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Several studies indicate that gender is often portrayed stereotypically in mathematics textbooks worldwide. Based on the premise that such representations need to be examined with particular attention to the cultural context within which they exist, this study focuses on the upper-primary mathematics textbooks of the Republic of Cyprus, which are nationally produced and mandatory for all public schools. Specifically, the eight individual parts of grades 5 and 6 (four for each grade) were examined. By approaching both written and visual references from a critical discourse analysis perspective, the findings highlight that (a) gender is represented within the binary system, and (b) there are essential differences in depictions of men and women across three dimensions: professional status, everyday activities, and references to real people. These differences allude to stereotypical performative aspects of gender in this specific socio-cultural context. In closing, I make recommendations for future research directions in this area. [ABSTRACT FROM AUTHOR]

Irrational numbers, a fundamental set that extends rational numbers to real numbers, have been a subject of limited study in the context of textbook analyses. This study, therefore, examines how square root expressions and irrational numbers have been addressed in middle school mathematics textbooks throughout the history of the Republic of Türkiye. The research was conducted using a comprehensive approach, with qualitative research methods and content analysis was applied to 37 mathematics textbooks (seven 5th grade, twelve 6th grade, nine 7th grade, and nine 8th grade) from 1932 to 2022. Data were collected from mathematics textbooks available at the Ferit Ragıp Tuncor Archive and Documentation Library affiliated with the Ministry of National Education. The results of this study indicate that changes in mathematics curricula are reflected in textbooks, and this reflection is directly influenced by the learning theory adopted in the curriculum. The study also provides insights into how irrational numbers are introduced in textbooks based on the sequence of topics, and recommendations are made based on the findings. [ABSTRACT FROM AUTHOR]

Presently, in Malta, syllabi are being replaced by learning outcomes. For ages 3–7, the outcomes are framed holistically (e.g. identity, communication, etc.), and it is recommended that children learn mathematics informally through play and projects. For ages 8–11, learning outcomes are subject-based, and new mathematics textbooks are being phased in. I discuss the importance of a smooth transition between informal and structured approaches to learning mathematics. I draw on Anna Sfard's 4-element definition of discourse, linking the theory with my research classroom data. I argue that a discourse perspective can provide a basis for ensuring continuity across Grade levels. [ABSTRACT FROM AUTHOR]

This article describes UMA (Unified Model of Arithmetic), a theory of children's arithmetic implemented as a computational model. UMA builds on FARRA (Fraction Arithmetic Reflects Rules and Associations; Braithwaite et al., 2017), a model of children's fraction arithmetic. Whereas FARRA—like all previous models of arithmetic—focused on arithmetic with only one type of number, UMA simulates arithmetic with whole numbers, fractions, and decimals. The model was trained on arithmetic problems from the first to sixth grade volumes of a math textbook series; its performance on tests administered at the end of each grade was compared to the performance of children in prior empirical research. In whole number arithmetic (Study 1), fraction arithmetic (Study 2), and decimal arithmetic (Study 3), UMA displayed types of errors, effects of problem features on error rates, and individual differences in strategy use that resembled those documented in the previous studies of children. Further, UMA generated correlations between individual differences in basic and advanced arithmetic skills similar to those observed in longitudinal studies of arithmetic development (Study 4). The results support UMA's main theoretical assumptions regarding arithmetic development: (a) most errors reflect small deviations from standard procedures via two mechanisms, overgeneralization and omission; (b) between-problem variations in error rates reflect effects of intrinsic difficulty and differential amounts of practice; and (c) individual differences in strategy use reflect underlying variation in parameters governing learning and decision making. [ABSTRACT FROM AUTHOR]

Probability is an area of mathematics focused on predicting chances, making decisions and analyzing risks, making it one of the main areas of knowledge developed at school. Knowing that the textbook is an essential tool in the teacher's work, this article aims to analyse the perspective of teaching probability in the Probability and Statistics textbooks approved by the PNLD 2021 for High School. Based on documental research, we analyzed the activities considering the meanings of probability, sample spaces and the structuring of events. We found an asymmetry in relation to the meanings, with a great predominance of the classical meaning, the expressive use of discrete sample spaces and limitations in the conceptual approach to important theorems, such as conditional probability for the composition of events. As a result, teachers' skills are fundamental for complementing and correcting the teaching and learning process of probability. [ABSTRACT FROM AUTHOR]

