• Journal of Educational Research in Mathematics
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• v.13 no.3
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• pp.309-327
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• 2003

In this paper, we deal with the teaching of algebra in the elementary school mathematics, and call this algebra teaching method as ‘early algebra’. Early algebra is appeared in the 1980's with the discussion of ‘algebraic thinking’. And many studies about early algebra is in progress since 1990's. These studies aims at reducing difficulties in the teaching of algebra and the development of algebra curriculum. We investigate the background of early algebra, and justify teaching of early algebra. Also we examine the projects and studies in progress around the world. Finally through these discussions, we compare our elementary textbooks with early algebra, and verify the characters of early algebra from our arithmetic curriculum.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.2
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• pp.115-142
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• 2018

This research analyzed domestic researches on early algebra education which are published in six major mathematics education journals in Korea. The purpose of this work is to grasp trends of early algebra education in Korea and to draw up future tasks. From 2000 to 2017, 89 papers which are related to early algebra education published in 6 journals. The 89 papers were categorized by research period, academic journals, research topics, and research subjects. As a result, the number of researches on early algebra education in Korea has increased since 2000. Although early algebra education belongs to the field of elementary mathematics education, lots of papers were published in other math education journals than in the math education journals for elementary school mathematics. Most research focused on proportional reasoning across the algebraic content area. The majority of the research subjects were students, especially upper-grade students of elementary school. Based on the results of this study, some implications for early algebra education in Korea were suggested.

• Journal of Educational Research in Mathematics
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• v.17 no.4
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• pp.453-475
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• 2007

School algebra starts with introducing algebraic expressions which have been one of the cognitive obstacles to the students in the transfer from arithmetic to algebra. In the recent studies on the teaching school algebra, algebraic thinking is getting much more attention together with algebraic expressions. In this paper, we examined the processes of the transfer from arithmetic to algebra and ways for teaching early algebra through algebraic thinking factors. Issues about algebraic thinking have continued since 1980's. But the theoretic foundations for algebraic thinking have not been founded in the previous studies. In this paper, we analyzed the algebraic thinking in school algebra from historico-genetic, epistemological, and symbolic-linguistic points of view, and identified algebraic thinking factors, i.e. the principle of permanence of formal laws, the concept of variable, quantitative reasoning, algebraic interpretation - constructing algebraic expressions, trans formational reasoning - changing algebraic expressions, operational senses - operating algebraic expressions, substitution, etc. We also identified these algebraic thinking factors through analyzing mathematics textbooks of elementary and middle school, and showed the middle school students' low achievement relating to these factors through the algebraic thinking ability test. Based upon these analyses, we argued that the readiness for algebra learning should be made through the processes including algebraic thinking factors in the elementary school and that the transfer from arithmetic to algebra should be accomplished naturally through the pre-algebra course. And we searched for alternative ways to improve algebra curriculums, emphasizing algebraic thinking factors. In summary, we identified the problems of school algebra relating to the transfer from arithmetic to algebra with the problem of teaching algebraic thinking and analyzed the algebraic thinking factors of school algebra, and searched for alternative ways for improving the transfer from arithmetic to algebra and the teaching of early algebra.

• 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.

• Communications of Mathematical Education
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• v.26 no.4
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• pp.351-362
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• 2012

Until the 1950s, linear algebra was considered only as one of abstract and advanced mathematics subject among in graduate mathematics courses, mainly dealing with module in algebra. Since the 1960s, it has been a main subject in undergraduate mathematics education because matrices has been used all over. In Korea, it was considered as a course only for mathematics major students until 1980s. However, now it is a subject for all undergraduate students including natural science, engineering, social science since 1990s. In this paper, we investigate the early history of linear algebra and its development from a historical perspective and mathematicians who made contributions. Secondly, we explain why linear algebra became so popular in college mathematics education in the late 20th century. Contributions of Chinese and H. Grassmann will be extensively examined with many newly discovered facts.

