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Understanding mathematics textbooks through reader-oriented theory
Abstract
Textbooks have the potential to be powerful tools to help students develop an understanding of mathematics. However, many
students are unable to use their textbooks effectively as learning tools. This paper presents a framework that can be used
to analyze factors that impact the ways students read textbooks. It adapts ideas from reader-oriented theory and applies them
to the domain of mathematics textbooks. In reader-oriented theory, the reader is viewed as actively constructing meaning from
a text through the reading process; this endeavor is shaped and constrained by the intentions of the author, the beliefs of
the reader, and the qualities the text requires the reader to possess. This paper also discusses how reading mathematics textbooks
is further constrained by the authority and closed structure of these textbooks. After describing the framework, the paper
discusses recommendations for future avenues of research and pedagogy, highlighting the importance of teachers' roles in mediating
their students' use of textbooks.
KeywordsMathematics education-Content area reading-Reader-oriented theory-Textbooks
... How a reader responds to a text is shaped by the reader's goals, motivation, background, and the historical and social context in which the transaction is situated. Weinberg and Wiesner (2011) adopted this theory and formulated concepts about three types of readers: the intended reader, the empirical reader, and the implied reader. The intended reader is the reader profile in the author's mind; the empirical reader is the person who actually reads the text; and the implied reader reflects what is required of the empirical reader to interpret the text in the way intended by the author. ...
... Authors of mathematics textbooks, many of whom are mathematicians, are generally experts in a specific subject. At the same time, the empirical readers of textbooks, most likely to be students, do not always match the implied readers (Weinberg & Wiesner, 2011), who many authors imagine to be experienced mathematicians. When the mismatch happens, Weinberg and Wiesner (2011) pointed out that students "will be unable to use the textbook effectively as a tool for learning the mathematics intended by the author" (p. ...
... At the same time, the empirical readers of textbooks, most likely to be students, do not always match the implied readers (Weinberg & Wiesner, 2011), who many authors imagine to be experienced mathematicians. When the mismatch happens, Weinberg and Wiesner (2011) pointed out that students "will be unable to use the textbook effectively as a tool for learning the mathematics intended by the author" (p. 60). ...
Covariational reasoning is a cognitive activity that attends to two or more varying
quantities and how their changes are related to each other. Previous studies indicate that
covariational reasoning seems to have levels.
Content analysis was used to examine the pedagogy and development of covariational
reasoning levels in the sections that conceptually introduce derivatives in four calculus
textbooks. One widely used calculus textbook was selected for the study in each of the four
categories: U.S. college, U.S. high school, China college, and China high school. Two qualified
investigators and I conducted the study. We used a framework of five developmental levels for
covariational reasoning.
The conceptual analysis of four calculus textbooks found that the U.S. college and the
U.S. high school textbooks emphasize the average and instantaneous rate of change. However,
both lack development of the direction and magnitude of change. On the other hand, this study's
Chinese high school calculus textbook has a greater degree of development in the direction and
magnitude of change while having a deficit in the average rate of change. This study's Chinese
college calculus textbook does not have any meaningful development regarding covariational
reasoning pedagogy.
The relational analysis of the concepts previously identified in the conceptual analysis
phase revealed that this study's U.S. college calculus textbooks provide abundant examples and
exercises to transition between the average and instantaneous rate of change. On the other hand,
all other calculus textbooks in this study lack any significant transition among passages that
stimulate covariational reasoning.
The textbook analysis in this study provides insights into the current focus of calculus
textbooks in both the U.S. and China. In addition, the study has implications for learning and
teaching calculus at both high school and college, as well as future editions of calculus
textbooks. Finally, limitations and recommendations are discussed.
... This network is not a real reader but offers the real reader a role to play. The concept has been used in research on history textbooks (Garske, 2017) and has been adapted in more detail concerning mathematics textbooks (Berger, 2019;Weinberg & Wiesner, 2011;Wiesner, Weinberg, Fulmer, & Barr, 2020). Weinberg and Wiesner (2011) define the implied reader as "the embodiment of the behaviours, codes and competencies that are required for an empirical reader to respond to the text in a way that is both meaningful and accurate" (Weinberg & Wiesner, 2011, p. 52). ...
... The concept has been used in research on history textbooks (Garske, 2017) and has been adapted in more detail concerning mathematics textbooks (Berger, 2019;Weinberg & Wiesner, 2011;Wiesner, Weinberg, Fulmer, & Barr, 2020). Weinberg and Wiesner (2011) define the implied reader as "the embodiment of the behaviours, codes and competencies that are required for an empirical reader to respond to the text in a way that is both meaningful and accurate" (Weinberg & Wiesner, 2011, p. 52). From their definition, it is clear that the goal is to find out what is needed for an accurate reading of the textbook, and that lack of comprehension is seen as shortcomings on the student reader's part due to a discrepancy between the implied reader and the student reader. ...
