• Korean Journal of Child Studies
• /
• v.14 no.1
• /
• pp.23-37
• /
• 1993

The purpose of this study was to examine the development of rational counting, addition and subtraction competence and the correlation between competence in rational counting, addition, and subtraction in three-, four- and five-year-old children. The subjects were 156 preschoolers living in Seoul. The experimental materials consisted of a set of 20 props for rational counting, addition, and subtraction tasks. The addition and subtraction tasks each consisted of a set of 6 problems. The data were analyzed by ANOVA, Duncan multiple range test, and Pearson's r. The results indicated that 1) there were significant differences in the development of competence in rational counting, addition, and subtraction by age, 2) there were no significant differences in competence in rational counting, addition, and subtraction by gender, 3) there were positively high correlations of competence rational counting, addition, and subtraction by age.

• Journal of Educational Research in Mathematics
• /
• v.19 no.2
• /
• pp.307-319
• /
• 2009

Current school mathematics introduces addition/subtraction between natural numbers, fractions, decimal fractions, and square roots, step-by-step in order. It seems that, however, school mathematics focuses too much on learning the calculation method of addition/subtraction between each stages of numbers, to lead most of students to understand the coherent principle, lying in addition/subtraction algorithm between real numbers in all. This paper raises questions on this problematic approach of current school mathematics, in learning addition/subtraction. This paper intends to clarify the fact that, if we recognize addition/subtraction between numbers from the viewpoint of 'measuring' and 'common measure', as Dewey did when he argued that the psychological origin of the concept of number was measuring, then we could find some common principles of addition/subtraction operation, beyond the superficial differences among algorithms of addition/subtraction between each stages of numbers. At the end, this paper suggests the necessity of improving the methods of learning addition/subtraction in current school mathematics.

• Education of Primary School Mathematics
• /
• v.27 no.2
• /
• pp.187-198
• /
• 2024

The addition and subtraction relationship and the multiplication and division relationship are explicitly dealt with in second and third grade mathematics textbooks. However, these relationships are not discussed anymore in the problem situations and activities in the 4th, 5th, and 6th grade mathematics textbooks. In this study, we investigate the calculation principles of subtraction and division in the elementary school mathematics textbooks. Based on our investigation, we justify the addition and subtraction relationship and the multiplication and division relationship at the level of children's understanding so that we discuss some problem situations and activities where the relationships can be applied to subtraction and division. In addition, we suggest educational implications that can be obtained from children's applying the relationships and the properties of equations to subtraction and division.

• School Mathematics
• /
• v.19 no.1
• /
• pp.137-151
• /
• 2017

This study aims to investigate the possibility of elementary students' generalization from three-digit numbers to multi-digit numbers in principles for addition and subtraction. One of main changes was the reduction of range of numbers for addition and subtraction from four-digit to three-digit. It was hypothesized that the students could generalize the principles of addition and subtraction after learning the three-digit addition and subtraction. To achieve the purpose of this study, we selected two groups as a sampling. One is called 'group 2015' who learned four-digit addition and subtraction and the other is called 'group 2016' who learned addition and subtraction only to three-digit. Because of the particularity of these subjects, this study covered two years 2015~2016. We applied our addition and subtraction test which contains ten three-digit or four-digit addition and subtraction items, respectively. We collected their results of the test and analyzed their differences using t-test. The results showed statistically meaningful difference between the mean score of the two groups only for four-digit subtraction. Based on the result, we discussed and made some didactical suggestions for teaching multi-digit addition and subtraction.

• International Journal of Advanced Culture Technology
• /
• v.6 no.3
• /
• pp.117-128
• /
• 2018

This study attempts to derive the possibility of literary therapy through addition and subtraction of emotional codons. It is presumed that the remnants of the emotions formed by the addition and subtraction of emotions will remain in the human body and cause chemical reactions. When this research is activated, cluster of emotional codons will be created by a combination of literary emotions. This is expected to accelerate therapeutic action of sentences by encoding certain emotional codons in AI.