This study analyses the instruction and organisation of the measurement domain by comparing textbooks from China, Japan, and Malaysia. Focusing on length measurement, we adopted the use of praxeology from the Anthropological Theory of the Didactics as a framework to reveal the knowledge to be taught in the transposition process, and developmental progression of levels of thinking from Learning Trajectories as a framework to reveal the mental processes or actions generated to achieve the learning goals from the domain. The findings are assembled in three dimensions: types of tasks, accumulation of practice blocks per thinking levels, and instruction sequences. The results indicate that all three countries promote, in different degrees according to their education goals, the development of measurement knowledge by: understanding how to use measurement tools, coordinating the relationship between standard units, and estimating measurements. Lastly, the theoretical framework is proposed as a tool to justify instructional decisions. [ABSTRACT FROM AUTHOR]

The current moves by many African countries including Kenya to reform their mathematics education to adopt learner-centred pedagogies presents a need to fill the knowledge gap on learner-textbook relationships there. The mathematics textbook remains a key resource for teaching and learning and is increasingly being expected to play a pedagogical role in addition to making the national curriculums manifest to both teachers and students. In Kenya, the textbooks published by the state-owned company are regarded as core and occupy a central role in mathematics teaching. We present findings on the perceptions of students at three Kenyan public secondary schools on what they value in textbooks and what they find lacking in their core text in their efforts towards engagement with mathematics through self-regulated learning. Implications for practice are presented. [ABSTRACT FROM AUTHOR]

This study explores how three widely used US kindergarten mathematics textbooks, each written to align with the Common Core State Standards for Mathematics (CCSSM), vary in terms of content coverage, instructional grouping, and use of representational strategies. Results show that all textbooks (i) primarily emphasize math practices related to Numbers and Operations, (ii) use concrete or pictorial representation frequently to explain and help children solve math problems, and (iii) most often suggest whole-group, teacher-centered classroom instruction. However, they also differ in important ways. Two of the textbooks place a stronger emphasis on more advanced mathematical practices, such as Composing Numbers, to which students may have had limited exposure prior to kindergarten. One covers a wider range of mathematical topics, including Graphing and Measuring, and introduces and reintroduces topics frequently. One emphasizes depth over breadth while focusing more on foundational topics, and utilizing seatwork more often. [ABSTRACT FROM AUTHOR]

The mathematics education literature indicates a consensus regarding the importance of developing algebraic thinking in elementary school mathematics. However, the approaches used to implement this concept vary around the world. This study examines how a popular standards-based elementary mathematics textbook series in China provides opportunities to learn about functional thinking, which is a key component of algebraic thinking. Building on the literature, an analytical framework was generated to examine the features of function-related tasks in the textbook series across grades. The results of the fine-grained coding analysis show that four categories of function-related tasks in the textbook provide opportunities to learn about multi-modes of functional thinking. These tasks primarily serve to enhance arithmetic learning, while offering opportunities to learn about functional thinking as an embedded component. Elaborated design and arrangement of the function tasks promote opportunities to learn about multiple modes of functional thinking. In addition, two pathways to support the development of functional thinking are identified. Finally, the implications for task design and textbook development which attempt to develop functional thinking are discussed. [ABSTRACT FROM AUTHOR]

This article focuses on students' meaning-making when working with mathematics textbooks from a multimodal approach that encompasses all resources for communication, which is an under researched area. Central to this study are the designed meanings of the textbooks and the affordances discovered by students when working with the textbooks. Video transcripts from 18 Year 1 (ages 7–8) students working with seven textbook pages were analysed. The results show that the designs of exercises are complex, that the students use different approaches when working with the textbook – from one exercise to another as well as within the same exercise – and that they sometimes discover content other than what the textbook was designed to offer. Conclusions drawn from this are that textbooks can be improved as learning tools – multimodal aspects of this are highlighted – and that more awareness of multimodality in mathematics teaching could support students' mathematical learning. [ABSTRACT FROM AUTHOR]