... The concept of the implied reader is not used in the same way in this paper and in Weinberg and Wiesner's study (2011). Whereas the goal of this study is to both disclose the gaps in the text and to explore how the text can enable and invite students to close these gaps, the focus of Weinberg and Wiesner (2011) is not on the potential shortcomings of the textbook, but rather on investigating what competence a student must possess in order to match the implied reader. The present study investigates how the implied reader can be structurally inscribed in the text in a way that is ambiguous, and so opens up the need for a better understanding of the textbook genre, and in particular, the need for a better understanding of the consequences of fragmentizing the running text by a large amount of various bulletpointed peritexts. ...
This study investigates the relationship between the running text and the many peritexts commonly found in newer textbooks, along with the associated consequences for textbased learning. The paper is a theoretically driven case study that looks at the textual composition patterns in a language arts textbook for lower secondary schools in Norway. In particular, I investigate how these textual composition patterns facilitate learning from text—a main tool in the text analysis is comparing the signaled intentions in the text with the implied reader’s fulfillment. The main finding of the study is that by enriching a textbook with many peritexts that contain essential content, one risks inviting the implied reader to employ a memorization strategy, even though the intention is to invite the implied reader to use deep-comprehension cognitive strategies. This is connected with the lack of running text. Without enough running text to synthesize the content, the running text appears dead, and rather than learning from the text, students are more likely to receive a memorization invitation from the text.
... This network is not a real reader but offers the real reader a role to play. The concept has been used in research on history textbooks (Garske, 2017) and has been adapted in more detail concerning mathematics textbooks (Berger, 2019;Weinberg & Wiesner, 2011;Wiesner, Weinberg, Fulmer, & Barr, 2020). Weinberg and Wiesner (2011) define the implied reader as "the embodiment of the behaviours, codes and competencies that are required for an empirical reader to respond to the text in a way that is both meaningful and accurate" (Weinberg & Wiesner, 2011, p. 52). ...
... The concept has been used in research on history textbooks (Garske, 2017) and has been adapted in more detail concerning mathematics textbooks (Berger, 2019;Weinberg & Wiesner, 2011;Wiesner, Weinberg, Fulmer, & Barr, 2020). Weinberg and Wiesner (2011) define the implied reader as "the embodiment of the behaviours, codes and competencies that are required for an empirical reader to respond to the text in a way that is both meaningful and accurate" (Weinberg & Wiesner, 2011, p. 52). From their definition, it is clear that the goal is to find out what is needed for an accurate reading of the textbook, and that lack of comprehension is seen as shortcomings on the student reader's part due to a discrepancy between the implied reader and the student reader. ...
... The concept of the implied reader is not used in the same way in this paper and in Weinberg and Wiesner's study (2011). Whereas the goal of this study is to both disclose the gaps in the text and to explore how the text can enable and invite students to close these gaps, the focus of Weinberg and Wiesner (2011) is not on the potential shortcomings of the textbook, but rather on investigating what competence a student must possess in order to match the implied reader. The present study investigates how the implied reader can be structurally inscribed in the text in a way that is ambiguous, and so opens up the need for a better understanding of the textbook genre, and in particular, the need for a better understanding of the consequences of fragmentizing the running text by a large amount of various bulletpointed peritexts. ...
This study investigates the relationship between the running text and the many peritexts commonly found in newer textbooks, along with the associated consequences for textbased learning. The paper is a theoretically driven case study that looks at the textual composition patterns in a language arts textbook for lower secondary schools in Norway. In particular, I investigate how these textual composition patterns facilitate learning from text—a main tool in the text analysis is comparing the signaled intentions in the text with the implied reader's fulfilment. The main finding of the study is that by enriching a textbook with many peritexts that contain essential content, one risks inviting the implied reader to employ a memorization strategy, even though the intention is to invite the implied reader to use deep-comprehension cognitive strategies. This is connected with the lack of running text. Without enough running text to synthesize the content, the running text appears dead, and rather than learning from the text, students are more likely to receive a memorization invitation from the text.
... However, several studies have pointed out that traditional mathematics textbooks are closed in that they restrict the readership to very narrow activities (Love, Pimm, 1996). It is also emphasized that many students cannot effectively use their textbooks as learning tools (Weinberg, Wiesner, 2011). ...
