Elementary Mathematics Textbooks Research Articles

The Analysis of Vietnamese Elementary Mathematics Text Book: focused on Number and Operations Strand

The Analysis of Vietnamese Elementary Mathematics Text Book: focused on Number and Operations Strand

우리나라 초등학교 수학 교과서에 나타난 최적화 문제 유형 분석

This study analyzes how optimization problems handled in middle school mathematics education and real life are handled in elementary mathematics textbooks. The purpose of this study is to identify the applicability of the optimization problem in elementary school. According to DCMEG, the optimization problem classification criterion of Ono-ri (2006), 12 mathematics textbooks of elementary school according to 2009 revision curriculum were analyzed. The optimization problem (13 questions) ), And optimization problem (7 questions) applied in real life. However, the term or concept of optimization was not mentioned in the curriculum or the teacher's guidebook. However, if we renew our perception of optimization problems, it will be possible to deal with optimization problems in elementary schools. This type of problem-solving experience allows students to find the meaning of optimization in problem situations, to understand mathematical concepts meaningfully, and to understand real life situations It is expected that it will help to recognize the value of mathematics.

2015 개정 교과서의 ‘놀이수학’에 대한 실태 분석

The purpose of this thesis is to analyze and compare ‘Game Activities’ of elementary mathematics textbooks developed in the national curriculum revised in 2015, and to find suggestions to improve ‘Game Activities’ of the textbooks based on the results. The main results of this study are as follows. First, as for materials, various types of materials were used in ‘Game Activities’. Also, more various materials were included in 2nd grade textbooks and 1st, 2nd grade teacher’s guidebooks than 1st grade textbooks. Second, this study analyzed the patterns of organization. The result showed that group and pair activities accounted for the highest rate among other patterns of organizations. Textbooks should include more pattern types of organizations that teachers could use them properly according to numbers of students in classes. For the ‘Game Activities’, students need to understand basic concepts of the chapter first. Students with lower levels would have difficulty participating in the ‘Game Activities’. Thus, there is a need to include activities for students with lower levels in teachers’ guidebooks, reflecting a variety of students levels.

남한과 북한 초등학교 수학 교과서의 구성 체제 및 학습 내용 비교 -1,2,3학년을 중심으로-

In this study, we analyzed the elementary school mathematics textbooks are used in 1st to 3rd grade in South Korea and North Korea. Specifically, the textbooks were compared in terms of unit and lesson frameworks, and the learning contents of mathematics covered in the 1st grade textbooks were compared and analyzed. As the results, some implications on the similarities and differences between the two textbooks were derived. First, we identified the emphasis on the textbooks for the South and North Korean mathematics, as well as similarities and differences in the composition of the textbooks, the structure of textbooks, and the system of teacher’s guidebooks. Second, South and North Korean mathematics textbooks share the largest proportion of units in the number and operation domain, and differ in the number of units and presentation of names. Third, both textbooks contain the introductions are composed of illustrations and the lessons are comprised of play activities, while there are differences in terms of the use of icons. Fourth, among the learning contents covered in the 1st grade mathematics textbooks, we identified the contents covered in thr 1st grade of South Korea and in the 1st grade of North Korea.

한국 초등학교 수학교과서에 제시된 각(角)의 정의에 대한 고찰

The present research work considers that there are many contradictory elements in the way ‘angle’ is defined and presented in the Korean elementary mathematics textbooks (KEMT). Henceforth, an effort has been made to systematically analyze the problems and seek solutions from the past KEMT. All the textbooks from the starting to the recent curriculum were collected and definitions and subsequent activities of angle, right angle, and angle measure from the books were analyzed. Based on the analysis, it was apparent that KEMT had commonly defined angle as a geometric standpoint, but illustrations of angle and views on the 'sides of angle' included in the definitions of angle were significantly different between curriculums. In addition, contradictory elements were continuously found in the definitions of the angle, between the definitions of angle and right angle, and between the definitions of angle and subsequent activities. Accordingly, it is proposed to reconsider the way angle is defined and design subsequent activities so as not to reveal the contradictory elements in the futuristic development of textbooks.

