• Journal for History of Mathematics
• /
• v.20 no.4
• /
• pp.23-48
• /
• 2007

This study begins from posing a problem, 'formal introduction of mathematical induction in school mathematics'. Most students may learn the mathematical induction at the level of instrumental understanding without meaningful understanding about its meaning and structure. To improve this didactical situation, we research on the historical progress of mathematical induction from implicit use in greek mathematics to formalization by Pascal and Fermat. And we identify various types of thinking included in the developmental process: recursion, regression, analytic thinking, synthetic thinking. In special, we focused on the role of regression in mathematical induction, and then from that role we induce the implications for teaching mathematical induction in school mathematics.

• Journal of Educational Research in Mathematics
• /
• v.21 no.2
• /
• pp.181-199
• /
• 2011

The area formula for a plane figure represents the relations between the area and the lengths which determine the area of the figure. Students are supposed to understand the relations in it as well as to be able to find the area of a figure using the formula. This study investigates how 5th grade students understand the formulas for the area of triangle, rectangle and parallelogram, focusing on their understanding of functional relations in the formulas. The results show that students have insufficient understanding of the relations in the area formula, especially in the formula for the area of a triangle. Solving the problems assigned to them, students developed three types of strategies: Substituting numbers in the area formula, drawing and transforming figures, reasoning based on the relations between the variables in the formula. Substituting numbers in the formula and drawing and transforming figures were the preferred strategies of students. Only a few students tried to solve the problems by reasoning based on the relations between the variables in the formula. Only a few students were able to aware of the proportional relations between the area and the base, or the area and the height and no one was aware of the inverse relation between the base and the height.

• School Mathematics
• /
• v.19 no.3
• /
• pp.533-551
• /
• 2017

The statistical education researchers advise instructors to educate informal statistical inference and they are paying close attention to the progress of the statistical inference in general. This study was conducted by analyzing the levels and the traits of each levels of the informal statistical inference of the middle and high school students for comparing the samples of data and estimating the graph of a population. Research has shown that five levels of the informal statistical inference were identified for comparing the samples of data: responses that are distracted or misled by an irrelevant aspect, responses that focus on frequencies of individual data points and hold a local view of the sample data sets, responses that the student's view of the data is transitioning from local to global, responses that hold a global view but do not clearly integrate multiple aspects of the distribution, and responses that integrate multiple aspects of the distribution. Another five levels of the informal statistical inference were identified for estimating the graph of a population: responses that are distracted or misled by an irrelevant aspect, responses that focus only on representativeness, responses that consider both representativeness and variability and focus on one particular aspect of the distribution, responses that focus on multiple aspects of distribution but do not clearly integrate them, and responses that integrate multiple aspects of the distribution.

• Journal for History of Mathematics
• /
• v.22 no.3
• /
• pp.31-44
• /
• 2009

Anyone wishing to understand cognitive science, a converging science, need to become familiar with three major mathematical landmarks: Turing machines, Neural networks, and $G\ddot{o}del's$ incompleteness theorems. The present paper aims to explore the mathematical foundations of cognitive science, focusing especially on these historical landmarks. We begin by considering cognitive science as a metamathematics. The following parts addresses two mathematical models for cognitive systems; Turing machines as the computer system and Neural networks as the brain system. The last part investigates $G\ddot{o}del's$ achievements in cognitive science and its implications for the future of cognitive science.

• School Mathematics
• /
• v.6 no.2
• /
• pp.119-134
• /
• 2004

China becomes more and more important for Koreans in political and social aspects as well as in educational aspect. However, there hasn't been any study regarding the mathematics curriculum of China. Thus, it is necessary to introduce the recent mathematics curriculum of China, compare the curriculum of China with that of Korea, and find the features of the curriculum. Several characteristics of the mathematics curriculum of China were identified; 1) mathematics strands were combined, 2) condensed and linear structure of contents, 3) providing examples for mathematics topics stated in the curriculum, and etc. Based on these characteristics, some implications were elicited for the next mathematics curriculum revision in Korea.

