• Research in Mathematical Education
• /
• v.7 no.1
• /
• pp.1-10
• /
• 2003

This research reviewed literatures on proof in mathematics education. Several views of proof can be classified (and identified) such as psychological approach (Platonism, empiricism), structural approach (logicism, formalism, intuitionism) and social approach (ontology, axiomatic systems). All these views of proof are valuable in mathematics education society. The concept of proof can be found in the form of analytic knowledge not of constructive knowledge. Human beings developed their knowledge in the sequence of constructive knowledge to analytic knowledge. Therefore, in mathematics education, the curriculum of mathematics should involve the process of cognitive knowledge development.

• The Mathematical Education
• /
• v.39 no.1
• /
• pp.1-9
• /
• 2000

Now, mathematics textbook is being developed in accordance with the 7th educational curriculum. It is expected that qualified textbook reflecting 'differentiated education' concept be developed and published. But there are still many limitations of textbook authorization system to develop 'such' textbook. Many authors of textbook have difficulty in developing creative and qualified textbooks in their own way. In this paper, we deal with what the authors should keep in mind and could reflect related on textbook authorization system in developing textbook. For this purpose, focusing on new 'content principle' of mathematics textbook authorization, the paper presented its educational background.

• Journal of the Korean Chemical Society
• /
• v.67 no.5
• /
• pp.319-332
• /
• 2023

Ever since the development of the Guide to the Expression of Uncertainty in Measurement (GUM) in 1993, the concept of measurement uncertainty has been considered a core concept in metrology and the importance of proper uncertainty evaluation has continuously been increasing. Unfortunately, few papers in Korean are available that introduce the concept of measurement uncertainty and the GUM correctly and in sufficient detail. This review describes in detail the mathematical, historical, and philosophical background behind the concept of measurement uncertainty and the GUM, and also discusses some special aspects of uncertainty evaluation in chemical analysis.

• The Mathematical Education
• /
• v.40 no.1
• /
• pp.15-25
• /
• 2001

The purpose of this thesis is to search the situation of an outbreak of the fallacy and methods of its treatment. We regard intuition as origins of genuine knowledge, but it sometimes raises the fallacy by intrinsic characters of itself. It makes an examination of the fallacy of the sense of sight like an optical illusion to instance that of sense. The sense of sight is an important factor in an intuitive cognition. However, its activity without thinking raises the fallacy of intuition in the process to observe and judge the things. I point out the fallacy of intuition which originates from terms and concepts in mathematical problems. The concept of mean velocity is representative. In this case, students make a mistake which means velocity can be solved by dividing the sum of v$_1$ and v$_2$ into two. The methods which overcome the fallacy of intuition are balance of intuition and logic, overcome of functional fixedness, the development of intuitive models and the development of metacognitive ability.

• The Mathematical Education
• /
• v.42 no.5
• /
• pp.647-672
• /
• 2003

This study sought to determine the impact of the graphing calculator on prospective math-teachers' mathematical thinking while they engaged in the exploratory tasks. To understand students' thinking processes, two groups of three students enrolled in the college of education program participated in the study and their performances were audio-taped and described in the observers' notebooks. The results indicated that the prospective teachers got the clues in recalling the prior memory, adapting the algebraic knowledge to given problems, and finding the patterns related to data, to solve the tasks based on inductive, deductive, and creative thinking. The graphing calculator amplified the speed and accuracy of problem-solving strategies and resulted partly in students' progress to the creative thinking by their concept development.

• Research in Mathematical Education
• /
• v.10 no.3 s.27
• /
• pp.189-203
• /
• 2006

Teaching of fractions is very challengeable for elementary and middle school teachers. Many teachers feel uncomfortable teaching the subject. How shall we introduce the concept of fractions? Shall we focus more on concept development or computational procedures and skills? What methodology can be used in teaching those important topics? These are the kind of questions many teachers and researchers try to answer. In this article, the authors are to look at this issue from a cross nation perspective, by examining how the Chinese mathematics curriculum and the Chinese teachers deal with this subject.

• Research in Mathematical Education
• /
• v.25 no.3
• /
• pp.227-244
• /
• 2022

The concrete-representational-abstract integrated (CRA-I) sequence is an explicit approach for teaching students who struggle in mathematics. This approach is beneficial because it assists students in the development of conceptual understanding. This article describes how the approach is used in general as well as its use with a specific geometry concept, area of a rectangle. The author will describe why one might choose CRA-I and the steps needed for implementation. Finally, the CRA-I steps will be shown with a lesson series related to teaching the concept of area. The article will describe lesson activities, methods, materials, and procedures.

• The Mathematical Education
• /
• v.58 no.1
• /
• pp.55-77
• /
• 2019

Textbooks play a very important role as a medium for implementing curriculum in the school. This study aims to analyze tasks for mathematical competencies in the high school 'mathematics' textbooks based on the 2015 revised mathematics curriculum emphasizing competencies. And our study is based on the following two research question. 1. What is the relationship between core competencies and mathematical competencies? 2. What is the distribution of competencies of tasks for mathematical competencies presented in the textbooks? 3. How does the tasks for mathematical competencies reflect the meaning of the mathematical competencies? For this study, the tasks, marked mathematical competencies, were analyzed by elements of each mathematical competencies based on those concept proposed by basic research for the development of the latest mathematics curriculum. The implications of the study are as follows. First, it is necessary to make efforts to strengthen the connection with core competencies while making the most of characteristics of subject(mathematics). Second, it needs to refine the textbook authorization standards, and it should be utilized as an opportunity to improve the textbook. Third, in order to realize competencies-centered education in the school, there should be development of teaching and learning materials that can be used directly.

• Communications of Mathematical Education
• /
• v.32 no.2
• /
• pp.131-146
• /
• 2018

Differentiation with integration is an important subject which is widely applied in mathematics, natural science, and engineering. Derivative is an important concept of differentiation. But students don't understand its concept well and concentrate on acquiring only the skill to solve the standardized calculus problem. So they are poor at understanding of the concept of differentiation. In this study, after making a survey of differentiation on college students, we try to analyze errors which appeared in solving differentiation problem and investigate mathematics process of limiting process inherent in the derivative and historical development about derivative. Thus, we try to analyze the understanding of differentiation and present the results about this.

• The Mathematical Education
• /
• v.40 no.1
• /
• pp.93-102
• /
• 2001

The world we live in is called the age of information. Thus communication and computers are doing the central role in it. When one studies the mathematical problem, the use of tools such as computers, calculators and technology is available for all students, and then students are actively engaged in reasoning, communicating, problem solving, and making connections with mathematics, between mathematics and other disciplines. The use of technology extends to include computer algebra systems, spreadsheets, dynamic geometry software and the Internet and help active learning of students by analyzing data and realizing mathematical models visually. In this paper, we explain concepts of transformation, linear transformation, congruence transformation and homothety, and introduce interesting, meaningful and visual models for teaching of a plane transformation geomeoy which are obtained by using Mathematica. Moreover, this study will show how to visualize linear transformation for student's better understanding in teaching a plane transformation geometry in classroom. New development of these kinds of teaching-learning methods can simulate student's curiosity about mathematics and their interest. Therefore these models will give teachers the active teaching and also give students the successful loaming for obtaining the concept of linear transformation.