초등학교 수학 지도를 위한 이중수직선의 활용 방안 탐색

Although the double number line is regarded as a useful teaching tool not only for the proportional reasoning but also for the content domain of ‘number and operation’ in elementary school mathematics, it is hard to find it in Korean elementary school mathematics textbooks. This study aims to explore the principles for representing a double number, the advantages of using it, and several problems caused by dealing with it and their solutions, and to design specific plans to apply the double number line to elementary school mathematics. To do these, various related researches were reviewed. Moreover the elementary school mathematics textbooks of Japan, Taiwan and Singapore were analyzed. Based on the results, we extracted the applicable contents of double number lines and suggested specific applicable plans for their teaching practice in Korean elementary school levels. Four of them were applied to 4th grade and 6th grade elementary school students and the results were analyzed qualitatively to draw out implications for effective application of the double number line.

A Comparative Analysis of Division in Elementary Mathematics Textbooks in Korea and Japan

The purpose of the study is to examine how Korean and Japanese elementary mathematics textbooks series present division in terms of the perspective of making connections. For this purpose, units dealing with division of whole numbers, fractions, and decimal numbers were analyzed with foci on the meanings of division and procedures of division. Findings showed that, in the textbooks of both countries, the various meanings of division were consistently applied not only to whole numbers but also to fractions and decimal numbers. Moreover, the procedures of division were connected as numbers were expanded from whole numbers to fractions. Noticeable differences included: as for the organization of the contents of division, Korean textbooks presented division of fractions first, whereas Japanese textbooks dealt with division of decimal numbers first. Regarding the meanings of division, the Korean textbooks dealt mainly with partition and measurement division situations, while the Japanese counterparts were more inclusive with multiple situations, such as determination of a unit rate. This study is expected to provide information on how Korean and Japanese textbooks present division and to give implications for textbook developers and teachers to connect division meaningfully as students deal with whole numbers, fractions, and decimal numbers.

U.S. grade 4–6 students’ rational-number substitutions for odd-sum unknown addend tasks

ABSTRACTResearch findings have established common student misconceptions for literal symbolic representations of variables but lack corresponding findings of when or how these misconceptions arise. This article reports findings from an exploratory study of U.S. grade 4–6 students’ conception(s) for various representations of unknown addends commonly found in U.S. elementary mathematics textbooks. Thirty-six U.S. grade 4–6 students participated in two semistructured task-based interviews designed to explore their conception(s) of conventional and nonconventional representations of unknown addends as revealed by their number substitutions across task types and core mathematical tasks. Results showed that participants initially demonstrated a bias toward positive integers, upon further questioning a bias toward non-negative integers, potential conflict factors related to rational-number substitutions, and did not demonstrate common difficulties with literal symbols exhibited by students in algebra and higher-level mathematics courses.

Elementary Mathematics Textbook Analysis from Multicultural Mathematics Education Perspective

Elementary Mathematics Textbook Analysis from Multicultural Mathematics Education Perspective

Study of fractions in elementary mathematics textbooks from Finland and Taiwan

This study examines the different ways in which fractions are dealt with in two elementary mathematics textbook series: Kang Hsuan (KH) in Taiwan and Laskutaito in Finland. The results showed that the total number of fraction questions in Laskutaito is higher than that in KH and that Laskutaito highlights the basic definition of fractions to help children develop higher levels of reasoning. Fraction questions in Laskutaito were presented with a number of pictorial representations to clarify the concepts. Laskutaito includes more symbolic representation of questions. Moreover, the questions posed in the Laskutaito reflect real-life situations, whereas the questions posed in KH do not connect with real life. The implications of this study are discussed and suggestions for future studies are made in this paper.

