• 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.

• East Asian mathematical journal
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• v.29 no.4
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• pp.355-392
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• 2013

Generally school algebra is to start with introducing variables and algebraic expressions, which have major cognitive obstacles to students in the transfer from arithmetic to algebra. But the recent studies in the teaching school algebra argue the algebraic thinking from an early algebraic point of view. We compare the Korean elementary mathematics textbooks with Americans from this perspective. First, we discuss the history of school algebra in the school curriculum. And Second, we investigate the recent studies in relation to early algebra. We clarify the goals of this study(the importance of early algebra in the elementary school) through these discussions. Next we examine closely the number sense in the arithmetic and the symbol sense in the algebra. And we conclude that the operation sense can connect these senses within early algebra using the algebraic thinking. Finally, we compare the elementary mathematics books between Korean and American according to the components of the operation sense. In this comparative study, we identify a possibility of teaching algebraic thinking in the elementary mathematics and early algebra can be introduced to the elementary mathematics textbooks from aspects of the operation sense.

• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.275-292
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• 2010

In this study, we discussed the way to teach algebra earlier through investigating to research trends of Early Algebra and researching about nature of subject involving algebra. There is a strong view that arithmetic and algebra have analogous forms and that algebra is on extension to arithmetic. Nevertheless, it is also possible to present a perspective that the fundamental goal and role of symbols and letters are difference between arithmetic and algebra. And, we could recognize that geometry was starting point of algebra trough historical perspectives. To consider these, we extracted some of possible directions to approaches to teach algebra earlier. To access to teaching algebra earlier, following ways are possible. (1) To consider informal strategy of young children. (2) Arithmetic reasoning considered of the algebraic relation. (3) Starting to algebraic reasoning in the context of geometrical problem situation. (4) To present young students to tool of letters and formular.

• 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.

• Research in Mathematical Education
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• v.16 no.4
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• pp.217-232
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• 2012

While many studies on early algebra have been conducted, there have been only a few studies on the operation sense as the fundamental element of algebraic thinking, especially the fraction operation sense. This study explored the dimensions of fraction operation sense and then investigated students' fraction operation sense. A total of 183 of sixth graders were surveyed and 5 students who showed high operation sense were clinically interviewed in order to analyze their algebraic thinking in detail. The results showed that students had a tendency to use direct calculation or employ inappropriate operation sense rather than to use the structure of operation or the relation between operations on the basis of algebraic thinking. This study implies that explicit instruction on early algebra is necessary from the elementary school years.

• Journal of Educational Research in Mathematics
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• v.12 no.1
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• pp.29-48
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• 2002

The purpose of this paper is to investigate the transfer in mathematics learning, especially focussing on arithmetic and algebra. There are many obstacles at the stage of transfer in learning. In the case of mathematics, each learning contents are definitely categorized by the learning level, therefore these obstacles are more happened than other subjects. First of all, this paper investigates the historical transfer from arithmetic to algebra by Sfard's perspectives. And we define prealgebra as the stage between arithmetic and algebra, which may be revised obstacles or misconceptions happened in the early algebra learning. Also, this paper discusses various obstacles and concrete examples happened in the transfer from arithmetic to algebra. To advance the understanding in the learning of algebra, we consider the core contents of the algebra learning which should be stressed at the prealgebra stage. Finally we present the teaching units of (pre)algebra which are sequenced from the variable concepts to equations.

• Research in Mathematical Education
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• v.8 no.2
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• pp.107-114
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• 2004

University teachers of linear algebra often feel annoyed and disarmed when faced with the inability of their students to cope with concepts that they consider to be very simple. Usually, they lay the blame on the impossibility for the students to use geometrical intuition or the lack of practice in basic logic and set theory. J.-L. Dorier [(2002): Teaching Linear Algebra at University. In: T. Li (Ed.), Proceedings of the International Congress of Mathematicians (Beijing: August 20-28, 2002), Vol. III: Invited Lectures (pp. 875-884). Beijing: Higher Education Press] mentioned that the situation could not be improved substantially with the teaching of Cartesian geometry or/and logic and set theory prior to the linear algebra. In East Asian countries, science-orientated mathematics curricula of the high schools consist of calculus with many other materials. To understand differential and integral calculus efficiently or for other reasons, students have to learn a lot of content (and concepts) in linear algebra, such as ordered pairs, n-tuple numbers, planar and spatial coordinates, vectors, polynomials, matrices, etc., from an early age. The content of linear algebra is spread out from grades 7 to 12. When the high school teachers teach the content of linear algebra, however, they do not concern much about the concepts of content. With small effort, teachers can help the students to build concepts of vocabularies and languages of linear algebra.

• 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.

• 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.