Despite the use of axiomatic definitions for mathematical concepts, scholars struggle to produce a single definition of angle that does not have some limitations. Textbooks' treatment of angle and its measure reflects this multifaceted nature of the angle concept while informing the different ways learners conceive of these concepts. In this study, I investigated the concept definitions provoked by textbook representations (e.g. diagrams) of radian angle measure. Seven prospective mathematics teachers (PMTs) participated in a think-aloud semi-structured interview and defined radian angle measure through examining six diagrams. A thematic analysis of concept definitions indicated that interacting with different representations provoked various concept definitions. Some provoked concept definitions focused on defining one radian. Other definitions indicated different quantitative operations (e.g. iteration, partitioning, proportionality). To provide learners opportunities to conceptualise radian angle measure quantitatively, teachers and curriculum developers are encouraged to incorporate multiple representations of radian angle measure into instructional materials. [ABSTRACT FROM AUTHOR]

The floor and ceiling functions appear often in mathematics and manipulating sums involving floors and ceilings is a subtle game. Fortunately, the well-known textbook Concrete Mathematics provides a nice introduction with a number of techniques explained and a number of single or double sums treated as exercises. For two such double sums we provide their single-sum analogues. These closed-form identities are given in terms of a dual partition of the multiset (regarded as a partition) of all b-ary digits of a nonnegative integer. We also present the double- and single-sum analogues involving the fractional part function and the shifted fractional part function. [ABSTRACT FROM AUTHOR]

In this case study, we investigate how an inquiry-oriented interactive calculus textbook supported one U.S. college instructor’s classroom teaching. We utilized analytical inquiry-oriented frameworks on observation data from a small classroom to capture textbooks’ influence on the instruction conceptualized by the Teacher-Mathematics-Student face of the socio-didactical tetrahedron [Rezat, S., & Sträßer, R. (2012). From the didactical triangle to the Rezat and Sträßer’s tetrahedron model socio-didactical tetrahedron: Artifacts as fundamental constituents of the didactical situation. ZDM - Mathematics Education, 44(5), 641–651. https://doi.org/10.1007/s11858-012-0448-4]. Operationalizing specific inquiry-oriented processes allowed us to examine the depth of the interactions conceptualized by the tetrahedron. The instructor’s reliance on the textbooks, their activities, and their supplemental materials created opportunities for meaningful classroom interactions about calculus, supporting a shift towards inquiry. We conclude by suggesting further research on the role of textbooks in supporting undergraduate mathematics instruction with inquiry and discussing implications for practice. [ABSTRACT FROM AUTHOR]

It is no secret that textbooks are expensive and that their costs are increasing faster than the inflation rate. Open textbooks - textbooks made available for free or at a low cost and distributed with an open license - offer a viable alternative to commercially published textbooks. To this end, the Initiative created criteria that could be used to evaluate open textbooks and have conducted in-depth reviews of well over a hundred books resulting in a list of approved open texts determined to have met those criteria. [Extracted from the article]

In this paper we present analyses of three textbooks currently used in the teaching of mathematics to year-one children in England. One is an established English-authored textbook, while the others are Singaporean-authored imports promoted by government as solutions to perceptions of systemic failure. Every task in each textbook was coded against a set of eight number-related competences known to support children's learning in both short and long terms. Such a framework, which is literature-derived and curriculum-independent, enables meaningful comparison of materials deriving from different cultural contexts. Analyses of the proportions of all tasks coded for the different competences showed that none of the three books adequately addresses all eight competences, although the English-authored comes closest. Moving averages, undertaken to show the temporal location of the opportunities presented for children to acquire the eight competences, showed them distributed throughout the school year in the English-authored textbook but only during the first half of the school year in the two Singaporean-authored textbooks. Some implications for the importation of such materials are discussed. [ABSTRACT FROM AUTHOR]

