Mathematics Textbooks Research Articles

Didactic Transposition Analysis on Line and Angle Concepts

Mathematics knowledge in schools should be sourced from scholarly knowledge. Education not sourced from scholarly knowledge will risk errors in concepts, such as invalidly taught material, that can lead to misconceptions. This study aims to analyze the transposition of knowledge on the concept of lines and angles from scholarly knowledge to knowledge to be taught. This study uses a qualitative descriptive approach. The data source in this study, namely scholarly knowledge, was obtained by analyzing books in universities, while knowledge to be taught was obtained by analyzing mathematics textbooks used in schools. This study's results show a transposition process in the concept of lines and angles, namely in the definition of lines, the types of lines, the position of two lines, and the relationship of angles in two parallel lines. This research can later be the basis for improving mathematical knowledge so that student's understanding of the concept of lines and angles is expected to be more complete based on scholarly knowledge.

Teachers’ perceptions: What happened after more than 10 years of developing the mathematics textbook

This qualitative study describes teachers’ perceptions of a mathematics textbook after more than a decade of developments in Saudi textbooks, including introducing English terms into Arabic textbooks. The sample of this study was 14 mathematics teachers at the high school level. The analysis of teachers’ interviews allowed the researcher to develop a deep understanding of the perceptions of fundamental changes in mathematics education. The findings expose the concerns of teachers regarding resource adequacy in light of the modern learning style that considers students as the center of the education process, and language issues in connection with textbook comprehensibility. These findings indicate that the Saudi Ministry of Education and leaders in mathematics education should focus on all elements of constructive alignment if they seek to meet the targets set to reform mathematics education.

Opportunities to Learn Geometric Transformation in Chinese Mathematics Textbook: A Primary School Example

Opportunities to Learn Geometric Transformation in Chinese Mathematics Textbook: A Primary School Example

An Integrated RME and PBL Mathematics E-Module for Vocational High School Learning: A Need Analysis

In this digital era, we can access information that we need easily. Including mathematics learning material. The are a lot if digital based learning materials that can be accessed anytime anywhere. However, the are still limited studies about developing mathematics e-modul as one of learning resources for vocational high school students. Therefore, this study investigates the need to develop An Integrated RME and PBL Mathematics E-Module for Vocational High School learning. This study is a descriptive survey involving 52 tenth grade students consist of 27 students from the Pharmaceutical Technology Expertise Field, 10 students from the Industrial Chemical Engineering Expertise Field, and 15 students from the Beauty and Spa Expertise Field, and also four mathematics teachers from four different vocational high schools with various expertise field in a city of Surakarta, Central Java, Indonesia. The data collection was conducted using printed questionnaires (for students) and online questionnaires (for teachers). The data was summarized and analyzed descriptively. Based on the data analysis, it can be concluded that there are still limited realistic problems in Indonesian mathematics textbook for vocational high school based on each expertise fields. Therefore, developing an integrated RME and PBL mathematics e-module is necessary. The characteristic of the integrated RME and PBL mathematics e-module are: (1) the e-module’s content should be presented in Bahasa Indonesia, providing realistic contexts by the certain expertise field and can also be from various expertise fields; (2) the learning activities should be carried out in groups, held inside or outside the classroom and involve problems that are related to the expertise field; (3) the learning media can be in the form of electronic and non-electronic media; (4) The assessment activities can be carried out in writing or authentic assessment.

Content Analysis of Algebra and Functions in Three 9th Grade Mathematics Textbooks in Albania: Supporting PISA Results

The analysis of textbooks is crucial to understanding their impact on students' skills and on the results of international assessments such as PISA. This study examines mathematics textbooks for the 9th grade in Albania, focusing on the algebra and functions sections in texts from the publishers Pegi, Mediaprint and Ideart. The aim is to compare content structure, progression in the development of concepts, connections with the real world, the relationship between images and explanations, suitability for the curriculum and the use of technological tools. The research reveals that, despite having a similar structure, the texts have many unsolved tasks and significant differences in the hours devoted to the same topics, without clear explanations. The progression of concepts and connections to the real world vary, with the use of pictures and practical situations more effective in some cases. Although the books conform to the 9th grade curriculum, none clearly incorporate technology as a learning support tool, leaving this choice to the teachers. Finally, beyond the constraints of the educational context, the results have implications for future research on the incorporation of experimental studies and may facilitate more effective learning by supporting teachers and students to overcome the difficulties highlighted by the PISA results. Received: 15 November 2024 / Accepted: 31 December 2024 / Published: 05 January 2025

