• School Mathematics
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• v.19 no.2
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• pp.229-248
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• 2017

This study investigated the factors that should be considered when teaching proportional expression and proportional distribution through literature review. Based on these results, we analyzed and compared Korean and foreign mathematics textbooks on proportional expression and proportional distribution longitudinally and horizontally to search for desirable methods of organizing the unit of proportional expression and proportional distribution in mathematics textbooks. For longitudinal analysis, we took the mathematics textbooks according to the national curriculum since the 5th one. For horizontal analysis, we selected the mathematics textbooks of Japan, Singapore, and China. In each textbook, the contents and the order in relation to proportional expression and proportional distribution, the definitions of terminology, and the contexts and the visual representations for introducing related concepts are selected as the analysis framework. The results of analysis revealed many characteristics and the differences in ways of dealing contents about proportional expression and proportional distribution. Based on these results, we suggested some implications for writing the unit of proportional expression and proportional distribution in elementary mathematics textbooks.

• School Mathematics
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• v.19 no.2
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• pp.385-403
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• 2017

This paper analyzed the units of capacity and weight in the mathematics textbooks in terms of units, relationship between the units, and the need of standard units. The results of this study showed that there were differences in the representation of the units, the notation of units, the types of units, and the representation of basic amount of units in the mathematics textbooks developed by the 5th, 6th, 7th, 2007 revised, and 2009 revised national mathematics curriculum respectively. The mathematics textbook developed by the 2009 revised mathematics curriculum was found to be generally consistent with the International System of Units (SI). However, the way of defining 1kg through the weight of water was found to be different from the SI. The relationship between the units was consistently described only with a written sentence in the previous mathematics textbooks, but the 2009 revised mathematics textbook presents questions and pictures to foster students' understanding of the relationship. Finally, activities and questions are required for students to recognize the universality and convenience of the standard units through the inconvenience of arbitrary units. Based on these results, this paper provides implications for the development of mathematics textbooks in the units of capacity and weight.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.363-384
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• 2001

The purpose of this thesis is, through analysing the characteristics of the definitions in Korean school mathematics textbooks, to explore the levels of them and to make suggestions for definition - teaching as a mathematising activity, Definitions used in academic mathematics are rigorous. But they should be transformed into various types, which are presented in school mathematics textbooks, with didactical purposes. In this thesis we investigated such types of transformation. With the result of this investigation we tried to identify the levels of the definitions in school mathematics textbooks. And in school mathematics textbooks there are definitions which carry out special functions in mathematical contexts or situations. We can say that we understand those definitions, only if we also understand the functions of definitions in those contexts or situations. In this thesis we investigated the cases in school mathematics textbooks, when such functions of definition are accompanied. With the result of this investigation we tried to make suggestions for definition-teaching as an intellectual activity. To begin with we considered definition from two aspects, methods of definition and functions of definition. We tried to construct, with consideration about methods of definition, frame for analysing the types of the definitions in school mathematics and search for a method for definition-teaching through mathematization. Methods of definition are classified as connotative method, denotative method, and synonymous method. Especially we identified that connotative method contains logical definition, genetic definition, relational definition, operational definition, and axiomatic definition. Functions of definition are classified as, description-function, stipulation-function, discrimination-function, analysis-function, demonstration-function, improvement-function. With these analyses we made a frame for investigating the characteristics of the definitions in school mathematics textbooks. With this frame we identified concrete types of transformations of methods of definition. We tried to analyse this result with van Hieles' theory about levels of geometry learning and the mathematical language levels described by Freudenthal, and identify the levels of definitions in school mathematics. We showed the levels of definitions in the geometry area of the Korean school mathematics. And as a result of analysing functions of definition we found that functions of definition appear more often in geometry than in algebra or analysis and that improvement-function, demonstration-function appear regularly after demonstrative geometry while other functions appear before demonstrative geometry. Also, we found that generally speaking, the functions of definition are not explained adequately in school mathematics textbooks. So it is required that the textbook authors should be careful not to miss an opportunity for the functional understanding. And the mathematics teachers should be aware of the functions of definitions. As mentioned above, in this thesis we analysed definitions in school mathematics, identified various types of didactical transformations of definitions, and presented a basis for future researches on definition teaching in school mathematics.

