• The Mathematical Education
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• v.50 no.1
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• pp.41-59
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• 2011

Given the importance of algebra in the early grades, this paper analyzed the contents of whole numbers and their operations from the perspectives of generalized arithmetic. In particular, the focus of analysis was given to the properties of 0 and 1, those of operations such as commutativity, associativity, and distributivity, and the relations between operations. As such, this paper analyzed in detail how such properties and relations were introduced and expanded across different grades. It is expected that many issues in this paper will serve basic information to develop instructional materials in a way to fostering students' algebraic thinking in the elementary grades.

• Journal of Gifted/Talented Education
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• v.7 no.1
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• pp.51-76
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• 1997

The purpose of this study was to investigate the effects of Structure of Intellect( SOI) program for children. To achieve this purpose, 81 second grade children were sampled in a elementary school located In Seoul-city and randomly assigned to the experimental group and control group The SO1 training program were treated to the experimental group for 10 weeks, and the 'Thinking Abilities Test developed by Korea Creativity Research Institute were administered to them for pre-test and post-test. The collected data were analyzed by t-test for comparing the group means of experimental group and control group 'I'he results of this study were as follows : Firstly ere were statistically significant differences between experimental group and control group on the post-test scores of arithmetic[t(79)=2.73p,< .01] and visual memory[t(79)-3.68,p <.001]. The mean scores of experimental group(M=8.63) u ere higher than that of control group(Mz7.34) on arithmetic, and the mean scores to experimental group(M=16.68) were higher than that of control group(M=15 32) on visual memory Secondly there were no statistically significant differences between experimental group and control group on the post-test scores of logistic thinking abilities[t(79)=0.22, p>.05] and abstract thinking abilities[t(79)-0.22, p>.051. Thirdly, the post-test scores of visual memory and logical thinking abilities were more increased in the low intelligence group than the high intelligence group. This result showed that the SO1 program were more effective for the low intelligence group. Fourthly, the post-test scores of visual memory and logical thinking abilities were more increased in the low achievement group than the high achievement group. This result showed that the SO1 program were more effective for the low achievement group.

• The Mathematical Education
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• v.40 no.2
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• pp.335-343
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• 2001

Algebra is important part of mathematics education. Recent days, many mathematics educators emphasize on real world situation. Form real situation, pupils make sense of concepts, and mathematize it by reflective thinking. After that they formalize the concepts in abstract. For example, operation in numbers develops these course. Operation in natural number is an arithmetic, but operation on real number is algebra. Transition from arithmetic to algebra has the cutting point in representing the concepts to mathematics sign system. In this note, we see the cognitive tendency of 10th grade about operation of real number, their cutting point of transition from arithmetic to algebra, and show some methods of helping pupils.

• Journal for History of Mathematics
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• v.12 no.2
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• pp.99-118
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• 1999

This study aims to find the significance of the ancient Egyptian arithmetic in mathematics education and to analyze the educational value by practical teaching of the Egyptian multiplication. In this study, we confirmed that application of historical materials in mathematics instruction enable students to awaken their interest, to offer the opportunities of exploration, and furthermore to develop their mathematical thinking ability.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.4
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• pp.655-676
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• 2016

The purpose of this study is to examine the effects of teaching on functional thinking, one of the algebraic thinking in sixth grade students level. For this study, we developed functional thinking based-teaching through analyzing mathematical curriculum and preceding research, which consisted of 12 classes, and we investigated the effects of teaching through quantitative and qualitative analysis. In the results of this study, functional thinking based-teaching was statistically proven to be more effective in improving algebraic reasoning skills and lower elements which is an algebraic reasoning as generalized arithmetic and functional thinking, compared to traditional textbook-centered lessons. In addition, the functional thinking based-teaching gave a positive impact on the functional thinking level. Thus functional thinking based-teaching provides guidance on the implications for teaching and learning methods and study of the functional thinking in the future, because of the significant impact on the mathematics learning in six grade students.