Variability of definitions in modern textbooks and violation of the rights of students

Can a situation be considered fair when the variable presentation of definitions in current mathematics textbooks affects understanding, solution, and therefore the answer to those problems for which this is essential? It is unlikely, this becomes especially important when writing test tasks, since when communicating you can justify your own thoughts, but when writing tests this can no longer be done. Unfortunately, our students are not protected from such situations when writing the National Multi-subject Test (NMT). But if we talk about fairness, about respecting the rights of students, then the difference in the presentation of definitions should not affect the number of points scored by students in NMT who can solve problems, but solve them in accordance with the content of the textbooks they studied with. It is a shame, because mathematics experts from the Ukrainian Center for Educational Quality Assessment (UCEQA) note in their defense that assessing the quality of textbooks is beyond their competence. The question is not for UCEQA to take on additional functions of examining textbooks. The question is that writing high-quality NMT tests should include knowledge of the content of existing textbooks and take into account different approaches to definitions when writing test items, since the unwillingness to realize and correct what is indicated leads to a violation of the rights of Ukrainian students. The above demonstrates the existence of a serious problem associated with the biased assessment of applicants' knowledge when writing NMT tests in mathematics, which requires attention and the development of ways to overcome it. This may be a more responsible work of UCEQA mathematics experts in the preparation of test tasks; perhaps this should be a certain collaboration of authors and scientists in order to develop common approaches to defining concepts or their consensus when writing textbooks. The latter direction is relevant in the context of the «New Ukrainian School» (NUS) reform carried out by the Ministry of Education and Science, the implementation of which also involves the writing of a new generation of textbooks. I would like to hope that the educational community will find better directions and approaches to solving the issue raised.

Argumentation in mathematics and science university textbooks: Similarities and differences in linguistic structures

Argumentation is a key skill in most school subjects and academic disciplines, including mathematics and science. It is possible that similarities and differences between how argumentation is expressed in different subjects can contribute to, or disrupt, students’ transferrable argumentation skills. The purpose of this study is therefore to increase the understanding of such similarities and differences concerning the use of argumentation in mathematics and science texts. To reach this goal, the study compares argumentation with a focus on argumentation markers and argumentative structures in first-semester university textbooks in mathematics, chemistry, and biology. Results show that common linguistic argumentation markers in mathematics and science textbooks include for example <i>because</i>, <i>if</i>, <i>thus</i>, <i>so,</i> and <i>therefore </i>and that there is significantly more argumentation in the mathematics textbook compared to the science textbooks. Further, the results indicate differences in patterns of how argumentation is used, including for example that the mathematics textbook contains more complex argumentation compared with the chemistry textbook. Thereby, the subject-specific languages in the disciplines have the potential to offer students different examples of argumentation.

대응의 관점에서 음함수 또는 매개변수로 나타낸 함수의 미분에 관한 교과서 분석

Mathematics textbooks are considered essential teaching and learning materials that teachers rely on for conducting lessons and assessments. The content of these textbooks can significantly influence students' logical understanding of mathematical concepts. This study analyzes the descriptions related to the differentiation of functions represented by implicit functions or parameters in high school calculus textbooks. The findings are as follows: First, all eight textbooks indicated that it is possible to appropriately restrict the domain and codomain when describing implicit functions to define them as functions. Second, only one textbook expressed the relationship of y as a function of x when describing functions represented by parameters, while the other seven textbooks described the relationship between the two variables x and y. Third, seven textbooks presented y not a function of x as the differentiation tasks concerning functions represented by parameters. The descriptions in mathematics textbooks can be a source of misconceptions and may lead to logical issues regarding concepts.

Algebra Problems in Middle School Textbooks from Six Countries

This study compared the algebra content of middle school mathematics textbooks from Finland, the United States, Singapore, China, Taiwan, and Nepal. Content analysis was employed to investigate five aspects of the algebra problems: the total number of algebra problems, representational forms, contextualization, response types, and cognitive demand. The results revealed that the six mathematics textbook series differed in all five aspects, indicating uneven opportunities to learn middle school algebra across countries. The insights gained can be valuable in designing mathematics textbooks and curricular materials. We provide recommendations for stakeholders and curriculum developers based on the results.