초등예비교사의 '어림하기' 이해에 대한 고찰

The purpose of this study is to investigate and analyze the understandings of elementary pre-service teachers about 'estimation' in the elementary mathematics. Together with this analysis, we identify elementary pre-service teacher's Mathematical Pedagogical Contents Knowledge(MPCK), especially focusing to Subject Matter Knowledge(SMK). In order to this goals, we investigate contents relating to 'estimation' from <TEX>$1^{st}$</TEX> curriculum to 2009 revised curriculum and compare 'rounding up', 'rounding off', 'rounding' in the elementary mathematics textbooks. As results of investigations, 'estimation' has been teaching at the 'Measurement' domain from <TEX>$3^{rd}$</TEX> curriculum, but contexts of measuring weaken from <TEX>$7^{th}$</TEX> curriculum. 'Rounding up(off)' is defined three types in the textbooks from <TEX>$1^{st}$</TEX> to 2009 revised curriculum. And we examine elementary pre-service teachers through the questions on these 'estimation' contents. On the analysis of pre-service teacher's understanding relating MPCK, four themes is summarized as followings; the understanding of '0' in the 'rounding up', the cognitive gap between 'rounding up' and 'rounding off', the difference of percentage of correct answers according to types of question in the 'rounding up', and the difference between the definition of 'rounding up' and the definition of 'rounding'.

초등학교 수학 교과서 및 익힘책에 제시된 변수 개념에 관한 분석

초등학교 수학 교과서 및 익힘책에 제시된 변수 개념에 관한 분석

초등학교 수학 교과서의 이해에 유클리드 원론이 주는 시사점

초등학교 수학 교과서의 이해에 유클리드 원론이 주는 시사점

An Analysis of Storytelling in Elementary Mathematics Textbooks -Focused on the 1st semester of elementary grade 4-

An Analysis of Storytelling in Elementary Mathematics Textbooks -Focused on the 1st semester of elementary grade 4-

초등학교 수학 교과서 내용 적정성 분석 - 단원 구성 및 어휘 사용을 중심으로 -

There has being developed elementary mathematics textbooks currently based on the 2015 revised mathematics curriculum. Vocabularies used in mathematics textbooks are mainly determined by the authors to develop textbooks. The purpose of this study was to investigate the adequacy of elementary school mathematics textbooks based on the unit structure and vocabulary, and to provide implications for elementary mathematics textbooks which is currently in development, in accordance with the 2015 revised curriculum. As a result, there were found some problems in the unit structure and vocabulary of elementary mathematics textbooks.

초등수학에서의 곱셈구구 지도 순서에 대한 고찰

The purpose of ths study is to compare and analyze the sequence of teaching multiplication facts in the elementary school mathematics. Generally, the multiplication in the elementary school mathematics is composed of the followings; concepts of multiplication, situations involving multiplication, didactical models for multiplication, and multiplication strategies for teaching multiplication facts. This study is focusing to multiplication facts, especially to the sequence of teaching and multiplication strategies. The method of this study is a comparative and analytic method. In order to compare textbooks, we select the Korean elementary mathematics textbooks(1st curriculum~2009 revised curriculum) and the 9 foreign elementary mathematics textbooks(Japan, China, Germany, Finland, Hongkong etc.). As results of comparative investigation, the sequence of teaching multiplication facts is reconsidered on a basis of elementary students’ mathematical thinking. And the connectivity of multiplication facts is strengthened in comparison with the foreign elementary mathematics textbooks. Finally multiplication strategies for teaching multiplication facts are discussed for more understanding and reasoning the principles of multiplication facts in the elementary school mathematics.

An Analysis of Problem-Posing Tasks in Chinese and US Elementary Mathematics Textbooks

