Elementary Mathematics Textbooks Research Articles

Mathematical creativity in upper elementary school mathematics curricula

Textbooks should promote creative tasks for teachers to enhance students' math skills through creative thinking, instead of relying on memorization of step-by-step procedures.The aim of this study is to analyze elementary school mathematics curricula commonly employed in the U.S., namely GoMath, enVision Math, Math Connects, MyMath, and Investigations. The selection of these curricula is based on their widespread usage, and the analysis seeks to evaluate their effectiveness in fostering the development of students' creative thinking skills. We employed Bicer et al.'s (2021) framework for creativity-directed tasks to analyze 1,000 mathematical tasks within each curriculum. The analysis unveiled that Eureka, followed by Investigations, incorporated a higher proportion of creativity-directed tasks compared to the remaining three curricula. For some categories and subcategories of creativity-directed tasks (e.g., communication, connection), the results are less varied across five curricula. The present study enables school districts, schools, and classroom teachers to know what curricula support the development of creative thinking of students by including various options of creativity-directed tasks in their upper elementary mathematics textbooks.

A Study on the Instruction of Ratios Involving External Ratios in Korean Elementary Mathematics Textbooks

A Study on the Instruction of Ratios Involving External Ratios in Korean Elementary Mathematics Textbooks

초등학교 수학 교과서에 나타난 수학적 추론 양상 탐색

The purpose of this study was to explore how mathematical reasoning, one of the most important topics in school mathematics, is implemented in elementary school mathematics textbook. To this end, this study analyzed the type of reasoning, level of cognitive demands, and structural characteristics of mathematical reasoning tasks provided in the elementary school mathematics textbooks. As a result of this study, it was revealed that the mathematics textbooks had the strength of providing sufficient tasks dealing with pattern recognition type, but were deficient in providing tasks dealing with multiple types of mathematical reasoning, such as making a conjecture, investigating a conjecture, developing a justification, finding a counterexample, and evaluating an argument. Regarding the level of cognitive demands of mathematical reasoning tasks, the mathematics textbooks provided sufficient tasks of procedures with connections, but insufficiently provided tasks of doing mathematics requiring complex thinking. In relation with the structural characteristics of mathematical reasoning, the mathematical reasoning tasks in the mathematics textbooks embodied only the aspects of pattern recognition-making a conjecture and pattern recognition-developing a justification, but were insufficient in embodying the structural flow of mathematical reasoning. In addition, this study suggested that elementary school mathematics textbooks need to provide a wealth of tasks dealing with multiple types of mathematical reasoning, tasks of doing mathematics, and tasks reflecting the structural characteristics of mathematical reasoning.

Analysis of Gender Images in Elementary School Mathematics Textbooks of Jiangsu Education Press

This dissertation analyzes gender role images in elementary school mathematics textbooks of Jiangsu Education Press in China. The study aims to identify whether gender stereotypes and discrimination exist in textbooks and develop strategies to address these issues. The results showed that male characters were more frequently portrayed than female characters in both text and images, and they tended to be depicted as active and confident problem solvers. In contrast, female characters were often shown as passive and dependent learners. Additionally, gender stereotypes were found in portraying male and female characters roles and activities, with males frequently engaging in activities related to science and technology, while females were associated with more traditional roles such as homemakers and caregivers. The results of this study will shed light on the nature and extent of gender bias in mathematics textbooks published by Jiangsu Education Press and contribute to their improvement. This study contributes to the broader field of gender bias in education by providing a more specific and focused analysis of gender role representations in elementary school mathematics textbooks.

핀란드 1~2학년 초등 수학 교과서에 제시된 프로그래밍 교육을 위한 수학적 요소 분석

Since 2016, Finland has been implementing programming education in elementary school mathematics. This study analyzed Finnish first and second grade elementary mathematics textbooks and tutorials that reflected programming education. Previous studies on programming were analyzed to extract mathematical elements for programming instruction, and based on the extracted sequence, rules, selection, variables, possibilities, logic elements, functions, and algorithm, the contents of elementary mathematics textbooks in Finland were analyzed. As a result of the analysis, in Finnish mathematics textbooks, activities suitable for programming learning were evenly presented by utilizing all content elements as a whole, and a separate lesson for programming was also organized. In addition, the basic content of programming suitable for the student level was presented mathematically, and the level was changed and presented as the grade level went up. Looking at each element, activities for variables and logic elements accounted for a large part, and students were provided with opportunities to learn various mathematical elements related to programming during the first and second grades of elementary school. Based on these results, this study is expected to provide significant resources for applying programming to mathematics education in Korea.