한국과 일본 초등학교 수학 교과서의 나눗셈 도입 단원 비교·분석

This study aims to compare and analyze the structure and instructional approaches of division introduction units in elementary school mathematics textbooks of Korea and Japan. For this purpose, two Korean textbooks based on the 2015 revised curriculum and one Japanese textbook were analyzed, focusing on unit structure, methods for introducing division and division expression, the relationship between multiplication and division, and division quotient calculation methods. The analysis revealed that Korean textbooks structurally connect partitive and measurement division, enabling students to understand the relationship between multiplication and division and to learn quotient calculation through multiplication tables of the divisor. Korean textbooks emphasize a quotient calculation method using multiplication expressions limited to the measurement context, where the quotient serves as the multiplier and the divisor as the multiplicand. In contrast, Japanese textbooks guide students to intuitively distinguish partitive and measurement division through contextual situations represented with models and language. Quotient calculation is taught by using the multiplication tables of the divisor, incorporating multiplication expressions in both contexts to link division expressions and quotients. While Korea’s approach emphasizes abstract and formal mathematical knowledge, Japan’s approach focuses on maintaining the coordination of the two division contexts and guiding students to understand the relationship between multiplication and division. Based on these findings, this study presents suggestions for teaching the division introduction unit in elementary schools.

Opportunity to learn flexible and adaptive strategy use in current and past Dutch mathematics textbooks

Opportunity to learn flexible and adaptive strategy use in current and past Dutch mathematics textbooks

Development of a rigorous mathematical thinking-based textbook in the house of worship context to enhance conceptual understanding

Background: This research develops a foundational mathematics textbook for PGMI students based on the Rigorous Mathematical Thinking (RMT) framework, contextualized within houses of worship to foster deeper understanding of mathematical concepts.Aim: The study aims to design and evaluate the feasibility and effectiveness of the textbook while gauging students’ responses and performance improvements.Method: Using a research and development (R&D) model, this study validated the textbook through expert reviews and tested its practicality and effectiveness in small-scale and broader applications. Data were obtained through a combination of observations, interviews, surveys, and tests measuring students' conceptual comprehension. Statistical evaluations, including descriptive analysis and t-tests, were employed.Results: The textbook received validation from subject matter, presentation, and language experts, who confirmed its content and structural accuracy. Trial phases categorized the textbook as highly practical, while broader field testing indicated that students using the textbook demonstrated significantly greater improvement in conceptual understanding compared to those without it.Conclusion: The RMT-based textbook aligns with its intended objectives and provides a contextually appropriate tool for improving mathematical comprehension. These findings highlight its potential as an effective resource for mathematics learning in PGMI contexts.

Algebra discourses in mathematics and physics textbooks: comparing the use of algebraic symbols

It is agreed that algebra has an important role in physics, particularly through handling symbols. A lot of previous research has focused on how mathematics is used in physics from perspectives where mathematics is taken for granted, and not addressing potential differences of mathematics in the physics classroom and in the mathematics classroom. Studies addressing differences between both subjects have been based on researchers’ own experiences of mathematics in both subjects. Thus, more focused empirical research is needed. The purpose of this study is to clarify similarities and differences between mathematics and physics concerning the use of algebraic symbols. Analyses were based on comparisons between upper secondary textbooks in mathematics and in physics from a discourse perspective. Statistical methods were used to decide if there were any significant differences between the subjects. Results showed an overlap in the algebra discourse in both subjects, but also several differences concerning core aspects of algebra. For example, a higher number of different algebraic symbols in equations in physics than in mathematics, and algebraic symbols are more seldom referred to by words in mathematics than in physics. This can make it difficult for students to identify similarities in the algebraic discourses in both subjects.

The relevance of mathematics textbook tasks to indigenous cultural context

This paper reports about a study, which examines the mathematics textbooks used by the schools in the Sámi area of Norway. The Sámi are Indigenous people of Norway and neighboring countries (Finland, Russia and Sweden). Handcraft and reindeer herding are prevalent activities in Sámi culture. Drawing on the theory of didactical phenomenology, the study examines the relevance of textbook tasks to the cultural background of Indigenous children. Document analysis was used to extract and analyze the data from the old and new textbooks. The results indicate that the tasks in the old textbook are hardly relevant to Sámi culture. Though the old textbook had tasks, which could be adopted, the topic containing such tasks is no longer available in the new textbook. The adoption of such tasks could have helped to achieve the goal set in the new curriculum about teaching Sámi history and culture to all Norwegian children. It could also have helped to achieve another goal, which is about interdisciplinarity, because the tasks are about timeline in Norwegian history. The study has implications. In addition to using the tasks in the already available studies about the Sámi, we need more studies about designing tasks which utilize the Sámi cultural context. Additionally, adopting tasks, which use Indigenous contexts similar to the Sámi context, should also be considered instead of a mere translation of the mandated textbook into the Indigenous language. Another option is, consistent with earlier studies, designing a separate textbook for the Indigenous children based on their culture. Keywords: mathematics curriculum, Indigenous culture, measuring, textbook.

