Search

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 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]

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]

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]

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]

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]

Despite the central role of proofs in mathematics, research often shows that school textbooks offer limited support for the teaching and learning of proof-related reasoning. This study contributes to this field of research by studying Swedish and Finnish upper secondary textbooks on logarithms and combinatorics. Justifications in expository sections are analysed and students' tasks are categorized according to the type and nature of reasoning they require. The findings imply that opportunities to learn proof-related reasoning are few, and are more oriented towards deductive reasoning in Finnish textbooks and towards empirical reasoning and conjecturing in Swedish textbooks. The results are discussed in relation to similar studies from both Scandinavian and United States contexts, and address future research and development of the theoretical framing of proof-related reasoning. [ABSTRACT FROM AUTHOR]

In this paper we present statistical analyses of three textbooks used by Swedish teachers to support year one children's learning of mathematics. One, Eldorado, is authored by Swedish teachers, another, Favorit, is a Swedish adaptation of a popular Finnish series and the third, Singma, is a Swedish adaptation of a Singapore series. Data were coded against the eight categories of foundational number sense, which are the number-related competences literature has shown to be essential for the later mathematical success of year one learners. Two analyses were undertaken; the first was a frequency analysis of the tasks coded for a particular category, the second was a time-series analysis highlighting the temporal location of such opportunities. The frequency analyses identified statistically significant differences with respect to children's opportunities to acquire foundational number sense. Additionally, the time series showed substantial differences in the ways in which such tasks were located in the structure of the textbooks. Such differences, we argue, offer substantial didactical challenges to teachers trying to adapt their practices to the expectations of such imports. [ABSTRACT FROM AUTHOR]

The analysis of the content of school textbooks, particularly in a time of cross-cultural borrowing, is a growing field restricted by the tools currently available. In this paper, drawing on the analyses of three English year-one mathematics textbooks, we show how two approaches to the analysis of sequential data not only supplement conventional frequency analyses but highlight trends in the content of such textbooks hidden from frequency analyses alone. The first, moving averages, is conventionally used in science to eliminate noise and demonstrate trends in data. The second, Lorenz curves, is typically found in the social sciences to compare different forms of social phenomena. Both, as we show, extend the range of questions that can be meaningfully asked of textbooks. Finally, we speculate as to how both approaches can be used with other forms of ordered classroom data. [ABSTRACT FROM AUTHOR]

A selection of secondary school mathematics textbooks from twelve countries on five continents was analysed to better understand the support they might be in teaching and learning mathematical problem solving. Over 5700 tasks were compared to the information provided earlier in each textbook to determine whether each task could be solved by mimicking available templates or whether a solution had to be constructed without guidance from the textbook. There were similarities between the twelve textbooks in the sense that most tasks could be solved using a template as guidance. A significantly lower proportion of the tasks required a solution to be constructed. This was especially striking in the initial sets of tasks. Textbook descriptions indicating problem solving did not guarantee that a task solution had to be constructed without the support of an available template. [ABSTRACT FROM AUTHOR]

This paper examines three elementary school mathematics textbooks (one textbook from each of 6th, 7th, and 8th grade) to determine to what extent these textbooks present questions with multiple outcomes and multiple solution methods. Document analysis as a qualitative research method is adopted. The findings reveal that only 8% of all three textbook questions have multiple correct outcomes and 92% of them have only one correct outcome. Further analysis of questions with multiple outcomes shows that the majority of these questions have limited correct outcomes rather than limitless ones. It is also found that only 6.2% all worked-examples are solved through different solution methods. Given that textbooks are often considered to have influences on both teaching and learning, these findings present important implications for mathematics learning and teaching. The issues of student creativity and higher-order thinking are especially discussed as they are closely associated with the use of questions with multiple solution methods and outcomes. [ABSTRACT FROM AUTHOR]

The rapid growth in diversity of information and communication technologies (ICT) enables a range of teaching methods, learning support strategies, and education settings to be developed. Questions about appropriate, effective, and efficient use of educational technology in teaching mathematics have been gaining more attention. This study focuses on the design and testing of an interactive learning textbook (eBook), created with Geogebra applets and up-to-date web technologies. The eBook is designed to meet the pedagogical and didactic needs of learners, allowing a high degree of interactivity and feedback during the learning process. In order to determine the effect of the created materials on students' achievements, tests of knowledge as well as tests of retention of knowledge were used. Moreover, questionnaires and interviews for students were developed to assess the impact of interactive textbooks on the perceptions of learners concerning mathematics, interactive materials, and the learning process. Students who have used the interactive eBook show statistically significant increased knowledge and knowledge retention compared to students who have attended the standard classes. Students also emphasized that tasks with interactive applets and new kind of learning materials inspired them to learn more, both in school and at home. [ABSTRACT FROM AUTHOR]