식 지도 관점에서 역량중심 초등수학 영재교육 프로그램 및 교과서 분석

In this study, ‘Mathematical expression connection’ and ‘Mathematical expression transformation’ patterns were analyzed to see if activities related to expressions appearing in competency-based mathematics education programs for gifted students and elementary mathematics textbooks were appropriately constructed from the standpoint of establishing internal connectivity between various mathematical objects. I got the same conclusion. First, it was found that there needed to be more opportunities to observe the presented equations in terms of the expression connection aspect, express them as phenomena, and interpret new expressions, mathematical relationships, and thought processes. Second, from the viewpoint of the expression transformation aspect, the purpose of transforming the expression was mostly the process of deriving the value of the expression. Therefore, it is necessary to supplement the activities of transforming expressions in various directions.

3~4학년군 수학 교과서의 문제 만들기 과제 유형에 따른 학생들의 반응 분석

In order to enhance students' mathematical problem solving competency, the 2015 revised mathematics curriculum emphasized problem posing as a sub-factor of problem solving competency. In this study, we analyzed task types of problem posing in the 3rd and 4th grade mathematics authorized textbooks and students' responses to the representative types of problem posing task. As the results of analysis, even though they are the same lesson units, the number and types of problem posing tasks in the units varied by publishers, and there are differences in students' responses to each type. From the results of this study, some implications for constructing problem posing tasks in elementary mathematics textbook and teaching problem posing were suggested.

우리나라 초등학교 수학에서 그림그래프 지도에 대한 고찰과 개선 방안 탐색

This study tried to analyze the problems by critically examining how the pictographs are taught for statistical literacy education in the Korean elementary school mathematics curriculum. First, I analyzed pictographs presented from the 4th mathematics curriculum to 2015 revised curriculum of Korea, in order to find the pedagogical goals of the pictographs in the elementary school mathematics textbooks. In addition, I derived some implications for teaching of pictographs by analyzing the shape of the pictographs in Australia, Singapore, and MiC mathematics textbooks. As a result, pictographs were taught for enhancing algebraic thinking in Korea by combining different sizes of pictures based on the power of 10 units. However, in other countries, the shape of pictographs were chosen based on the comprehension of the unit idea with the aim of developing the statistical literacy required to interpret the various pictographs found in daily life. For the teaching of pictographs for statistical literacy education, it is suggested to use the pictographs with only one size of pictures representing units and various units represented by pictures that are not powers of 10 in the elementary school mathematics curriculum.

Exploring Opportunities to Develop Algebraic Thinking Presented in Elementary Mathematics Textbooks in Korea and the United States

Knowledge of algebra is known to be critical for not only school mathematics but also higher-level studies in mathematics. However, many students find learning algebra problematic and experience difficulty, particularly in transitioning from arithmetic to algebra. Therefore, the mathematics education research community has endeavored to develop students’ algebraic thinking in the elementary grades to help them learn algebra successfully. Although research on early algebra has been extensively conducted overseas since the 1990s, in Korea, this research began only in the 2000s and is relatively scarce. Therefore, in this study, we aim to compare the elementary mathematics textbooks of Korea and the U.S. based on the five big ideas of early algebra and draw implications for early algebra education in Korea. The results demonstrate that Korean textbooks contain significantly less content related to early algebra than U.S. textbooks. It was also found that the U.S. textbooks than that of Korea more emphasize the relational meaning of the equal sign. Furthermore, there were differences in the textbooks of the two countries in the way of handling the properties of numbers, analyzing patterns in functional relationships, and presenting the meaning of variable. Based on the results, we discussed ways to develop elementary school students’ algebraic thinking through textbooks in Korea.