Women and people of color continue to be underrepresented in science, technology, engineering, and mathematics (STEM), even while STEM fields are faced with recruitment issues and shortages of workers. Mathematics textbooks may be complicit in this issue, with past research indicating that textbooks are not fairly representing women and people of color. Even in instances when representation appears equal, further inspection indicates that men and white characters are given more meaningful and scientific roles in textbooks. Our study investigated the 15 precalculus honors textbooks used in public schools across a county to determine the message that is communicated to potential STEM majors about who uses mathematics and how. To do so, we identified the presence of context, human presence, genders, names, and hobbies/occupations within the textbook exercises. Our study reveals an overall low proportion of real‐life contexts, of humans in general, of women and of gender non‐binary characters, and of STEM careers. Examples of women in STEM careers are strikingly low. To improve recruitment of students to STEM careers, in general, as well as recruitment of marginalized populations, in particular, we must improve representation such that all students are able to see themselves in mathematics and their textbooks. [ABSTRACT FROM AUTHOR]

This paper addresses the intersectionality theme in mathematics education to clarify the existing epistemic racism. Through the presentation of excerpts from Brazilian high school mathematics textbooks, more specifically the pages that deal with the history of mathematics, we argued that, in these analyzed textbooks, mathematics is European, male and white, because the narrative constructed by the creators of these books reproduces the Eurocentric logic of mathematical knowledge, erasing other histories of mathematics and creating a very specific narrative about the construction of human knowledge. The analyses were intersectional as a fundamental concept, as multiple aspects, such as gender, ethnicity, race, and nationality, were taken into consideration. The discourse analysis was the analytical tool that made it possible to look at the math textbooks and describe how the materialization of discourses about teaching and learning occurs, producing a history of mathematics teaching in our time; of what is idealized and what is invisibilized. The 24 volumes of the eight collections approved in PNLD 2018 were analyzed. Using the Atlas TI software, six characteristics were investigated: (i) the content addressed; (ii) the continent of origin of that character; (iii) whether it was a quote in text form or whether, in addition to the text (character's name), there was also a figure or photo; (iv) gender; (v) race; (vi) name. We found 554 references to scientists and mathematicians, showing that, in the analyzed books, mathematics is constructed by white and European-origin men. [ABSTRACT FROM AUTHOR]

As formal demonstrations in mathematics textbooks and classroom presentations provide conclusions of inquiries, students tend not to gain insight into the problem-solving process. Heuristics provides the latter, as it is a language of investigation that helps students choose potentially valuable mental actions in their problem-solving efforts. This would suggest that heuristics be seen as content worth sharing as part of students' mathematics education. This Classroom Capsule demonstrates the value of heuristics with informing Oresme's thinking in his developing an indirect proof that the harmonic series diverges. [ABSTRACT FROM AUTHOR]

The mathematics curriculum for lower secondary education stipulates that technology should not only provide a means of information and communication but also support key learning. However, for various reasons, the scope of technology in classrooms is limited. This research examines 189 mathematics tasks from eight textbooks, each using technology. The tasks were classified based on expected learning in one of three technological dimensions (informational, technical or didactic) by means of content analysis. The results show differences both between textbooks following the SEP 2011 and SEP 2017 models and between content areas. There is, however, a positive trend toward promoting a well-reasoned use of technology in the classroom. Conversely, the study also identified difficulties that may serve as guidelines for teachers, publishers, and authorities in using, publishing, and selecting textbooks, respectively. [ABSTRACT FROM AUTHOR]

Learning mathematics in an inclusive classroom is challenging for many students with disabilities. The adapted digital mathematics textbooks for Grades 3 to 6 in South Korea were designed to support these students' access to the general mathematics curriculum. This study evaluates these textbooks according to the Universal Design for Learning (UDL) guidelines. The design features of the mathematics textbooks varied within and across various UDL checkpoints. Overall, the aspect of providing multiple means of action and expression was the most frequently observed, followed by providing multiple means of representation and providing multiple means of engagement. Special education teachers and textbook developers can use these results as a resource for designing curricula and lessons for students with disabilities in the inclusive classroom. [ABSTRACT FROM AUTHOR]

