• Education of Primary School Mathematics
• /
• v.22 no.4
• /
• pp.223-237
• /
• 2019

There is a close interaction between the linguistic-syntactic representation system and the affective representation system that appear in the mathematical process. On the other hand, since the mathematical conceptual system is fundamentally metaphoric, the analysis of the mathematical concept structure through linguistic representation can help to identify the source of cognitive and affective obstacles that interfere with mathematics learning. In this study, we analyzed the problem-solving protocols of mathematical gifted children from the perspective of cognitive language and meta-affect to identify the relationship between the functional characteristics of the text and metaphor they use and the functional characteristics of meta-affect. As a result, the behavior of the cognitive and affective characteristics of mathematically gifted children differed according to the success of problem solving. In the case of unsuccessful problem-solving, the use of metaphor as an internal representation system was relatively more frequent than in the successful case. In addition, while the cognitive linguistic aspects of metaphors play an important role in problem-solving, meta-affective attributes are closely related to the external representation of metaphors.

• School Mathematics
• /
• v.7 no.1
• /
• pp.55-75
• /
• 2005

Mathematical symbolizing is an important part of mathematics learning. But many students have difficulties m symbolizing mathematical ideas formally. If students had experiences inventing their own mathematical symbols and developing them to conventional ones natural way, i.e. learning mathematical symbols via expressive approaches, they could understand and use formal mathematical symbols meaningfully. These experiences are especially valuable for students who meet mathematical symbols for the first time. Hence, there are needs to investigate how early elementary school students can and should experience meaningful mathematical symbolizing. The purpose of this study was to analyze students' mathematical symbolizing processes and characteristics of theses. We carried out teaching experiments that promoted meaningful mathematical symbolizing among eight first graders. And then we analyzed students' symbolizing processes and characteristics of expressive approaches to mathematical symbols in early elementary students. As a result, we could places mathematical symbolizing processes developed in the teaching experiments under five categories. And we extracted and discussed several characteristics of early elementary students' meaningful mathematical symbolizing processes.

• Education of Primary School Mathematics
• /
• v.27 no.2
• /
• pp.139-153
• /
• 2024

This analysis was intended to present pedagogical implications related to the guidance of solid figures in elementary mathematics textbooks. The definitions of mathematical concepts and visually represented examples presented in the prism and pyramid units were analyzed. As a result of the analysis, differences were observed in both the method and content of defining mathematical concepts, even though the same curriculum was reflected. Additionally, various forms of visual examples were provided during the learning process of prisms and pyramids. Based on the results of this analysis, it is necessary to understand the definition of mathematical concepts and to teach students in an appropriate manner, considering the goals of each session and the objectives of the activities involved in presenting visual examples.

• Journal of the Korean School Mathematics Society
• /
• v.20 no.3
• /
• pp.211-237
• /
• 2017

Depending on the type of textbook, the word and mathematical notation expression used in high school mathematics textbooks varied and there were also some differences on the mathematical definition and the content description methods. Not only the composition of textbooks but also various expressing ways of textbooks have significant impacts on teaching and learning of teacher and student. The diversity of expression had pros and cons like both sides of a coin. There is a positive aspect that we can pursue pedagogical diversity. Simultaneously there is a negative aspect that the possibility of acting as a learning burden exists in the viewpoint of the student and the equality of evaluation may be undermined. In this study, Preferentially we focused on analyzing the actual situation rather than judging what is more appropriate about the diversity of words and notation expressions used in mathematics textbooks which is based on the current curriculum. For this purpose, we analyzed 56 kinds of mathematics textbooks based on the 2009 revised mathematics curriculum, and presented four aspects(terms expressing, notations expression, mathematical definition, content description method) with examples about differences of the various expressions used in textbooks including 'terms and notations'.

• Journal of the Korean School Mathematics Society
• /
• v.23 no.1
• /
• pp.25-44
• /
• 2020

This study investigated the representation and algorithms of western mathematics reflected on the algebra domains of Chosun-Sanhak in the 18th century. I also analyzed the co-occurrences and replacement phenomenon between western algorithms and traditional algorithms. For this purpose, I analyzed nine Chosun mathematics books in the 18th century, including Gusuryak and Gosasibijip. The results of this study are as follows. First, I identified the process of changing to a calculation by writing of western mathematics, from traditional four arithmetical operations using Sandae and the formalized explanation for the proportional concept and proportional expression. Second, I observed the gradual formalization of mathematical representation of the solution for a simultaneous linear equation. Lastly, I identified the change of the solution for square root from traditional Gaebangsul and Jeungseunggaebangbeop to a calculation by the writing of western mathematics.

