• 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.

• Journal of Elementary Mathematics Education in Korea
• /
• v.3 no.1
• /
• pp.21-39
• /
• 1999

In this paper, we first exam the relation between Piaget's theory of cognitive development and cognitive constructivism. With it's outcome We find three principles of constructivist teaching-learning methods for primary mathematics These are as follows 1) active learning based on self-regulatory process 2) empirical learning by self initiated activities 3) individual learning derived from present cognitive structure and fits of new experiences. Finally we introduce several examples for classroom practice applied the above principles in primary mathematics.

• The Journal of the Korea Contents Association
• /
• v.17 no.9
• /
• pp.437-448
• /
• 2017

This study was conducted as a qualitative case study for examining what transformed primary concepts and transformed schemas were formed for the addition of decimals and how they were formed, and how the relational understanding of the addition of decimals was in three 3rd grade elementary school children who had studied the primary concepts of division, fraction and decimal. That is, this study investigated how the subjects approached problems of decimal addition using transformed primary concepts and transformed schemas formed by themselves, and how the subjects formed concepts and transformed schemas in problem solving. According to the results of this study, transformed primary concepts and transformed schemas formed through the learning of the primary concepts of division, fraction, and decimal functioned as important factors for the relational understanding of decimal addition.

• Journal of Educational Research in Mathematics
• /
• v.13 no.4
• /
• pp.447-462
• /
• 2003

The purpose of this study was to Investigate the preservice elementary teachers' pedagogical content knowledge of addition and subtraction. The subjects for data collection were 29 preservice elementary teachers and data were collected through open ended problems. The findings imply that the preservice elementary teachers show low level of understanding of addition and subtraction such as the word problem posing and the contexts of part-part-whole and compare. The research results indicate that the preservice elementary teachers possess primarily a procedural knowledge of pedagogical content knowledge and don't understand relationship with real-world situation. This study provide the information available on developing program for preservice elementary teachers.

• Communications of Mathematical Education
• /
• v.37 no.3
• /
• pp.419-442
• /
• 2023

This study investigated fifth graders' understanding of variables from a generalized arithmetic and a functional perspectives of early algebra. Specifically, regarding a generalized perspective, we included the property of 1, the commutative property of addition, the associative property of multiplication, and a problem context with indeterminate quantities. Regarding the functional perspective, we covered additive, multiplicative, squaring, and linear relationships. A total of 246 students from 11 schools participated in this study. The results showed that most students could find specific values for variables and understood that equations involving variables could be rewritten using different symbols. However, they struggled to generalize problem situations involving indeterminate quantities to equations with variables. They also tended to think that variables used in representing the property of 1 and the commutative property of addition could only be natural numbers, and about 25% of the students thought that variables were fixed to a single number. Based on these findings, this paper suggests implications for elementary school students' understanding and teaching of variables.

• Journal of Gifted/Talented Education
• /
• v.24 no.1
• /
• pp.17-43
• /
• 2014

On the subjects of elementary 3rd grade three child prodigies who had learned the four fundamental arithmetic operations and primary concepts of fraction, this study conducted a qualitative case research to examine how they composed schema of addition and multiplication of fractions and transformed schema through recognition of precise concepts and linking of concepts with addition and multiplication of fractions as the contents. That is to say, this study investigates what schema and transformed schema child prodigies form through composition of primary mathematic concepts to succeed in relational understanding of addition and multiplication of fractions, how they use their own formed schema and transformed schema for themselves to approach solutions to problems with addition and multiplication of fractions, and how the subjects' concept formation and schema in their problem solving competence proceed to carry out transformations. As a result, we can tell that precise recognition of primary concepts, schema, and transformed schema work as crucial factors when addition of fractions is associated with multiplication of fractions, and then that the schema and transformed schema that result from the connection among primary mathematic concepts and the precise recognition of the primary concepts play more important roles than any other factors in creative problem solving with respect to addition and multiplication of fractions.

• Journal of the Institute of Electronics Engineers of Korea SD
• /
• v.45 no.2
• /
• pp.44-48
• /
• 2008

According to increment of stage, the speed of changeable stage Carry-increment adder can be close to $O(\sqrt{2n})$ because the word length which is computed in stage can be lengthened by 1 bit. But the number of stage bits is increased, fan-out of carry which is inputted in stage is increased. So tile speed can be slow. This paper presents a new carry-increment adder design method to fix the number of fan-outs regardless of the number of stages. By layout simulation of 37-bit adder, the area can be Increased up to 40%, but speed improvement up to 75% can be achieved, by the proposed method, compared with a conventional method.

• 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.

• Lingua Humanitatis
• /
• v.1 no.1
• /
• pp.235-251
• /
• 2001

According to Chomskyan grammar, humans can generate and understand an unbounded number of grammatical sentences. Against the background of pure and idealized linguistic competence, this linguistic productivity is argued and understood. In actual utterances, however, there are many limitations of productivity but they are said to come from the general constraints on performances such as capacity of short term memory or attention. In this paper I discuss a problem raised against idealized productivity. I argue that linguistic productivity idealizes our linguistic competence too much. By separating idealized competence from the various constraints of performance, Chomskyan theorists can argue for unlimited productivity. However, the absolute distinction between grammar (pure competence) and parser (actual psychological processes) makes little sense when we explain the low acceptability(intelligibility) of center embedded sentences. Usually, the problem of center embedded sentence is explained in terms of memory shortage or other performance constraints. To explain the low acceptability, however, we need to assume specialized memory structure because the low acceptability occurs only with a specific type of syntactic pattern. 1 argue that this special memory structure should not be considered as a general performance constraint. It is a domain specific (specifically linguistic) constraints and an intrinsic part of human language processing. Recent development of Chomskyan grammar, i.e., minimalist approach seems to close the gap between pure competence and this type of specialized constraints. Chomsky's earlier approach of generative grammar focuses on end result of the generative derivation. However, economy principle (of minimalist approach) focuses on actual derivational processes. By having less mathematical or less idealized grammar, we can come closer to the actual computational processes that build syntactic structure of a sentence. In this way, we can have a more concrete picture of our linguistic competence, competence that is not detached from actual computational processes.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.12 no.3
• /
• pp.239-253
• /
• 1987

By the extension and the modification of the efficient aigorithms for the DCT-III, the fast algorithms to compute three versions for DCT, four versions of DST, and a DHT are developed. It is shown that the algorithms developed in this paper have simple structures and the numbers of multipication and addition are reduced as comparies with the existing efficient algorithms. The algorithms presentes in this paper indicate the close relationship amng different versions of the DCT and DST as well as a DHT. The formulas to compute the numbers of multiplication and addition of them are derived.