• Journal of the Korean School Mathematics Society
• /
• v.18 no.1
• /
• pp.15-37
• /
• 2015

As the value and importance of mathematical communication was recognized, mathematical communication in mathematics education has been strengthened more and more. Written communication as well as verbal communication is emphasized. On the other hand, storytelling is introduced for elementary students to learn mathematical concept more naturally and easily in the 2009 revised curriculum. So, we noticed that they are familiar with story. In this study, we analyze the story writing activity levels with a focus on story writing, and how to think about it. And we offer some suggestions about mathematical story writing activity.

• Journal of the Korean School Mathematics Society
• /
• v.24 no.1
• /
• pp.39-57
• /
• 2021

In this study, mathematical analysis is conducted by focusing to the 'size' of the 'point' and the 'line'. The textbook descriptions of the 'point' and the 'line' in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum and US geometry textbooks were compared and analyzed between. First, as a result of mathematical analysis of' 'the size of a point and a segment', it was found that the mathematical perspectives could be different according to 1) the size of a point is based on the recognition and exclusion of 'infinitesimal', and 2) the size of the segment is based on the 'measure theory' and 'set theory'. Second, as a result of analyzing textbook descriptions of the 'point' and the 'line', 1) in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum, after presenting a learning activity that draws a point with 'physical size' or line, it was developed in a way that describes the 'relationship' between points and lines, but 2) most of the US geometry textbooks introduce points and lines as 'undefined terms' and explicitly states that 'points have no size' and 'lines have no thickness'. Since the description of points and lines in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum may potentially generate mathematical intuitions that do not correspond to the perspective of Euclid geometry, this study suggest that attention is needed in the learning process about points and lines.

• Communications of Mathematical Education
• /
• v.37 no.3
• /
• pp.369-392
• /
• 2023

Equity in mathematics education focuses on the relationship between social inequality caused by factors including culture and race. Equity in mathematics education has recently been recognized as one of the important issues of mathematics education and may provide grounds for setting the new direction of mathematics education for the future society. However, research on mathematics education equity in South Korea is still insufficient. The purpose of the paper is to provide implications for mathematics education research by reviewing the the literature regarding mathematics education equity. Focusing on 195 previous studies, I analyzed the significance of discussions on mathematics education equity in mathematics education, the concept of mathematics education equity, and research questions. In addition, I divided the previous studies into five categories based on their research questions: mathematics teachers, mathematics curriculum, mathematics classrooms, mathematics assessment, and socio-cultural environments surrounding mathematics classrooms. The analysis of the study are expected to provide implications in terms of new research questions and methods to domestic mathematics education researchers.

• Journal for History of Mathematics
• /
• v.20 no.2
• /
• pp.19-32
• /
• 2007

This Paper aims to introduce Euler's life, works and thoughts, to show that it is his Christian worldview that enables his achievements. His life teaches us the lesson that examining philosophical base and historical background is crucial to understand mathematics or mathematicians, and that it is necessary to overcome given conditions and environments rather than expect better environments to reach meaningful achievements.

• Journal of Educational Research in Mathematics
• /
• v.24 no.4
• /
• pp.645-668
• /
• 2014

This study was designed to gain insights into contemporary secondary mathematics curriculum revision in Korea. The two secondary mathematics curriculum reports submitted in the 1920s, the Kilpatrick Reports and 1923 Reports were compared and contrasted as the origin of recent math wars, and their backgrounds, committee members, viewpoints of math and math education and contents were analyzed to understand the perspectives of the two extreeme parts. Kilpatrick Reports was selected at that time, but nevertheless 1923 Report had taken a role of guiding secondary mathematics in US until the New Math era. The direction and process of mathematics curriculum revision were suggested based on the analysis of reports' short- and long-term influences. A close examination of the curriculum revision process in US and in Korea and the implications from the results are also included in the suggestion.