Design of a pattern and correspondence unit to foster functional thinking in an elementary mathematics textbook

Design of a pattern and correspondence unit to foster functional thinking in an elementary mathematics textbook

Cognitive demands on geometrical tasks in Indonesian elementary school mathematics textbook

Examples and exercises in mathematics textbooks have an essential role in directing teaching and learning to achieve the objectives of the mathematics curriculum. This study examines mathematical tasks, i.e., examples and exercises, for a grade 4 elementary school mathematics textbook published by the Indonesian Government in 2018. We focus on geometry tasks and categorize them based on the dimensions of cognitive processes and knowledge of the revised Bloom’s taxonomy. Textbook research is used to achieve the objectives of this study. The validity of the data was carried out by employing peer debriefing. The findings of this study indicate that only about 30% of the geometry tasks in this mathematics textbook require high-level mathematical thinking skills. This study also shows that procedural knowledge is more dominant and becomes an orientation in presenting geometry tasks. This finding becomes less relevant to the orientation of researchers and policymakers who want the direction of mathematics education to be forming students as problem solvers.

2015 개정 초등학교 수학 교과서의 나눗셈 계산 원리 지도에 대한 고찰

In everyday life division appears in the two contexts, partitive or measurement context. Teaching division algorithm is based on analyzing the context through operating numerical models, consciousizing the division algorithm process consisting of the partial multiplications between divisor and quotient, and formalizing the calculation principle. In these processes, it is important to manipulate models and express the result of manipuation appropriately to the context. However, it is identified that the model manipulation and the sympbolic expression of model manipulation are not accord with. In the elementary school mathematics textbooks, the product of divisor and quotient appearing in division algorithm is expressed in the measuremet context. This inconsistency presents a significant educational challenge in elementary mathematics, which requires guiding the formalized principles of mathematics through manipulation activities for specific models. In this study, the characteristics of the product of divisor and quotient appearing in the division algorithm were analyzed, and based on this, some suggestion was presented to improve teaching division algorithm.

An Analysis of Sustainable Activities in Japanese, Korean, and Singaporean Elementary Mathematics Textbooks

The purpose of the study was to explore how contents related to sustainable development were presented in Japanese, Korean, and Singaporean elementary mathematics textbooks. For this purpose, the contents in the textbooks were analyzed at both macro and micro levels through a mixed method research. The results showed that the sustainability-related contents were included from the third or fourth grade in all the textbooks. The related contents were involved to mathematics content domains of Numbers and Operations, Pattern, and Data and Possibilities. The sustainability-related contents were used both to introduce and to apply mathematical concepts or principles. Most of the sustainable development activities led students to solve problems by using the mathematical contents they had learned, while some other activities induced students to consider sustainability as well as to solve problems. This study is expected to give implications for textbook developers and teachers to connect sustainable development meaningfully to elementary mathematics education.

Pemberdayaan Guru SD/MI Melalui Peningkatan Kualitas Pembelajaran Matematika

This activity aims to provide basic knowledge about learning mathematics how to use media and several learning models, one of which is RME, as well as knowledge about the 2013 curriculum. math. To increase the basic knowledge of mathematics learning, the trainees were given basic knowledge and skills on: 1) Mathematics Learning Problems at SD/MI Level, 2) Elementary Mathematics Textbooks according to the 2013 Curriculum, 3) RME, 4) Fun Mathematics Learning Methods. The service was held at SDI Makarimul Akhlak Building with ±30 participants on Saturday, May 14-19 2016. The methods used were lecture, practice, question and answer, discussion and practice methods. Based on the results of the evaluation, it turned out that in general there was an increase in the knowledge of the training participants for the empowerment of SD/MI teachers in improving mathematics learning, this was evidenced by the tasks given to the participants. In the future, the hope of this activity is that participants can practice in class during math lessons and can transfer the knowledge that has been obtained to other SD/MI teachers.
 Keywords: Mathematics, RME, Curriculum 2013

초등수학 교과서의 뺄셈 문제 상황 분석

Even in the daily life of elementary school students, it is often natural to think of ‘small number’ first and ‘large number’ later. However, in most elementary school mathematics textbooks, there are biased situations in which the ‘large number’ is presented first and the ‘small number’ is presented later. In this study, we discussed the conventions of setting the problem situation of subtraction, in which implicitly 'large number' is presented first and ‘small number’ is presented later. In addition, we discussed the pedagogical actions related to the actual problem situation of subtraction in which ‘small number’ is presented first and ‘large number’ is presented later. Through this, we searched an improvement direction for the biased setting method of subtraction problem in which 'large number' is presented first and 'small number' is presented later. For this purpose, we analyzed the subtraction problems presented in the mathematics textbooks and workbooks for grades 1 to 3 of elementary school by 8 types to identify their characteristics. This research shows that it is necessary to provide various problem-solving experiences for the actual problem situation of subtraction, and it can play a role in expanding the range of thinking about subtraction from the perspective of early algebra.