• Journal of Korea Game Society
• /
• v.12 no.5
• /
• pp.5-12
• /
• 2012

The information represented by graphic is preferred more than by text to the game generation familiar to computer games in the cognitive style. The learning to solve the math problems represented by graphic is significantly effective to improve learner's problem-solving power in math education. In this paper, we proposed a method of graphic representation of mathematical sentences for effective learning of the game generation. The proposed method arranges the unit informations in the logical structure and represent the logical interrelation between the informations by symbols, line segments, or arrows using the graphic elements with good visibility for the game generation to recognize easily and to understand accurately the logical meaning. The proposed method is able to represent accurately the math sentences until the detail level that appears the tense and the voice of the sentences differently from the previous graphic representation method's ability. The proposed method could be used as learning tools and used widely to represent graphically mathematical informations for the instructional scaffolding of an educational game in oder that the game generation could learn effectively.

• School Mathematics
• /
• v.18 no.3
• /
• pp.647-666
• /
• 2016

This study investigates pre-service teacher's understanding of the concept and representations of irrational numbers. We classified the representations of irrational numbers into six categories; non-fraction, decimal, symbolic, geometric, point on a number line, approximation representation. The results of this study are as follows. First, pre-service teachers couldn't relate non-fractional definition and incommensurability of irrational numbers. Secondly, we observed the centralization tendency on symbolic representation and the little attention to other representations. Thirdly, pre-service teachers had more difficulty moving between symbolic representation and point on a number line representation of ${\pi}$ than that of $\sqrt{5}$ We suggested the concept of irrational numbers should be learned in relation to various representations of irrational numbers.

• Education of Primary School Mathematics
• /
• v.26 no.4
• /
• pp.257-275
• /
• 2023

In this study, we designed and implemented a instruction emphasizing mathematical argument for fifth-grade students and analyzed the teaching practices. Through a literature review related to instruction emphasizing mathematical argument, we organized a teaching model of five phases that explain why the general claim that the sum of consecutive odd numbers equals a square number is true: 1) noticing patterns, 2) articulating conjectures, 3) representing through visual model, 4) arguing based on representation, 5) comparing and contrasting. Then, we analyzed the argumentation stream by phases to observe how the instruction emphasizing mathematical argument is implemented in the elementary classroom. Based on the results of this study, we discuss the implications of teaching a mathematical argument in elementary school.

• Proceedings of the Korean Information Science Society Conference
• /
• 2012.06b
• /
• pp.312-314
• /
• 2012

본 논문은 한글로 입력된 질의어를 이용하여 웹상의 MathML (Mathematical Markup Language) 수학식을 검색하는 시스템을 제안한다. 웹상의 수학식은 과거 이미지를 이용하여 표현되는 경우가 많았지만, 현재는 대부분 MathML과 같은 수학식 표현 마크업 언어로 작성되고 있다. 그러나 이러한 수학식을 검색하기 위해서는 해당 언어를 알고 있거나 수식 입력 툴을 이용해야 하는 경우가 대부분이기 때문에, 일반 사용자들이 수학식 검색을 하는 데에는 제약점이 따랐다. 본 연구에서는 사용자들이 전통적인 검색 방법을 이용하여 특정 마크업 언어가 아닌 일반 평문으로 작성된 질의어를 입력하여 수학식을 검색 가능 하도록 하기 위해, 평문 질의어를 MathML 표현으로 변환시키는 방법을 사용한다. 질의어로 입력될 수 있는 다양한 수학식 표현을 미리 구축한 사전을 이용하여 MathML 표현으로 변환하는 간결한 기법만으로도 MRR 0.495 의 높은 성능을 얻을 수 있었다.

• Communications of Mathematical Education
• /
• v.29 no.1
• /
• pp.51-72
• /
• 2015

This study aimed to analyze the characteristic of undergraduate students' perception and preference for mathematics. For this purpose, I surveyed 124 undergraduate students' metaphorical expressions about mathematics. I classified the expressions as four categories: a positive form, a negative form, a mixed form, an undecidable form. I investigated the proportion and characteristic of the metaphorical expressions according to the above four categories. Also, I surveyed the students' preference and nonpreference moments for mathematics and categorized them into 6-cases: elementary school, middle school, high school, university, always, and none. In addition, I examined the students' preference and nonpreference reasons for mathematics and classified them according to the 5-factors: grade factor, affective factor, content factor, teacher factor, and other factors. The results of this study as follows: First, the 27% of university students expressed their metaphorical expressions for mathematics as a positive form, 42% as a negative form, and 27% as a mixed form. Also, the preference rate for mathematics was higher as their school years increase and the main reasons of preference were grade and affective factors. The result of nonpreference rate was also higher as their school year increased. Students said that the contents and grade factor were the main factors among the 5-factors.