In this study, I analyzed and compared definitions of special quadrilaterals presented in the US and Turkish secondary school mathematics textbooks. To this end, seven textbooks from each country were examined based on the following features of mathematical definitions: form of presentation and mathematical correctness, minimality, the nature of definitions, and the reference sets and geometric properties used in definitions. The results showed that Turkish textbooks include both procedural and structural definitions of quadrilaterals, while procedural definitions are non-existent in the US mathematics textbooks. Meanwhile, all structural definitions and all procedural definitions excluding one are mathematically correct. Besides, in both country textbooks, there exists more number of minimal and inclusive definitions compared to the non-minimal and exclusive ones. Finally, textbooks from both countries mainly use quadrilaterals as reference sets and sides as geometric properties in definitions of special quadrilaterals. The results bring to light the varied opportunities provided to the students by the US and Turkish textbooks to experience and learn definitions of special quadrilaterals. [ABSTRACT FROM AUTHOR]

The cognitive domain in mathematics, defined as thinking and understanding in the process of learning mathematics, is a main focus of curricula in many countries. This study explores breadth and depth of understanding as addressed in mathematics textbooks certified as aligned to Israeli national mathematics curricula. We compare opportunities for students to engage with mathematics requiring different types and levels of understanding provided by the tasks in mathematics textbooks. Comparison of two fourth grade and two eighth grade mathematics textbooks showed significant differences in the opportunities to learn in the cognitive domain that each provides. These differences can be quantified; the quantification defines the cognitive demand of the textbook. The cognitive demand of the four textbooks varies. This reveals a potential source of inequity in students' opportunities to learn mathematics. Results should prompt discussion around standardization and alignment of textbooks to the cognitive goals of the curriculum. [ABSTRACT FROM AUTHOR]

Mathematics textbooks play a very important role in mathematics education and textbook tasks are used by students for practice to a large extent. Since the nature of the tasksmay influence the way students think it is important that the textbooks provide a balance of a variety of tasks. The analyses of the requirements in textbook tasks contain the usual dimensions of content, cognitive demands, question type and contextual features. The aim of this study is to embed a new fifth dimension into the framework: mathematical activities. This addresses the question of what a student should do in a particular textbook task: to represent, to compute, to interpret or to use argumentation. The analysis encompassed more than 22,000 tasks from the most commonly used Croatian mathematics textbooks in the 6th, 7th and 8th grade. The results show that the textbooks do not provide a full range of task types. There is an emphasis on computation, while argumentation and interpretation activities, reflective thinking and open answer tasks are underrepresented. The study revealed that incorporating mathematical activities into the multidimensional framework of textbook tasks may help to better understand the opportunities to learn which are afforded students by using mathematics textbooks. [ABSTRACT FROM AUTHOR]

This study analyzed the methods used to teach the multiplication of fractions in Turkish and American textbooks. Two Turkish textbooks and two American textbooks,Everyday Mathematics(EM) andConnected Mathematics 3(CM), were analyzed. The analyses focused on the content and the nature of the mathematical problems presented in the textbooks. The findings of the study showed that the American textbooks aimed at developing conceptual understanding first and then procedural fluency, whereas the Turkish textbooks aimed at developing both concurrently. The American textbooks provided more opportunities for different computational strategies. The solutions to most problems in all textbooks required a single computational step, a numerical answer, and procedural knowledge. Furthermore, compared with the Turkish textbooks, the American textbooks contained a greater number of problems that required high-level cognitive skills such as mathematical reasoning. [ABSTRACT FROM AUTHOR]

As part of recent scrutiny of teacher capacity, the question of teachers’ content knowledge of higher level mathematics emerges as important to the field of mathematics education. Elementary teachers in North America and some other countries tend to be subject generalists, yet it appears that some higher level mathematics background may be appropriate for teachers. An initial examination of a small sample of textbooks for teachers suggested the existence of a wide array of treatments and depth and quality of mathematics coverage. Based on the literature, a new framework was created to assess the mathematical quality of treatments for both specialized knowledge and horizon knowledge in mathematics textbooks for teachers. The framework was tested on a sample topic of the circle area formula derivation, chosen because it draws heavily on both specialized and horizon knowledge. The framework may contribute to similar analyses of other topics in a broader range of resources, in the overall quest to better describe the details of what constitutes appropriate mathematics horizon knowledge for teachers. [ABSTRACT FROM AUTHOR]