쌓기나무를 활용한 초등학교 수학 교과서의 단원 고찰

This study analyzes units of an elementary school mathematics textbook using wooden cubes in relation to the spatial sense of a solid figure in elementary mathematics education, and discusses implications for learning guidance and considerations in developing curriculum and textbooks. To this end, the related curriculum and textbooks from the 7th curriculum to the 2015 revised curriculum were analyzed, and these were divided into a solid figure made of wooden cubes and the aspect of activities using wooden cubes. As a result of the study, close guidance and attention were needed in terms of expression and activities using wooden cubes to present a solid figure made of wooden cubes. Based on these contents, specific implications for curriculum and textbooks development were proposed.

The Integration of Programming in Swedish School Mathematics: Investigating Elementary Mathematics Textbooks

ABSTRACT We characterize the recently included programming content in Swedish mathematics textbooks for elementary school. Especially, the connection between programming content and traditional mathematical content has been considered. The analytical tools used are based on the so-called 5E’s, a theoretical framework of action, developed within the ScratchMath project, and Brennan and Resnick’s (2012) terms computational concepts and practices. The result uncovers “follow a procedure” as the dominating action, in which the concepts stepwise instruction and repeated pattern were frequent. Bridging between programming and mathematics is weak in the sense that the programming content does not enhance the possibility to explore mathematical concepts and ideas.

Values in the geometry and measurement unit of the Palestinian Grade six mathematics book

ABSTRACT School textbooks affect the different aspects of students’ learning. One way that textbooks can affect students’ learning is through the values embedded in the texts. In the present research, we intend to study values in elementary school mathematics textbook. Specifically, we study values in the Geometry and Measurement unit of the Palestinian Grade six mathematics book. This unit is comprised of five lessons. To analyse the unit, we use a classification model suggested by Sam and Ernest. In this model, Sam and Ernest consider values in mathematics education as consisting of three categories: epistemological, social and personal values. Analysing the unit, we found that the epistemological component was the most frequent in the unit, while the second was the personal component and the third was the social. Alertness in thought, discriminating and rationality had the highest percentages as epistemological values, importance had the highest percentage as a social value and open-mindedness had the highest percentage as a personal value. Correlations between pairs of values in each component showed two significant strong positive correlations, while the other significant correlations were relatively strong or moderate. Further research needs to study correlations between pairs of values, and how these pairs affect students’ learning.

A Study on the Aspects of Social Justice in Korean Elementary Mathematics Textbooks

In this study, the researchers analyzed the 2015 revised 3rd~6th grade Korean mathematics textbooks from the aspects of social justice in mathematics education. For this study, the researchers constructed a textbook analysis framework for social justice subjects, which categorized by social issues, economy education, democratic education, personality education, safety education, environmental education, and career education. As a result, the 2015 revised elementary mathematics textbooks were reflected the subject matter of social justice in the order of social issues, economic education and democratic education, personality education and environmental education, safety education and career education. Also, the subject of social justice appears in all 3rd~6th grade mathematics textbooks, but it is not explicitly dealt with by combining it with mathematical content. The researchers suggested that mathematics lessons should be developed including social justice issues aligned with elementary mathematics contents.

중학교 사회 교과서 분석을 통한 초등학교 통계교육 개선 방안 탐색: 그래프 지도를 중심으로

In this study, in order to explore ways that statistical graphs teaching in elementary mathematics education can be improved, first, the types of statistical graphs that appear in middle school social textbooks were examined, and second, the characteristics that differentiated these from statistical graphs that appeared in elementary school mathematics were investigated. This analysis indicated that 88.2% of the graphs presented in the middle school social textbooks were addressed in the elementary mathematics curriculum. The frequency of use (excluding mixed graphs) was in the order of bar graphs, line graphs, ratio graphs, and picture graphs. However, most of the statistical graphs did not follow the standardized framework suggested in elementary school mathematics textbooks, as they were instead transformed in various ways. The features that differentiated middle school mathematics graphs from graphs experienced in elementary school mathematics differed for each type of graph. For example, in the case of bar graphs, there were the omission of axes, deformation of bars, and expression of multiple variables, while in the case of line graphs, there were expressions of multiple variables and accurate representations of variables.