... The text is the natural source that provides the learner with the necessary intellectual resources (new knowledge, new ways of thinking, new perspectives on this or that problem) for his or her life. In school education, the text is considered a prerequisite for productive learning, especially within the framework of "reading theory," according to which a student-reader actively constructs meanings (concepts) while working with texts (Weinberg, Wiesner, 2011). ...
Introduction. The most important factor for students’ intellectual development is the teaching content. A textbook text is a didactic unit of teaching content. Therefore, the question arises about the requirements for modern textbook texts in the framework of the psycho-didactic approach. Materials and Methods. The study was conducted based on an analysis of the psychological features of the intellectual development of students within the psycho-didactic approach, which is based on the psychological and pedagogical rationale of the multifunctionality of modern mathematics teaching materials. Results and Discussion. The concept of development-focused educational text, which should be constructed as a multidimensional semantic space (hypertext), is introduced. Classification of development-focused educational texts is presented (using school mathematics as an example) based on the ontological theory of intelligence, targeting the enrichment of the main components of students’ mental experience – cognitive, conceptual, metacognitive, and intensional experience. Typology of pedagogical developmental texts of different types in teaching mathematics in middle school is given. Conclusion. The use of developmental textbook texts contributes to understanding mathematical material and developing students’ intellectual resources.
... Textbook analysis was employed as the research design, following Arcavi's (2003) definition of visualization and Presmeg's (1986) five classifications of visual imageries. The inscriptions in both textbooks were analyzed through the lens of the implied reader based on the Reader-Oriented Theory of Weinberg and Wiesner (2011). Results of this study revealed that the dominant types of inscriptions used in the Probability chapter of both textbooks were generic drawings and real photographs. ...
... 4). Although the focus of the analysis is the visualization used in the textbooks, incorporated in this framework is the lens of Reader-Oriented Theory by Weinberg and Wiesner (2011). This means that the visualization opportunities accorded in the textbooks are investigated with the assumption that readers construct their own meaning and interpretation of the mathematical texts and other contents of the textbooks. ...
This study focused on examining the nature and extent of visualization found in the Probability chapters of Grades 8 and 10 Philippine Mathematics textbooks. Textbook analysis was employed as the research design, following Arcavi’s (2003) definition of visualization and Presmeg's (1986) five classifications of visual imageries. The inscriptions in both textbooks were analyzed through the lens of the implied reader based on the Reader-Oriented Theory of Weinberg and Wiesner (2011). Results of this study revealed that the dominant types of inscriptions used in the Probability chapter of both textbooks were generic drawings and real photographs. Concrete imagery was the most common type, although all five types of visual imagery were elicited by the inscriptions. Visualization in the textbooks was utilized to convey information to the readers. The variability in the number of elicited visual imageries contributes to visual gaps in students’ understanding of probability concepts. Lastly, approximately 8.44% and 5.06% of the text space were allotted to visualization in the Probability chapters of the Grades 8 and 10 mathematics textbooks, respectively. The study attempted to bring forth a different perspective in analyzing the role of mathematics textbooks and their visual structure in the teaching-learning process.
... According to Weinberg and Wiesner (2011), analysis of text comprehension also involves considering the characteristics of the learner-that is, how the reader relates to the text with which they are working. Here we overview previous research specific to three learner characteristics (interest, prior coursework in mathematics, and proof scheme) and their relation to comprehension of mathematical argumentation in text. ...
... Our findings are consistent with those who have described learners as having interpretive frames that influence their work with mathematical text (e.g., Weinberg & Wiesner, 2011). We add to this literature by showing differences in the frames of learners based on their mathematical immersion-their interest, prior coursework, and proof scheme. ...
This article describes the research design and findings from a use-inspired study of online text-based mathematics resources. We sought to understand whether and how existing mathematics interest, together with the learner characteristics of prior coursework in mathematics and proof scheme, influenced comprehension of mathematical argumentation and triggered interest in two types of mathematics text: (1) text featuring concrete, real-world applications (public domain) and (2) text with abstract and generalized modes of expression and content (abstract domain). Using an online assessment and person-centered analyses, we studied 64 (32 M, 32 F) undergraduate students who were and were not pursuing advanced mathematics coursework. Cluster analysis revealed two participant groups. Less mathematically immersed (LMI) participants improved comprehension of mathematical argumentation when working with public domain text, performing comparably to the more mathematically immersed (MMI) cluster in this domain; those in the MMI cluster performed comparably across text domains. In addition, LMI participants were more likely to identify public domain text as more interesting than abstract text, and they also were more likely than those in the MMI group to explain this by citing public rather than abstract domain reasons. Taken together, study findings suggest that interest in coordination with other learner characteristics scaffolds comprehension of mathematical argumentation. This study makes contributions to interest theory, understanding the role of interest in comprehension of mathematical argumentation, and ways in which practitioners might leverage student interest to promote comprehension.
