• Journal for History of Mathematics
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• v.32 no.2
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• pp.79-93
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• 2019

Choi Yoon Sik is a person who can not be omitted when discussing the history of mathematics in Korea. He is a mathematician who led Korean mathematics community after liberation from Japan. However, he took interests in mathematics education in middle and high school also. Choi Yoon Sik should be remembered as a leading person not only in the history of mathematics but also in the history of mathematics education in Korea. Choi Yoon Sik thought that histo-genetic principle, intuitive principle, and practical principle are important in mathematics education by help of Okura Kinnosuke's view, with hope to reform the mathematics education in Korea. He also argued that mathematics has educational values.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.1
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• pp.107-121
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• 2015

The purpose of the present study is to find out some implications from comparing mathematical education of Israel and Singapore. This study examined what values are represented in schooling of both Israel and Singapore and what factors are influencing mathematics teacher education of both countries. Education in Israel and Singapore plays a significant role for the survival of the nation and economic success, and the education system is focused on elitism, especially in terms that they have selective system of students and restrictive exams from the elementary school level. The educational system in both countries provides students with little opportunities for social mobility, because students from the low SES families are not equally exposed to educational facilities and experiences. The results of this study imply that the critical factor affecting students achievement in Israel and Singapore seems to be the quality of teacher education system and the quality of teachers. In particular, it seems that we need to be very careful of uncritically adopting mathematical ideas from both Israel and Singapore, because they both have very different contexts of educational goals, educational policies, racial and cultural factors from Korea.

• Journal of Educational Research in Mathematics
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• v.27 no.4
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• pp.811-831
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• 2017

The purpose of this study is to analyze the contents of pi of Chosun-sanhak and organize the teaching and learning activities to help to understand the concept of pi deeply using the analysis results. The results of this study are as follows. First, Chosun-sanhak used various approximate values of pi and those were represented as the form to reveal the meaning of the ratio of radius and circumference. Second, There were the freedom of selection of the approximate values of pi suitably. Lastly, the enriched leaning about pi need to draw a distinction pi from approximate values of pi, choose the suitable approximate values of pi and compare the method of calculation of circumference and the area of circle of Chosun-sanhak and today's mathematics. In conclusion, I proposed several issues which is worth exploring further in relation to pi and Chosun-Sanhak.

• East Asian mathematical journal
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• v.25 no.3
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• pp.399-413
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• 2009

Whitehead's philosophy is evaluated as an applicable philosophy and an accurate, logical explanation system about the world through mathematics. Whitehead's ideological development can be divided into mathematical research, critical consciousness about sciences and philosophical exploration. Although it is presented as a whole unified conceptual framework to understand nature and human beings which is based on modern mathematics and physics in the 20th century, Whitehead's philosophy has not been sufficiently understood and evaluated about the full meaning and mathematics educational values. In this paper, we study relations of Whitehead's philosophy and the mathematical education. Moreover, we study implicity of mathematical education.

• Research in Mathematical Education
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• v.22 no.3
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• pp.153-174
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• 2019

Measuring alignment of various educational components is an important issue in educational research because with aligned educational system, we can have clear expectations about what to teach and assess. In this study, we examined the alignment between mathematics curriculum standards and college entrance examinations from Korea and China. The results indicate that curriculum standards and high stakes assessments from both countries are not well aligned to each other. Their Surveys of Enacted Curriculum (SEC) indices were lower than what previous studies have found and the critical values (Fulmer, 2011; Liu & Fulmer, 2008; Liu et al., 2009). There are several topics that are not assessed in both countries' national assessments. Also, discrepancies between the most frequently covered topics in the curriculum standards and the most frequently assessed mathematical topics in the national assessments caused topic level misalignment. We also found misalignment in cognitive level. Both national assessments included more perform procedures and demonstrate understanding items than their respective curriculum standards. Thus, previous findings about the inclusion of more items with higher cognitive demand in assessments is only partially true for either country. With these results, it is difficult to say that whether mathematical topics in the curriculum standards appropriately represent and support students to do well on the CSAT and the NCEE or that the mathematical items in the CSAT and the NCEE validly assess students' level of mathematical understanding.

• School Mathematics
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• v.9 no.2
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• pp.223-240
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• 2007

The purpose of this study was to investigate the degree to which the middle school mathematics curriculum matched the item difficulty levels of representative mathematics items. The items used in this study were developed for the National Assessment of Educational Achievement. Ranks for difficulty values of the 60 multiple-choice item were calculated via both Classical Test Theory and Item Response Theory and correlated with the rank order of the mathematics content and cognitive domains sequence. There are six content domains; number and operation, algebra, measurement, figure, pattern and function, and probability and statistics. The cognitive domains include computation, understanding, reasoning and problem-solving. Results suggest a congruence between cognitive domain's sequence and item difficulty levels of items based on that sequence. This finding indicates that the linear or hierarchical assumptions concerning the sequence appears to be reasonable. The characteristics of items that were exceptions to this trend were addressed.