• The Mathematical Education
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• v.60 no.1
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• pp.111-131
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• 2021

This study aims to investigate how secondary mathematics teachers understand and intend to use textbooks for their mathematics instruction. For this purpose, we developed a set of survey items in order to unpack what the teachers understand the mathematical tasks suggested in the textbooks in terms of the levels of cognitive demand and how they intended to use the tasks in the textbooks for their teaching. Twenty-five teachers participated in the survey. The data from the survey were analyzed. The findings from the data analysis suggested as follows: a) the teachers seemed to closely follow textbooks without attempting to modify the tasks, even when the teachers consider it is necessary to modify textbook tasks to high-level tasks, b) the teachers seemed to be unstable in regards that they admitted themselves very competent for modifying tasks for developing students' mathematical thinking but, at the same time, they were uncomfortable with transforming tasks into cognitively demanding tasks that promote students' mathematical understanding, and c) the teachers appeared to consider textbooks as significant criteria in conducting tests including midterm and final exam. In conclusion, the teachers seemed to intend to follow closely the contents and sequence of mathematics textbooks in their mathematics classrooms.

• East Asian mathematical journal
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• v.33 no.4
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• pp.353-380
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• 2017

The purpose of this study is to analyze the multiplication units in the elementary school mathematics. In the 2015 revised curriculum, students learn multiplication in $2^{nd}$ grade. The multiplication units is divided into two: multiplication and multiplication facts. In these two units, we mainly analyze situations involving multiplication, models for teaching multiplication, and multiplication strategies for teaching multiplication facts in relation to Subject Matter Knowledge. We called these contents Multiplication Matter Knowledge. We examined the precedent study with regard to multiplication at the elementary mathematics. As results, we prepared an analysis framework for this study. This study was conducted according to qualitative research methods, expecially 'qualitative contents analysis'. The contents here refer to Multiplication Matter Knowledge that can be found in the elementary mathematics textbooks and working books etc. As results of analysis, We can confirm that various multiplication situations and multiplication models are presented in the textbooks. And it has been examined that various multiplication properties are presented in the textbook according to the multiplication strategy levels. We insist elementary school teachers should be aware of these Multiplication Matter Knowledge. This study aims to provide elementary school teachers with basic data in these contexts.

• Education of Primary School Mathematics
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• v.15 no.1
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• pp.41-52
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• 2012

The korean mathematics textbooks according to the 2007 revised mathematics curriculum and the MiC textbooks are similar in that they introduce mathematical materials in real life situations and are composed in such a way that require students to form their own mathematical concepts. However the MiC textbooks are focus more on situation-centered problems and context-centered problems where a set of procedures need to be followed in order to arrive at an answer. So, this paper is aim at comparing the units of statistics in the korean mathematics textbooks and the MiC textbooks in order to find the implications for writing textbook. By comparing the specific content and the used methods, I found Korean textbooks focused on understanding concepts and spending less time surveying and collecting data. On the other hand, MiC textbooks used activities that real mathematicians would be involved with, such as surveying and analyzing data to compose mathematical concepts.

• Communications of Mathematical Education
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• v.34 no.3
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• pp.373-391
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• 2020

This study is an analytical study on textbooks of , which was first presented in the 2015 revised high school mathematics curriculum. The textbook has a very high educational significance in that it is the first textbook developed for students majoring in economics. Analyzing whether these textbooks faithfully follow the spirit of the curriculum is an essential study for nurturing creative and convergent human beings and for personal self-realization. Therefore, in this study, a consistency analysis was conducted to determine whether the textbook fits the textbook development direction suggested by the curriculum developer and is appropriate for the state-approved mathematics curriculum. As a result of analysis, the contents of the textbook did not partially meet these criteria and lacked consistency. In conclusion, it is necessary to prepare more thorough standards for the examination and recognition of high school elective courses in the future.