The article describes an instrument consisting of 46 indicators organised under 10 dimensions to assess the presence and educational utility of historical resources in secondary education mathematics textbooks. The instrument was constructed on the basis of previous research on the didactic use of the history of mathematics, existing instruments on the analysis of mathematics textbooks, and mathematics teachers' assessments of the suitability of the indicators. The instrument can be used as a stand-alone tool or integrated into other procedures addressing textbook analysis more broadly. Its application is illustrated with a sample comparison of two secondary level mathematics textbooks. The instrument has proven to be a useful tool for comparing the historical resources in different publishers' textbooks, for it enables secondary school mathematics teachers to base their choice of resources on an appraisal of the indicators most relevant to classroom teaching. [ABSTRACT FROM AUTHOR]

Statistics is introduced in primary education in Spain, and its teaching is largely supported by textbooks, which are freely provided to the children. In this research, we analyse the activities based on statistical tables included in two complete collections of primary education mathematics textbooks. These activities are classified according to the type of table, the data presented in them, the activity requested from the student in relation to the table, and the data context, according to those suggested in the PISA studies. Using content analysis, we found that tables of distribution of a variable predominate, mainly with frequencies. The most frequent activity is the reading of information from the table, while the personal context appears in the majority of the activities. This analysis serves to highlight how the teaching of statistical tables is developed throughout primary education and inform the teachers about relevant variables that should be considered in their teaching. [ABSTRACT FROM AUTHOR]

Old mathematics books and textbooks have focused different researchers onto the history of mathematics and mathematics education. However, books are not the only information source for this field; for example, researchers can also study periodical-type publications from the past (such as diaries, weeklies, newspapers, etc.). Considering this, this study developed an instrument to analyze publications about mathematics and mathematics education included in newspapers, weeklies, journals, etc., which were not exclusively devoted to science, from the perspective of the history of mathematics and mathematics education. In order to do so, a descriptive research focused on the analysis of historical texts was carried out using the content analysis technique. The different labels and categories of this instrument are here exemplified by the categorization of some entries included in several periodical publications published in the 18th century in Spain. [ABSTRACT FROM AUTHOR]

Artificial Intelligence (AI) is one of the most crucial factor affecting future career choice of students. Accordingly, we offered students a semester-long Introductory Mathematics for Artificial Intelligence course. The course was developed to provide undergraduate students with various majors to navigate their career opportunities in AI-related jobs. This paper presents the newly published textbook and an online mathematics laboratory that integrated effective technology for this introductory course. In addition, we introduce a process-driven evaluation method based on the Problem/Project-Based Learning (PBL) report that worked well for this course. We also share trails of communications with our students and added the results of our students' performance analysis using principal component analyses (PCA) with the data generated from the class. [ABSTRACT FROM AUTHOR]

In India, a curriculum reform inspired by critical perspectives has sought to transform primary mathematics teaching and learning. It is aimed at strengthening socio-cultural-political connections between school mathematics and students' life experiences, thereby challenging traditional textbook culture. At the same time, this initiative has retained the textbook as a vehicle of reform while seeking to subvert many of its established conventions. Guided by Remillard's idea of modes of engagement, this paper analyses the innovative Math-Magic textbooks associated with the Indian National Curriculum Framework. It investigates how these textbooks represent and communicate the framework ideas, focusing on key curricular elements and on the teacher as reader. Analysing the 'voice' and 'structure' of the textbooks as well as the 'contexts' used, it is revealed that they use a radically unique voice to introduce school mathematics while also attempting to use authentic and socially relevant contexts within their tasks. However, they have limited structural support to communicate these ideas clearly to the teacher-reader. The paper has implications for studying reformed textbooks in primary school mathematics in the Global South, where they remain the main teaching resource for teachers. Further, by focusing on 'context', the notion of modes of engagement within textbooks is extended through socio-cultural perspectives. [ABSTRACT FROM AUTHOR]