• School Mathematics
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• v.13 no.4
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• pp.581-598
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• 2011

Given the growing agreement that algebra should be taught in the early stage of the curriculum, considerable studies have been conducted with regard to early algebra in the elementary school. However, there has been lack of research on how to organize mathematic lessons to develop of algebraic reasoning ability of the elementary school students. This research attempted to gain specific and practical information on effective algebraic teaching and learning in the elementary school. An exploratory qualitative case study was conducted to the fourth graders. This paper focused on the associative law of the multiplication. This paper showed what kinds of activities a teacher may organize following three steps: (a) focus on the properties of numbers and operations in specific situations, (b) discovery of the properties of numbers and operations with many examples, and (c) generalization of the properties of numbers and operations in arbitrary situations. Given the steps, this paper included an analysis on how the students developed their algebraic reasoning. This study provides implications on the important factors that lead to the development of algebraic reasoning ability for elementary students.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2003.04a
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• pp.237-241
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• 2003

본 연구에서는 강원도 속초시 쌍천에 위치한 쌍천지하댐이 지하수흐름에 미치는 영향을 범용 지하수 흐름해석 프로그램인 MODFLOW를 사용하여 검토하였다. 먼저 지하댐이 설치되기 전인 초기 정상류 상태를 모의하여 수두 분포를 확인하였으며, 그 후 지하댐 설치 전의 정상류 상태를 수위를 초기 수두로 하여 지하댐이 설치된 후의 대수층의 지하수위 변화를 모의하였다. 모의 결과 대수층에 지하댐을 설치하면 지하댐을 설치하기 전에 비하여 지하수위가 약 0.4m 정도 상승하는 것으로 나타났다.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.14 no.1
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• pp.71-77
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• 2004

It was proved that Hen is an algebraic ,elation of degree [n(l+1]/2] for an (n, 1)-combine. which consists of n LFSRs and l memory bits. For the summation generator with $2^k$ LFSRs which uses k memory bits, we show that there is a non-trivial relation of degree at most $2^k$ using k+1 consecutive outputs. In general, for the summation generator with n LFSRs, we can construct a non-trivial algebraic relation of degree at most 2$^{{2^{[${log}_2$}n]}}$ using [${log}_2$＋1 consecutive outputs.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.465-486
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• 2010

Studying the definition and building a foundation about variables during elementary school is a crucial factor before students study the variable in depth in middle school. So, forming a basis for understanding variable in this period should be treated with importance, because it is the first step in forming a clear understanding of the concept of variables. According to analysis of the types of letters used in current textbooks, we can see that too much emphasis was placed on type 1(letter evaluated), type 3(letter used as an Object). By not utilizing the various types of letter usage we reduce the situation to one which is removed from the context and an automatous style of learning. Therefore, the purpose of this study was the development about early algebra learning materials which use diverse types of letters. We have analyzed the types of letters used from the 4-ga to 6-na mathematics textbooks and the 4-ga to the 6-na workbooks. To make learning materials for well-balanced letter use, we developed learning materials focused on early algebra with the 6-ga and the 6-na textbooks.

• Economic and Environmental Geology
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• v.30 no.5
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• pp.433-442
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• 1997

A dual-permeability fractal model of fluid flow is proposed. The model simulates groundwater flow in fissured dual aquifer system composed of Aquifer 1 and Aquifer 2. For this model. groundwater flow originates only from Aquifer 1 on the pumping well. The model considers wellbore storage and skin effects at the pumping well and then shows exact drawdown at the early time of pumping. Type curves for different flow dimensions and for two cases are presented and analyzed. The case 1 represents the aquifer system which consists of Aquifer 1 with low permeability and high specific storage and Aquifer 2 with high permeability and low specific storage. The case 2 is inverse to the case 1. Dimensionless drawdown curves in Aquifer 1 and Aquifer 2 shows characteristic trend each other. Consequently, the model will be useful to analyze pumping test data of different draw down patterns on the pumping well and observation wells.