiment group improved considerably more than the control group.

• Communications of Mathematical Education
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• v.30 no.4
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• pp.469-497
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• 2016

In this research, we develop a systematic learning the materials on constructibility of cubic roots. We propose two sets of materials: one is based on concepts of field, vector space, minimal polynomial in abstract algebra, another based on properties of cubic roots in elementary algebra. We assess the validity, applicability, defects and merits of developed materials through prospective teachers, in-service teachers, and professionals. It could be expected that materials be used for advanced secondary students, mathematics majoring college students and mathematics teachers. Furthermore, we may expect the materials be useful for understanding and solving the (un)constructibility problems.

• The Mathematical Education
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• v.42 no.3
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• pp.353-368
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• 2003

Analogy, based on a similarity, is to infer the properties of the similar object from properties of an object. It can be a very useful thinking tool for learning mathematical patterns and laws, noticing on relational properties among various situations. The purpose of this study, when manipulating hint condition, figure and table conditions and the amount of original learning by using algebra word problems, is to verify the effects of analogical transfer in solving equivalent, isomorphic and similar problems according to the similarity of source problems and target ones. Five study questions were set up for the above purpose. It was 354 first grade students of S and G middle schools in Seoul that were experimented for this study. The data was processed by MANOVA analysis of statistical program, SPSS 10.0. The results of this studies would indicate that most of the students would be poor at solving isomorphic and similar problems in the performance of analogical transfer according to the similarity of source and target problems. Hints, figure and table conditions did not facilitate the analogical transfer. Merely, on the condition that amount of teaming was increased, analogical transfer of the students was facilitated. Therefore, it is necessary to have students do much more analogical problem-solving experience to improve their analogical reasoning ability through the instruction program development in the educational fields.

• Journal of Educational Research in Mathematics
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• v.11 no.1
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• pp.67-87
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• 2001

Variable concept plays a crucial role in understanding not only algebra itself but also school mathematics which is algebra-oriented. It solves as an essential means in applying mathematics to the real world because il enables us to describe varying phenomena in the real world. In this study, we examined some matters related to the learning of variable concept in school mathematics. In Particular, we discussed on the teaching of variable concept in the [7-first] stage of the 7th Mathematics Curriculum. We analysed the textbooks in the [7-first] stage and attempted to explain concretely the contents and teaching methods of variable concept which be taught in school mathematics. After reconsidering the practices on variable concept teaching, we pointed out the problems of formalistic teaching method and then proposed the direction in which variable concept teaching should go.

• Research in Mathematical Education
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• v.13 no.1
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• pp.1-4
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• 2009

We are considering the discovery and the promotion of the talent from the viewpoint of education of talented children. The education that develops the talent is from "Individual needs for all children." Computer Algebra System (CAS) can be used as a new possibility in the education that develops the talent. We will need to take advantage of the research results from cognitive science. In order to fully utilize CASs in education, teaching methods that are based on cognitive science will be needed, and these are clearly different from those used in paper and pencil teaching.