• Journal of Educational Research in Mathematics
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• v.25 no.1
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• pp.1-19
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• 2015

This paper aims to explore what we can improve in the curriculum, teaching-learning, and evaluation on the bases of the analyses of multiple-choice items set in National Assessment of Educational Achievement. For this goal, by using the distribution curves of the responses percentages, we will grasp the features of educational achievement which appear to students through an in-depth analysis about not only item itself but also the contents included in particular distracters. These analyses provide more information than the descriptive statistical values such as the mean of correct answer percentage and the discrimination of whole group and the mean of responses percentages of replies of subgroups. Because the distribution curves of the responses percentages reveal the transition from the lowest to the highest educational achievement very well. From these analyses we acquire the implications about the concept of prime factor or prime factorization, ratio(proportion) such as velocity, linear function, volume of cone, properties of solid figure, and probabilities of empty event and total event.

• Journal of Educational Research in Mathematics
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• v.12 no.1
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• pp.145-162
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• 2002

In this study, on the basis of the seventh national mathematics curriculum, the achievement standards were developed to specify the objectives and contents of teaching-learning and the assessment standards were also developed to differentiate students' levels of achievement at school mathematics. The achievement standards were developed on the following guidelines; 1) to present the minimum standards based on the national curriculum, 2) to develop the standards based on the order of curriculum, 3) to suggest the minimum but ultimate achievement target, 4) to comprise not only of the intellectual but also of psychological spheres such as knowledge, function, attitude, aptitude, etc., and 5) to suggest the standards comprehensively and concretely. The standards were developed on the basis of the middle areas of contents of the curriculum in order not to be too comprehensive, nor to be too detailed. Learning activities, on the other hand, were provided for the assistance of instructions with emphasis on creativity rather than on the routine instruction. The assessment standards were established based on the following principles; 1) to establish the assessment methods, contents, and situations which are to be used for assessment, 2) to establish the criteria of classifying the assessed into the upper, intermediate and lower levels, 3) to develop the assessment standards in a proportionate balance to achievement standards, 4) to establish the intermediate level as a standard, and 5) to establish the minimum level in the contents, concepts, values and attitudes of basic learning. This study also suggested the exemplary test items including short-answer and open-ended questions while putting emphasis on students' real performance to increase their ability in solving problems rather than in calculating. In addition to the test items, it introduced the grading system developed to grade the items with concrete guidelines and to report students' achievement on doing mathematics.

• The Mathematical Education
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• v.51 no.3
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• pp.223-246
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• 2012

Korean Ministry of Education Science, and Technology(MEST) has recommended the introduction of mathematics textbooks based on storytelling to improve the teaching and learning of mathematics in school. As part of the mathematics textbooks based on storytelling development, this research has investigated school mathematics teachers' perspectives on mathematics textbooks based on storytelling in order to identify implications for the development and the implementation of it. For the purpose, we have developed survey questionnaire and administered it to 113 high school mathematics teachers. The survey asked the teachers to address their conception of mathematics textbooks based on storytelling, its contribution to school mathematics, challenges and obstacles for the implementation. The survey shows that the mathematics teachers' conception of mathematics textbooks based on storytelling was not clear or limited. Most of them replied that they received information about mathematics textbooks based on storytelling from the materials provided by workshop or materials of school district office. While the teachers heard about that school will implement mathematics textbooks based on storytelling, they rarely had idea of how to use them in class. In the survey, the teachers identified which type of storytelling is effective for which purpose of mathematics education. They also identified the positive effect and the difficulties in the implementation of mathematics textbooks based on storytelling. The mathematics teachers pointed out that textbook is not enough. They urged that the implementation of mathematics textbooks based on storytelling should be integrated into classroom teaching and assessment to make a significant change in the educational practice of mathematics in school. Thus, mathematics teachers need support to implement mathematics textbooks based on storytelling into their teaching practice. Teacher workshop and teacher manuals need to be developed to help teachers understand educational visions and values of mathematics textbooks based on storytelling. These results of the survey would form the worthwhile base information for the development and the implementation of mathematics textbooks based on storytelling.

• School Mathematics
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• v.4 no.3
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• pp.361-373
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• 2002

In this paper, a series of tasks related on polygonal numbers and pyramidal numbers are suggested for using them as teaching unit materials for teaching and learning of sequences in junior high school mathematics. Especially, finding n-th term in those seque-nces, relations among polygonal numbers, and relations among Pyramidal numbers are focused on. A series of tasks related on polygonal numbers and pyramidal numbers have three math-eucational values. First, they have a value as natural materials for teaching and teaming of finding nth term of original sequences using pro-gression of differences. Second, they have a value as materials for teaching and learning of mathematical thinking such as general-ization, analogy, etc. Third, they have a value as materials for teaching and learning of algebraic operation, proof, and connecting mathematical knowledges.