• Communications of Mathematical Education
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• v.23 no.2
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• pp.399-428
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• 2009

2007 Renewed Korea Elementary Mathematics Curriculum introduce algebra 6th grade. According to many studies about introducing algebra, it is desirable to teach 6th graders algebra through generalization of patterns. In this study, 6th graders' understanding processes and difficulties in pattern generalization were analyzed and possiblities of introducing algebra to 6th graders through pattern generalization were examined.

• School Mathematics
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• v.12 no.3
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• pp.323-335
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• 2010

Linear algebra is not only applied comprehensively in the branches of mathematics such as algebra, analytics, and geometry but also utilized for finding solutions in various fields such as aeronautical engineering, electronics, biology, geology, mechanics and etc. Therefore, linear algebra should be easy and comfortable for not only mathematics majors but also for general students as well. However, most find it difficult to learn linear algebra. Why is it so? It is because many studying linear algebra fail to achieve a correct understanding or attain erroneous concepts through misleading knowledge they already have. Such cases cause learning disability and mistakes. This research suggests more effective method of teaching by analyzing difficulty and errors made in learning system of linear equations.

• Communications of Mathematical Education
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• v.19 no.2 s.22
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• pp.379-388
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• 2005

일차변환은 선형대수에서 가장 중요한 개념 중 하나이다. 그럼에도 많은 학생들에게서 나타나는 이 개념에 대한 오류는 무엇이며 또 어디에 근거하는가? 이 논문은 효과적인 선형대수 교수학습 연구의 일부로, 주어진 여러 함수 중에서 일차변환인 것을 찾는 과정 중에 나타난 학생들의 오류와 그 근거를 알아보았다. 본 연구 결과는 선형대수 학습에 어려움을 겪는 학생들에게 보다 효율적인 교수디자인 설계를 위한 기초 자료의 의미를 갖는다.

• Journal of the Korean School Mathematics Society
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• v.10 no.2
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• pp.187-206
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• 2007

The purpose of this study is to know what is the difficulties that mathematics underachievers are suffering from the area of mathematical function and how to overcome this difficulties. For this study, we have selected two mathematics underachievers and carried out the inspection. The mathematics underachievers have undergone the difficulties of understanding mathematical problems, the difficulties from the deficit of prerequisite and basic learning, the difficulties of finding the answer typically and the difficulties of classifying an algebraic symbol, the difficulties of calculating the gradient of the straight line passing through two points.

• School Mathematics
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• v.5 no.3
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• pp.343-360
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• 2003

In this paper, we deal with the teaching of algebra based on patterns and generalization. The past algebra curriculum starts with letters(variables), algebraic expressions, and equations, but these formal approaching method has many difficulties in the school algebra. Therefore we insist the new algebraic approaches should be needed. In order to develop these instructions, we firstly investigate the relationship of patterns and algebra, the relationship of generalization and algebra, the steps of generalization from patterns and levels of difficulties. Next we look into the algebra instructions based arithmetic patterns, visual patterns and functional situations. We expect that these approaches help students learn algebra when they begin school algebra.

• Journal of Gifted/Talented Education
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• v.26 no.1
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• pp.211-230
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• 2016

The study aimed to investigate the characteristics of algebraic thinking of the mathematically gifted students and search for how to teach algebraic thinking. Research subjects in this study included 93 students who applied for a science gifted education center affiliated with a university in 2015 and previously experienced gifted education. Students' responses on an algebraic item of a creative thinking test in mathematics, which was given as screening process for admission were collected as data. A framework of algebraic thinking factors were extracted from literature review and utilized for data analysis. It was found that students showed difficulty in quantitative reasoning between two quantities and tendency to find solutions regarding equations as problem solving tools. In this process, students tended to concentrate variables on unknown place holders and to had difficulty understanding various meanings of variables. Some of students generated errors about algebraic concepts. In conclusions, it is recommended that functional thinking including such as generalizing and reasoning the relation among changing quantities is extended, procedural as well as structural aspects of algebraic expressions are emphasized, various situations to learn variables are given, and activities constructing variables on their own are strengthened for improving gifted students' learning and teaching algebra.

• Journal of Educational Research in Mathematics
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• v.24 no.3
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• pp.359-374
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• 2014

Students' difficulties and errors in relation to mathematical proofs are worth while to say one of the dilemmas in mathematics education. The potential elements of their difficulty are scattered over the process of proving in geometry as well as algebra. This study aims to investigate whether middle school students understand the context of algebraic proof including literal expressions. We applied 24 third-grade middle school students a test item which shows a proof including a literal expression and missing the conclusion. Over the half of them responded wrong answers based on only the literal expression without considering its context. Three of them were interviewed individually to show their thinking. As a result, we could find some characteristics of their thinking including the perspective on proof as checking the validity of algebraic expression and the gap between proving and understanding of proof etc. From these, we also discussed about several didactical implications.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.503-521
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• 2013

For over 20 years, the issue of using an adequate CAS tool in teaching and learning of linear algebra has been raised constantly. And a variety of CAS tools were introduced in many linear algebra textbooks. In Korea, however, because of some realistic problems, they have not been introduced in the class and the theoretical aspect of linear algebra has been focused on in teaching and learning of it. In this paper, we suggest Sage as an alternative for CAS tools overcoming the problems mentioned above. And, we introduce full contents for linear algebra and matrix calculator that Sage was used to develop. Taking advantage of them, almost all the concepts of linear algebra can be easily covered and the size of matrices can be expanded without difficulty.

• School Mathematics
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• v.9 no.2
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• pp.313-326
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• 2007

Recently in algebra curriculum, to recognizes and explains general nile expressing patterns is presented as the one alternative and is emphasized. In the seventh School Mathematic Curriculum regarding 'regularity and function' area, in elementary school curriculum, is guiding pattern activity of various form. But difficulty and problem of students are pointing in study for learning through pattern activity. In this article, emphasizes generalization process through research activity of pictorial/geometric pattern that is introduced much on elementary school mathematic curriculum and investigates various approach and strategy of student's thinking, state of symbolization in generalization process of pictorial/geometric pattern. And discusses generalization of pictorial/geometric pattern, difficulty of symbolization and suggested several proposals for research activity of pictorial/geometric pattern.

• School Mathematics
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• v.16 no.4
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• pp.803-825
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• 2014

From the early stages of learning algebra, literal symbols are used to represent algebraic objects such as variables and parameters. The concept of parameters contains both indeterminacy and fixity resulting in confusion and errors in understanding. The purpose of this research is to compare the beginners of algebra and pre-service teachers who completed secondary mathematics education in terms of understanding this paradoxical nature of parameters. We recruited 35 middle school students in eight grade and 73 pre-service teachers enrolled in a undergraduate course at one university. Using them we conducted a survey on the perception of the nature of parameters asking if one considers parameters suggested in a problem as variables or constants. We analyzed the collected data using the mixed method of qualitative and quantitative approaches. From the analysis results, we identified several difficulties in understanding of parameters from both groups. Especially, our statistical analysis revealed that the proportions of subjects with limited understanding of the concept of parameters do not differ much in two groups. This suggests that learning algebra in secondary mathematics education does not improve the understanding of the nature of parameters significantly.