This paper reports on 2 studies that examine how mathematical problem posing is integrated in Chinese and US elementary mathematics textbooks. Study 1 involved a historical analysis of the problem-posing (PP) tasks in 3 editions of the most widely used elementary mathematics textbook series published by People’s Education Press in China over 3 decades. Study 2 compared the PP tasks in Chinese and US elementary mathematics textbooks. This allows for the examination of PP tasks from an international comparative perspective, which provides one point of view about the kinds of learning opportunities that are available to students in China and the USA. We found evidence that the inclusion of PP tasks in the Chinese textbook series reflected, to some degree, changes in the curricular frameworks in China. However, the distribution of PP tasks across grade levels and content areas, as well as the variety of types of PP tasks included, suggest a need for greater intentionality in the design and placement of PP tasks in both the Chinese and US textbook series. Findings from the 2 studies reported in this paper not only contribute to our understanding about the inclusion of PP tasks in curriculum both historically and internationally, but also suggest a great need to systematically integrate PP activities into curriculum and instruction. The fact that both Chinese and US curriculum standards have heavily emphasized PP in school mathematics, despite there being only a small proportion of PP activities in both Chinese and US elementary mathematics curricula, suggests the existence of challenges that are delaying the implementation of reform ideas such as problem posing in school mathematics.

An Analysis on the Sequences and Methods of Multiplication and Division with Decimals in the Elementary Mathematics Textbooks

An Analysis on the Sequences and Methods of Multiplication and Division with Decimals in the Elementary Mathematics Textbooks

What Conceptions have US Grade 4-6 Students' Generalized for Formal and Informal Common Representations of Unknown Addends?

This article reports findings from a study of grade 4-6 students' conception(s) for various representations of unknown addends [variables] commonly found in US elementary mathematics textbooks. Specifically, thirty-six US grade 4-6 students participated in two semi-structured task based interviews designed to explore their conception(s) of formal and informal representations of unknown addends as revealed by the types of numbers substituted across core mathematical tasks and task types.

초등학교 수학 교과서에 제시된 패턴 지도방안에 대한 분석

패턴을 다루는 여러 가지 활동은 초등학생들의 대수적 사고를 신장하는데 매우 효과적이다. 이에 본 연구는 초기 대수(early algebra)적 관점에서 패턴을 지도하는 세 가지 주요 활동인 패턴의 구조를 분석하는 활동, 패턴에서 두 변수 사이의 관계를 탐색하는 활동, 패턴의 일반화된 규칙을 추론하고 표현하는 활동을 중심으로 현행 초등학교 수학 교과서에 제시된 패턴 지도방안을 분석하였다. 분석결과 패턴의 구조를 분석하는 활동은 교과서 상에서 명시적으로 고려되지 않았다. 반면 패턴에서 두 변수 사이의 관계를 탐색하는 활동은 주로 대응표를 활용하여 전 학년에서 다루어졌고, 패턴의 일반화된 규칙을 추론하고 표현하는 활동은 저학년에서는 패턴의 규칙을 비형식적으로 표현하는 활동을 통하여, 고학년에서는 패턴의 규칙을 수식이나 기호를 사용하여 형식적으로 표현하는 활동을 통하여 다루어졌다. 한편 다른 수학 내용과의 연계성 측면에서 패턴의 지도방안을 분석한 결과, 현행 초등학교 수학 교과서에서는 패턴 활동이 규칙성 영역에 해당하는 일부 단원에서만 한정적으로 다루어지고 있었다. 이와 같은 연구결과를 토대로 본 연구는 초등학생들의 대수적 사고를 신장하기 위한 패턴 지도방안과 관련하여 구체적인 시사점을 제공하고자 한다. Patterns are of great significance to develop algebraic thinking of elementary students. This study analyzed teaching methods of patterns in current elementary mathematics textbook series in terms of three main activities related to pattern generalization (i.e., analyzing the structure of patterns, investigating the relationship between two variables, and reasoning and representing the generalized rules). The results of this study showed that such activities to analyze the structure of patterns are not explicitly considered in the textbooks, whereas those to explore the relationship between two variables in a pattern are emphasized throughout all grade levels using function table. The activities to reason and represent the generalized rules of patterns are dealt in a way both for lower grade students to use informal representations and for upper grade students to employ formal representations with expressions or symbols. The results of this study also illustrated that patterns in the textbooks are treated rather as a separate strand than as something connected to other content strands. This paper closes with several implications to teach patterns in a way to foster early algebraic thinking of elementary school students.