• Communications of Mathematical Education
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• v.36 no.1
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• pp.73-88
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• 2022

Mathematics is a way of thinking. To do mathematics means to think mathematically. In other words, mathematics education and mathematics literacy are related. In elementary and secondary school mathematics education in many countries, teaching of mathematics using textbooks is conducted mostly in their native language. So mathematics education takes place while reading, writing, listening, and speaking mathematics. Analysis of mathematics textbooks for the lower grades of undergraduate mathematics shows that most advanced countries in mathematics use excellent undergraduate mathematics textbooks written in their native language. However, the ratio of using imported textbooks from foreign countries is particularly high in the case of textbooks for mathematics majors at Korean universities. In this article, the effect of language used in university mathematics education is analized. In particular, the importance of high-quality leading-edge university mathematics textbooks in native language is introduced by analyzing the case of Bourbaki in France and 'War of language' at the Israel Institute of Technology. The innovation of French university mathematics education in the 20th century began with Bourbaki's 'Fundamentals of Mathematics', a French textbook written in his native language. Israel's Technion and the Hebrew University of Jerusalem continue to teach all subjects in their mother tongue. This has led to produce many Nobel Prize and Fields medal winners in these two countries. This study shows that textbooks and languages used in university mathematics education has affected mathematical literacy.

• Communications of Mathematical Education
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• v.38 no.2
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• pp.263-286
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• 2024

With the introduction of AI digital textbooks, interest in the use of technology tools in mathematics education is increasing. Technology tools have the advantage of visualizing mathematical concepts and discovering mathematical principles through experimentation and inquiry. The 2015 revised mathematics curriculum in Korea already mentions the use of technology tools, and accordingly, various teaching and learning activities using technology tools are presented in mathematics textbooks. However, there is still a lack of systematic analysis on the types and utilization methods of technology tools presented in textbooks. Therefore, this study analyzed the current status of the use of technology tools presented in high school mathematics textbooks based on the 2015 revised curriculum. To this end, the types of technology tools presented in mathematics textbooks were categorized, and the utilization ratio of each category was investigated. In addition, the utilization patterns of technology tools were analyzed by subject and content area, and the utilization ratio of technology tools according to the type of teaching and learning activities was examined. The results showed that technology tools were used in various types and ratios according to the subject and content area. In particular, technology tools in the symbol-manipulation graphing software category accounted for 58% of the total usage cases, showing the highest proportion. By subject, the use of symbol-manipulation graphing software was prominent in subjects dealing with the analysis area, while the use of dynamic geometry software was relatively high in the geometry area. In terms of teaching and learning activity types, the utilization ratio of auxiliary tool type (49%) and intended inquiry induction type (37%) was high. The results of this study show that technology tools play various roles in mathematics textbooks and provide useful implications for improving mathematics teaching and learning methods using technology tools in the future. Furthermore, it can contribute to the establishment of educational policies related to AI digital textbooks and the development of teacher training programs.

• The Mathematical Education
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• v.56 no.2
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• pp.131-145
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• 2017

The representation of irrational numbers has a key role in the learning of irrational numbers. However, transparent and finite representation of irrational numbers does not exist in school mathematics context. Therefore, many students have difficulties in understanding irrational numbers as an 'Object'. For this reason, this research explored how mathematics textbooks affected to students' understanding of irrational numbers in the view of process and object. Specifically we analyzed eight textbooks based on current curriculum and used framework based on previous research. In order to supplement the result derived from textbook analysis, we conducted questionnaires on 42 middle school students. The questions in the questionnaires were related to the representation and calculation of irrational numbers. As a result of this study, we found that mathematics textbooks develop contents in order of process-object, and using 'non repeating decimal', 'numbers cannot be represented as a quotient', 'numbers with the radical sign', 'number line' representation for irrational numbers. Students usually used a representation of non-repeating decimal, although, they used a representation of numbers with the radical sign when they operate irrational numbers. Consequently, we found that mathematics textbooks affect students to understand irrational numbers as a non-repeating irrational numbers, but mathematics textbooks have a limitation to conduce understanding of irrational numbers as an object.