Digital mathematics textbooks differ from traditional printed textbooks in, among other things, their dynamic structural elements, representing a potential that traditional textbooks cannot fulfil. Notably, dynamic structural elements, i.e., multimodal representations of mathematics, could be of particular importance for learning, which is why the scientific interest in digital mathematics textbooks has increased in recent years and many digital textbooks have been developed. However, research related to predicting teacher usage behavior of digital textbooks is still limited. Therefore, this research aims to analyze the predictors that may influence the intentions of mathematics teachers and the actual usage of digital textbooks by applying the Unified Theory of Acceptance and Use of Technology (UTAUT). Data were collected from 277 teachers in West Java Province, Indonesia, and analyzed using structural equation modeling (SEM). The results indicated that Performance Expectancy (PE) is the biggest significant factor, followed by Social Influence (SI), that influences the Behavioral Intention (BI) of mathematics teachers to use digital textbooks in Indonesia. Effort Expectancy (EE) does not affect the intention to use a digital textbook. In turn, BI has the largest and most significant effect on teachers' actual usage of digital textbooks. This result contributes to the understanding of the predictors that can increase the use of digital textbooks by mathematics teachers. [ABSTRACT FROM AUTHOR]

The paper is dedicated to analysing the role of "denominate numbers" in textbooks for Polish schools, whose author or co-author was Stefan Banach. Banach used the concepts of "number" and "denominate number" in his textbooks. The ways of introducing these concepts, as well as the associated manner of understanding numeration, are analysed in the paper. The methods of manipulating "denominate numbers" through various procedures are also discussed. The analysis is carried out in the context of the Polish ministerial ordinances related to teaching mathematics and the content of other textbooks, especially those used by Banach as a secondary school student. [ABSTRACT FROM AUTHOR]

Despite the recognized importance of emotion in learning (Kim and Pekrun in Handbook of research on educational communications and technology, 4th ed., Springer, pp. 65–75, 2014), instructional material design research primarily focuses on cognition, tending to ignore the affective dimension (Brom et al. in Educ Res Rev 25:100–119, 2018). To understand the complex phenomenon of how students' emotional responses to instructional materials are formed, this qualitative thematic study explored factors thought to affect their visual perceptions of instructional materials by utilizing the general framework of approach and avoidance motivation. Four sets of printed instructional materials were prepared, each with the same content drawn from finite mathematics, but with different visual designs. A total of 25 students were invited to a laboratory room and asked to select and study one out of the four sets of materials. The entire process was observed, and students were interviewed to share their experiences. The results showed that students selected instructional materials based on their holistic impression of the materials and on their individual expectations as shaped by previous experiences. For example, students who had math anxiety selected materials that did not look like math textbooks, although opinions regarding which materials did or did not look like textbooks were diverse due to different material experiences. While existing studies tend to be deterministic about the attractiveness of visual materials (e.g., Plass et al. in Learn Instruct 29:128–140, 2014), the present study confirms that there is no universal design that elicits comfortable experiences for everyone. This paper concludes with sets of guidelines and methods to accommodate students' diverse visual perceptions, which is critical for enhancing learning as a holistic experience. [ABSTRACT FROM AUTHOR]

The aim of this study is to determine how often middle school mathematics teachers use math textbooks in face-to-face and online classes. Teachers' views on the usefulness of math textbooks in online classes were also examined within the scope of the study. The mix method design was used in the study and the participants were 215 middle school mathematics teachers who participated in the study through the multilayer sampling technique. The data were obtained from the evaluation form and analyzed through inferential-descriptive statistical techniques. The results showed that the use of textbooks in online classrooms decreased, and digital resources were more preferred in these classes. A statistically significant difference was found between the usefulness scores of the mathematics textbooks in face-to-face and online classes, which were evaluated based on the participants' views in terms of the "In-class practices" dimension. In order to ensure the current mathematics textbooks more useful in online classes, the participants suggested designing the textbooks as econtents and increasing the qualification of examples. The other results were discussed in terms of teaching practices and student needs in future classrooms. [ABSTRACT FROM AUTHOR]