This study investigated whether the linguistic complexity of items leads to gender differential item functioning (DIF) on mathematics assessments. Two forms of a mathematics test were developed. The first form consisted of algebra items based on mathematical expressions, terms, and equations. In the second form, the same items were written as word problems without changing their contents and solutions. The test forms were given to a sample of 671 sixth-grade students from 10 middle schools in Turkey. The tests were administered to the students with a 4-week interval. Explanatory item response modeling and logistic regression approaches were used to examine gender DIF. Several word problems were flagged as having gender DIF in favor of female examinees, whereas mathematically expressed forms of the same items did not function differently across male and female examinees. The verbal content of word problems seems to influence the way males and females respond to items. [ABSTRACT FROM AUTHOR]

This research examines secondary mathematics teachers’ use of textbook curriculum materials within ‘typical’ cycles of planning and teaching in a school year. The curriculum use of four teachers from the western US was examined before and after engagement in a form of professional development focused on more purposeful and flexible curriculum use. A multiple case study approach was used in order to uncover and describe patterns of curriculum use over time in greater detail. Planning and teaching materials were collected, grouped, and coded for reflectivity of more effective adaptations. Overall, the number of textbook materials teachers usedas-isdropped dramatically while the number of materials theyadaptedincreased. This finding was true regardless of teaching experience, teaching context, textbook used, or content taught. Furthermore, the types of adaptations teachers made to their curricula were more deliberate and student-specific in the spring than they were in the beginning of the school year. This research sits within the broader domain of understanding how mathematics teachers use curriculum and raises new questions about how, when, and why teachers make changes to textbook materials. [ABSTRACT FROM PUBLISHER]

The debate on the differential effects of mathematics textbook series is a recurrent topic in the research literature. Research results remain inconclusive, pointing to a lack of evidence to decide on the relevance of the selection by schools of a mathematics textbook series. Studies also point to difficulties in comparing textbooks. Recently, in order to examine the influence of mathematics textbook series on student learning, the need to take into account mediating variables between the mathematics textbook series and the enacted curriculum is stressed. This paper focuses on one such mediating variable: teachers’ views of mathematics textbook series. Views of a mathematics textbook series of 814 teachers and mathematics performance results of 1579 students were analysed. The results point out that, with regard to teachers’ views of mathematics textbook series, the question ‘Does it really matter which mathematics textbook series schools choose’ has to be answered positively. Implications of the findings are discussed. [ABSTRACT FROM PUBLISHER]

The aim of this article is to present and discuss some results from an inquiry into mathematics textbooks authors’ visions about their texts and approaches they choose when new concepts are introduced. Authors’ responses are discussed in relation to results about students’ difficulties with approaching calculus reported by previous research. A questionnaire has been designed and sent to seven authors of the most used calculus textbooks in Norway and four authors have responded. The responses show that the authors mainly view teaching in terms of transmission so they focus mainly on getting the mathematical content correct and ‘clear’. The dominant view is that the textbook is intended to help the students to learn by explaining and clarifying. The authors prefer the approach to introduce new concepts based on the traditional way of perceiving mathematics as a system of definitions, examples and exercises. The results of this study may enhance our understanding of the role of the textbook at tertiary level. They may also form a foundation for further research. [ABSTRACT FROM PUBLISHER]

The present study used a new assessment technique, the story-generation task, to examine students' understanding of subtraction scenes. The students from four grade levels (110 first-, 107 third-, 110 fourth- and 119 sixth-graders) generated stories under the constraints provided by a picture (representing Change, Combine or Compare scene) and a number sentence. The results showed that the Change scene was the most intuitive, and the students tended to reinterpret Combine and Compare scenes as a form of Change scene, even when they understood that the identity of the objects in the Combine and the Compare scenes was different. The number of students generating correct stories for the Combine scene increased through the elementary school grades while for the Compare scene the number of students generating correct stories remained fairly constant from Grade 3 to Grade 6. This study also examined students' exposure to subtraction scenes in mathematics textbooks and discussed educational implications for supporting students' understanding of subtraction scenes. [ABSTRACT FROM AUTHOR]

The author examined the potential influence of learning opportunities provided in 1 U.S. and 1 Chinese mathematics textbook series on students' problem-solving performance. Also, the author studied learning opportunities provided in the textbooks by analyzing word problem distribution across various problem types, as well as the potential influence of learning opportunities on students' ability to solve arithmetic word problems, by determining student success rate (i.e., item difficulty measure) in relation to word problem distribution in adopted textbooks. Results indicated a different pattern with respect to word problem distribution in U.S. and Chinese textbooks. The relation between adopted textbook word problem task presentation and student success in solving problems suggests that the ability of U.S. participants to solve certain problem types better than other problem types may be related directly to the design of U.S. textbooks (e.g., unbalanced word problem distribution). [ABSTRACT FROM AUTHOR]