• Communications of Mathematical Education
• /
• v.36 no.2
• /
• pp.229-252
• /
• 2022

This study analyzed the introduction of addition and subtraction, including the composition and decomposition of numbers in the Korean, Singaporean, American, and Japanese elementary mathematics textbooks. The analytic foci of this study included visual models and their connections with the given problem contexts, the introduction of addition/subtraction or addition/subtraction sentences and their connections with the visual models, and additional activities for students to develop a relational understanding of the equal sign. The results of the analysis demonstrated diverse connections, mainly because the problem contexts, visual models, and the introduction of addition/subtraction or addition/subtraction sentences were implemented differently for each textbook. There were differences among the textbooks in what order of problem contexts were presented. Regarding the use of visual models, two textbooks tended to use one model consistently, whereas the other textbooks used various models depending on the problem contexts. There were subtle but significant differences in introducing addition/subtraction or addition/subtraction sentences. For a relational understanding of the equal sign, all textbooks included activities emphasizing that both sides of the equal sign are equal. Based on the results of this study, this paper closes with several implications related to the problem contexts to introduce addition/subtraction and addition/subtraction sentences as well as the use of visual models, which can serve as a basis for a new unit for the subsequent textbook.

• Communications of Mathematical Education
• /
• v.23 no.3
• /
• pp.707-734
• /
• 2009

The purpose of the study was to investigate how children understand addition and subtraction of fractions and how their understanding influences the solutions of fractional word problems. Twenty students from 4th to 6th grades were involved in the study. Children's understanding of operations with fractions was categorized into "joining", "combine" and "computational procedures (of fraction addition)" for additions, "taking away", "comparison" and "computational procedures (of fraction subtraction)" for subtractions. Most children understood additions as combining two distinct sets and subtractions as removing a subset from a given set. In addition, whether fractions had common denominators or not did not affect how they interpret operations with fractions. Some children understood the meanings for addition and subtraction of fractions as computational procedures of each operation without associating these operations with the particular situations (e.g. joining, taking away). More children understood addition and subtraction of fractions as a computational procedure when two fractions had different denominators. In case of addition, children's semantic structure of fractional addition did not influence how they solve the word problems. Furthermore, we could not find any common features among children with the same understanding of fractional addition while solving the fractional word problems. In case of subtraction, on the other hand, most children revealed a tendency to solve the word problems based on their semantic structure of the fractional subtraction. Children with the same understanding of fractional subtraction showed some commonalities while solving word problems in comparison to solving word problems involving addition of fractions. Particularly, some children who understood the meaning for addition and subtraction of fractions as computational procedures of each operation could not successfully solve the word problems with fractions compared to other children.

• Honam Mathematical Journal
• /
• v.30 no.2
• /
• pp.247-258
• /
• 2008

In this paper, we show how certain topologies associate with ideals of subtraction algebras on subtraction algebras. We show subtraction algebras to be topological subtraction algebras with respect to theses topologies. Furthermore, we show how certain standard properties may arise. In addition we demonstrate that it is natural for these topologies to have many clop en sets and thus to be highly disconnected via the ideal theory of subtraction algebras.

• School Mathematics
• /
• v.18 no.1
• /
• pp.175-191
• /
• 2016

In the elementary school mathematics textbook that has been revised in 2013, the instructional sequence for teaching addition and subtraction, which had remained unchanged for three decades since 1982, was finally changed in 2013. Particularly, the addition and subtraction of two-digit numbers without regrouping, such as 72+25=97 or 85-24=61, are taught earlier than the composing and decomposing of the number 10 using other numbers. This study examines the appropriacy and validity of these changes. However, the reason for these changes in the national curriculum or teacher's guide could not be determined. Further, several references emphasize the addition of two single-digit numbers, such as 7+8=15, and the subtraction of a single-digit number from a number between 11 and 19, such as 16-9=7, as basic facts. In other countries' textbooks, the teaching of addition and subtraction up to the number 20 is prioritized before teaching the addition and subtraction of two-digit numbers without regrouping. The results of this study indicate that these changes in the instructional sequence in the textbook that was revised in 2013 need to be reconsidered.

• Proceedings of the Korea Society of Design Studies Conference
• /
• 2001.05a
• /
• pp.20-21
• /
• 2001