The topic of recurrence relations has recently been introduced in many discrete mathematics textbooks. Recurrence relations are efficient modelling and problem-solving techniques used in mathematics. Combinatorial problems are often used to introduce recurrence relations. However, many textbooks consider problems that can be reduced only to the recurrence relations of the first or second order. To overcome this problem, in this paper, we propose a general combinatorial problem of path tiling with tiles of different sizes and colours. For especially selected tile sizes and for certain tile colours, the problem can be reduced to solving a recurrence relation of the third, fourth, or higher orders. Furthermore, through actual examples, we show that various cases can be derived from the roots of a characteristic equation: different real roots, different real and complex roots, and repeated real roots with different multiplicities. We hope that the presented problems will provide teachers with the opportunity to present this topic with better content. [ABSTRACT FROM AUTHOR]

We investigate how an inquiry-oriented, dynamic, open-source calculus textbook shaped one college instructor's planning. We rely on Dietiker et al.'s [(2018). Research commentary: Curricular noticing: A framework to describe teachers' interactions with curriculum materials. Journal for Research in Mathematics Education, 49(5), 521–532. ] curriculum noticing framework to situate the instructor's actions during lesson planning using data from surveys, logs and interviews. The instructor's planning practices are characterized by intense use of the textbook, including creating additional curricular material related to its content. Our observations suggest that the textbook supported and influenced the instructor in implementing his inquiry-oriented visions and goals while planning his lessons. We conclude by suggesting further investigation of how textbooks shape undergraduate mathematics education and the textbooks' role in shaping undergraduate mathematics planning practices. [ABSTRACT FROM AUTHOR]

The aim of this research is to make a comparative analysis of solved examples, exercises and evaluation questions on percentages of middle school mathematics textbooks, the country are used in Turkey, Singapore and Australia. This comparison was made using Smith and Stein (1998)'s cognitive desire level definitions in their study. It is examined how many steps the solutions of the questions should be realized and compared according to the countries. The research is a qualitative research, and the document analysis method was used to analyse the problem solved sample, practice and evaluation questions about percentages in textbooks. According to the findings of the research, it was observed that the most common exercise questions were included in the textbooks of the three countries. It was determined that Singapore has no questions in the evaluation category. As a result of the findings examined according to the cognitive desire levels, it was found that low level questions were higher in the countries in general, and more questions were included in the unrelated transactions level in the low level. In the textbooks of the three countries, no questions were found at the level of doing Mathematics. When looking at the solution steps, it is stated that 83% of the questions are in the single solution step. [ABSTRACT FROM AUTHOR]

In APOS theory (Action, Process, Object, Scheme), the design of a genetic decomposition is the result of Theoretical Analysis (first component of the theory's research cycle) where textbook analysis is one of the elements to be considered. However, as of the date of this report, there are no publications on how to perform textbook analysis and the process behind the construction of a genetic decomposition. In this writing, the criteria proposed by Campos (2017) are used to analyze three linear algebra textbooks, specifically in relation to the concept of eigenvalue and eigenvector along with a methodology that accounts for the design of a preliminary genetic decomposition for the concept of eigenvalue and eigenvector on linear operators considering: the input of textbook analysis, existing research reports and the experience of researchers as teachers and students. [ABSTRACT FROM AUTHOR]

HOTS instruction in mathematics is rarely explicitly programmed by the schoolteacher. As a result, students' HOTS is at the lowest level, especially in national or international assessments. The purpose of this research is to determine why mathematics education in Indonesia does not have a significant effect on student HOTS by conducting a review of several Indonesian publications on the subject. This research is a qualitative method of literature review related to the HOTS of Indonesian mathematics students, and an organized interview triangulated to support the data and information from the literature review. The interview consisted of two critical questions administered using Google Form: implementing active learning and mathematics textbooks on mathematics classroom activities. The results concluded that there were two primary sources of error in mathematics learning to increase HOTS in Indonesia: active learning and current mathematics textbooks. Besides, in teaching and learning practices, the active learning model is rarely used when using official texts that do not promote HOTS for mathematics students in Indonesia. [ABSTRACT FROM AUTHOR]