• International journal of advanced smart convergence
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• v.6 no.2
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• pp.24-33
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• 2017

Since 'teaching coding' or 'programming' classes for computational thinking (CT) education in K-12 are renowned around the world, a pre-service teachers' readiness for integrating CT into their teaching subjects is important due to the fact that CT is considered to be another 'R' from algoRitm for 21st century literacy, in addition to the traditional 3R (Reading, Writhing, and Arithmetic) [2] and CT roles to other disciplines. With this rationale, we designed a guided instruction based CT course for pre-service teachers. We show the effectiveness of the program with respect to the teachers' attitude toward combining CT into their teaching subjects, and mindset changes of learning computing connected with the career development of the teacher themselves. The research focused on the instructional methodology of teaching programing for non-Computer Science Education (CSE) majors who are not familiar with computer science for alleviating the cognitive load of first exposure to programming course under the CT concepts.

• Education of Primary School Mathematics
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• v.14 no.3
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• pp.261-275
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• 2011

We observed the process for solving linear equations of two 5th grade elementary students, who do not have any pre-knowledge about solving linear equation. The way of students' usage of fractional schemes and manipulations are closely observed. The change of their scheme adaptation are carefully analyzed while the coefficients and constants become complicated. The results showed that they used various fractional scheme and manipulations according to the coefficients and constants. Noticeably, they used repeating fractional schemes to establish the equivalence relation between unknowns and the given quantities. After establishing the relationship, equivalent fractions played important role. We expect the results of this study would help shorten the gap between the arithmetic and the algebraic thinking.

• Education of Primary School Mathematics
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• v.27 no.3
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• pp.281-301
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• 2024

Many students have experienced difficulties due to the discontinuity in instruction between arithmetic and algebra, and in the field of elementary education, algebra is often treated somewhat implicitly. However, algebra must be learned as algebraic thinking in accordance with the developmental stage at the elementary level through the expansion of numerical systems, principles, and thinking. In this study, algebraic thinking-based classes were developed and conducted for 6th graders in elementary school, and the effect on the ability to solve word-problems in fraction division was analyzed. During the 11 instructional sessions, the students generalized the solution by exploring the relationship between the dividend and the divisor, and further explored generalized representations applicable to all cases. The results of the study confirmed that algebraic thinking-based classes have positive effects on their ability to solve fractional division word-problems. In the problem-solving process, algebraic thinking elements such as symbolization, generalization, reasoning, and justification appeared, with students discovering various mathematical ideas and structures, and using them to solve problems Based on the research results, we induced some implications for early algebraic guidance in elementary school mathematics.

• Journal for History of Mathematics
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• v.16 no.3
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• pp.89-94
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• 2003

Though the concept of unique factorization was formulated in tile 19th century, Euclid already had considered the prime factorization of natural numbers, so called tile fundamental theorem of arithmetic. The unique factorization of algebraic integers was a crucial problem in solving elliptic equations and the Fermat Last Problem in tile 19th century On the other hand the unique factorization of the formal power series ring were a critical problem in the past century. Unique factorization is one of the idealistic condition in computation and prime elements and prime ideals are vital ingredients in thinking and solving problems.

• Communications of Mathematical Education
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• v.22 no.2
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• pp.137-164
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• 2008

Given the importance of early experience in algebraic thinking, we designed six consecutive lessons in which $4^{th}$ graders were encouraged to recognize patterns in the process of finding the relationships between two quantities and to represent a given problem with various mathematical models. The results showed that students were able to recognize patterns through concrete activities with manipulative materials and employ various mathematical models to represent a given problem situation. While students were able to represent a problem situation with algebraic expressions, they had difficulties in using the equal sign and letters for the unknown value while they attempted to generalize a pattern. This paper concludes with some implications on how to connect algebraic thinking with students' arithmetic or informal thinking in a meaningful way, and how to approach algebra at the elementary school level.