• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.485-494
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• 1998

This study is on the theory of Piaget's reflective abstraction and the mechanism of the development of knowledge and the history of algebra and its application to understand the difficulties that many students have in learning algebra. Piaget considers the development of knowledge as a linear process. The stages in the construction of different forms of knowledge are sequential and each stage begins with reorganization. The reorganization consists of the projection onto a higher level from the lower level and the reflection which reconstructs and reorganizes within a lager system that is transferred by profection. Piaget shows that the mechanisms mediating transitions from one historical period to the next are analogous to those mediating the transition from one psychogenetic stage to the next and characterizes the mechanism as the intra, inter, trans sequence. The historical development of algebra is characterized by three periods, which are intra inter, transoperational. The analysis of the history of algebra by the mechanism explains why the difficulties that students have in learning algebra occur and shows that the roles of teachers are important to help students to overcome the difficulties.

• 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.

• Research in Mathematical Education
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• v.7 no.1
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• pp.59-67
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• 2003

In linear algebra course, the theory of vector space is usually presented in a very formal setting, which causes severe difficulties to many students. In this study, the effect of teaching the theory of vector space in linear algebra from the geometrical point of view on students' learning was investigated. It was found that the teaching of the theory of vector space in linear algebra from the geometrical point of view increases the meaningful loaming since it increases the visualization.

• Communications of Mathematical Education
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• v.23 no.4
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• pp.1131-1148
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• 2009

Algebra is one of the important subjects that not only mathematics but many science major students should know at least at the elementary level. Unfortunately abstract algebra, specially, is seen as an extremely difficult course to learn. One reason of difficulties is because of its very abstract nature, and the other is due to the lecture method that simply telling students about mathematical contents. In this paper we study about the teaching and learning abstract algebra in universities in corporation of a programming language such as ISETL. ISETL is a language whose syntax closely imitates that of mathematics. In asking students to read and write code in ISETL before they learn in class, we observe that students can much understand and construct formal statements that express a precise idea. We discuss about the classroom activities that may help students to construct and internalize mathematical ideas, and also discuss about some barriers we might overcome.

• East Asian mathematical journal
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• v.26 no.2
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• pp.319-336
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• 2010

There are serious difficulties with management of general mathematics education courses because of enormous gap between freshman's ability of mathematics and lack of problem solving ability. In this paper, we try to find methods so we can reduce the difficulties. By utilizing students survey, management of Mathematics Cafe and setting example classes for Calculus and Linear Algebra we suggest effective management strategies and teaching-learning methods.

• Journal of Educational Research in Mathematics
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• v.10 no.1
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• pp.85-102
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• 2000

The concept of variables is central to mathematics teaching and learning in junior and senior high school. Understanding the concept provides the basis for the transition from arithmetic to algebra and necessary for the meaningful use of all advanced mathematics. Despite the importance of the concept, however, much has been written in the last decade concerning students' difficulties with the concept. This Thesis is based on research to investigate the hypothesis that LOGO programming will contribute to 6th grader' learning of variables. The aim of the research were to; .investigate practice on pupils' understanding of variables before the activity with a computer; .identify functions of LOGO programming in pupils' using and understanding of variable symbols, variable domain and the relationship between two variable dependent expressions during the activity using a computer; .investigate the influence of pupils' mathematical belief on understanding and using variables. The research consisted predominantly of a case study of 6 pupils' discourse and activities concerning variable during their abnormal lessons and interviews with researcher. The data collected for this study included video recordings of the pupils'work with their spoken language.

• School Mathematics
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• v.10 no.2
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• pp.139-154
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• 2008

The primary purpose of this study was to investigate how sixth grade elementary school students react to the types of letters use, what levels of understanding letters students are in and what difficulties are in understanding letters, and to raise issues about instructional methods of algebra. A descriptive study through pencil-and- paper tests was conducted. The test instruments consisted of 18 questions with 6 types of letters use. According to the results of testing, students' types of letter use and the levels of understanding letters were classified. The conclusions from the results of this study were as follows: First, the higher the types of letters use, the more sixth grade elementary school students had low scores on the types. Therefore, teaching methodologies of letters and expressions in the classroom need to encourage for students to improve their ability of using and understanding letter. Second, approximately 40% of students were categorized in level 3. Accordingly it is necessary to have a program of teaching and learning to improve their understanding levels of letters. Third, approximately 15% of students were categorized in level 0. In order to develop understanding of letters, it is important that students use letter evaluated and letter used as an object. Fourth, students had the difficulties in understanding letters. It is informative for teachers to understand these students' difficulties and thinking processes. Finally, we must treat the different uses of letters and introduce them successively according to the student's understanding levels of letters.

• 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.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.525-541
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• 2010

The purpose of this thesis is to investigate the effects of the topics in basic mathematics on academic achievement in order to improve the problem-solving abilities of low achievement students in university general mathematics. This program has been conducted from P University as a part of Education Capacity Enhancing Project. The goals of this program are to make students who have fear to mathematics feel confident for mathematics, and make easier to study general mathematics and major field without any difficulties for the students. The topics in basic mathematics was enforced with solving problem based on comprehension of the basic concept and computer-based learning. The classes were organized as Algebra-Geometry, Calculus, and General mathematics class by students' applications for classes and basic academic ability. As a result, the topics in basic mathematics has been evaluated as positive way to effect satisfaction and learning effect for the students who have low-level in basic academic ability. And also, according to the survey, the result shows that assignment through Webwork system and Mathematica program practice are helpful for learning basic mathematics. But several measures are asked for participation in the class and prevention for quitter of participants.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.1
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• pp.1-22
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• 2017

The properties of arithmetic are considered as essential to understand the principles of calculation and develop effective strategies for calculation in the elementary school level, thanks to agreement on early algebra. Therefore elementary students' misunderstanding of the properties of arithmetic might cause learning difficulties as well as misconcepts in their following learning processes. This study aims to provide elementary teachers a part of pedagogical content knowledge about the properties of arithmetic and to induce some didactical implications for teaching the properties of arithmetic in the elementary school level. To do this, elementary school mathematics textbooks since the period of the first curriculum were analyzed. These results from analysis show which properties of arithmetic have been taught, when they were taught, and how they were taught. Based on them, some didactical implications were suggested for desirable teaching of the properties of arithmetic.