An Analysis of the Context Types in Probability and Statistics Tasks Presented in Elementary School Mathematics Textbooks of South Korea and Finland

An Analysis of the Context Types in Probability and Statistics Tasks Presented in Elementary School Mathematics Textbooks of South Korea and Finland

Analysing the Tasks in Middle School Mathematics Textbooks According to the Levels of Cognitive Demand

Analysing the Tasks in Middle School Mathematics Textbooks According to the Levels of Cognitive Demand

Collaging illustrated mathematical word problems

In a mathematical educational context, mathematical word problems are an established practice with the aim to connect to students’ everyday life. Drawing on Neo-material perspectives and art based research methods we explore collage as a way to critically engage with illustrated mathematical word problems. We challenge the view of mathematical knowledge production as an objective, value-neutral and disembodied process by performing agential cuts with(in) illustrated mathematical word problems from two Swedish mathematical textbooks. The perspectives and methods mobilize sensibilities that advance new points of views. Hence, contributing to broaden the range of qualitative research methods and paradigms studying mathematical word problems.

The mathematics textbook – from artefact to instrument

The mathematics textbook – from artefact to instrument

Praxeological analysis in Indonesian and Singaporean mathematics textbooks: An understanding geometrical similarity by students

Mathematics textbooks are essential tools for facilitating the achievement of learning objectives, yet their use varies across classrooms, even when the same mathematical concepts are being taught. This study aims to investigate students' understanding of geometrical similarity through praxeological analysis within the framework of the Anthropological Theory of the Didactic (ATD). The analysis identifies differences in the structuring of geometrical similarity tasks between Indonesian and Singaporean textbooks. According to ATD praxeology, mathematical content is analyzed through the "praxis" and "logos" blocks, where praxis encompasses task types (T) and techniques (τ), while logos involves technology (θ) and theory (Θ). The findings highlight distinct priorities in how geometrical similarity is presented in textbooks from both countries, with implications for students’ conceptual and procedural understanding. Specifically, the absence of pantograph tasks in Singaporean textbooks and the lack of scale factor exercises in Indonesian textbooks reflect differences in knowledge construction and task emphasis. These variations impact students' ability to relate textbook knowledge to real-world applications. The study underscores the significance of incorporating a diverse range of task designs and practical experiences to enhance students' geometric reasoning abilities. A well-structured textbook not only supports students in achieving learning objectives but also fosters a continuous process of building, connecting, and deepening their mathematical understanding.

AN INTEGRATED ANALYSIS OF HIGH SCHOOL ENTRANCE EXAMINATION MATHEMATICS QUESTIONS AND 8TH GRADE MATHEMATICS TEXTBOOK QUESTIONS

This study aims to examine the mathematics questions in the 8th-grade mathematics textbook and the mathematics questions in the central exam for secondary education institutions (2018-2022) in the context of the Revised Bloom's Taxonomy. In the study, the document analysis technique was employed. The study used as a document the 8th-grade mathematics textbook and the central examination in 2018-2022. Teacher opinions were also taken to support the documents. Descriptive analysis was used for the analysis of the qualitative data. The study findings revealed that 4% of the questions asked in the last five years' central exams for secondary education institutions (2018-2022) were at the level of understanding, 56% at the level of practice, 39% at the level analyzing, 39% at the level of analyzing, and 1% at the level of evaluating, with no questions at the level of remembering and creating. The unit evaluation questions in the 8th-grade mathematics textbook were at level of remembering, 41.66% at the level of understanding, 47.50% at the level practice, and no questions were asked at the level of analyzing, evaluating, and creating. The study determined that the problem was teachers not using the textbook as a result of exam-oriented education.At least 3 and at most 5 keywords reflecting the integrity of the work should be written by the author in the places specified in the template.