... Through the textbook the students could are directly involved in the learning process [17]. The textbook becomes one of the main requirements in the learning process [18][19] and the media which become the key elements to increase effectiveness in the teaching and learning process [20]. Moreover, in the mathematics lessons, textbooks can help students build their understanding of mathematics and represent mathematics [19,21]. ...
... The textbook becomes one of the main requirements in the learning process [18][19] and the media which become the key elements to increase effectiveness in the teaching and learning process [20]. Moreover, in the mathematics lessons, textbooks can help students build their understanding of mathematics and represent mathematics [19,21]. Since the existence of textbooks is closely related to the curriculum [18,20]; therefore, mathematics textbooks should support the achievement of competencies that must be mastered. ...
As part of abstract algebra, the group theory is considered as a difficult subject for pre-service mathematics teachers (PMTs) since it seems not related to the future teaching. In line with the Klein's double discontinuity that the learning of group theory at the university did not bring the content from school mathematics and in the school level mathematics' content did not connected to the university mathematics. Therefore, the current study intends to develop the group theory textbook which connected to the school mathematics that provide the PMTs with the mathematical connection. The study involves the educational research and development cycle refers to Borg and Gall's model, which is adjusted to the need of this study. The research procedures consist of three main stages: collecting data, planning, and developing the product. There is a significant need for further studies to be done in this area to implement this group theory textbook to obtain how PMTs aware to the mathematical connection from school mathematics and vice versa. Furthermore, it is essential to conduct the study about the effectiveness of this textbook. Particularly, in overcoming the PMTs' difficulty in the learning process of group theory subject.
... In the past two decades, there have been increased efforts by mathematics education researchers to go beyond teacher-focused textbook research to explore student-textbook relationships (for example, Berger, 2019;Pepin & Haggarty, 2001;Törnroos, 2005), probably linked to preceding research on the shortcomings of the sole-mediator role of the teacher, with student use of textbooks being largely teacher-mediated (Haggarty & Pepin, 2002). Such a position has been found to be fairly limiting (MacIntyre & Hamilton, 2010;Weinberg & Wiesner, 2011) especially in the current mathematics education context across the globe which is characterised by a shift towards pedagogies in which learners are asked to take a more active part. ...
... Accordingly, researchers are increasingly keen to understand the interaction between specific features of the textbooks and the students' ability to use them as core resources for independent learning. Some of the aspects that have been explored include: the pedagogical intentions of the textbook (Haggarty & Pepin, 2002); the influence of textbooks' content and presentation on students' engagement and participation in learning (Macintyre & Hamilton, 2010;Weinberg & Wiesner, 2011); how explicit textbooks are, through their examples, in supporting the development of the students' reasoning and verification strategies (Mesa, 2010a); and the influence of textbooks on students' achievement (Ham & Heinze, 2018). Other foci have been an interest in control structures (Lithner, 2004) which links to exploring how effective textbooks are for self-instruction by modelling the process of working out specific problems; the extent to which textbooks use elaborated sentences (Mesa, 2010a) or the rhetorical voice (Pepin & Haggarty, 2001) to show and justify the connections of ideas presented in the argumentation; and the potential of examples (Mesa, 2010b) for developing metacognition. ...
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.
... Theoretical Framing: Reader-Oriented Theory Weinberg and Wiesner (2011) wrote that most academic research on textbooks has framed textbooks as static collections of ideas, simply describing students' reading of the texts as extracting information. They sought to characterize the ways in which students interpret textbooks using reader-oriented theory. ...
... Three ideas about the readers of textbooks emerge from reader-oriented theory: the intended reader, the implied reader, and the empirical reader. The intended reader is "the idea of the reader that forms in the author's mind" (Wolff, 1971, p.166, as cited in Weinberg & Wiesner, 2011). The empirical reader is the person who actually reads the textbook. ...
... Not all textbooks are easy to learn from and students' avoidance sometimes makes sense. Weinberg and Weisner [2] argued there are several links between texts and readers that need to align for a textbook to effectively support learning. For example, links may be broken when a student lacks the necessary background knowledge or misunderstands how the textbook format functions. ...
... Weinberg and Weisner [2] contrasted expert and novice readers in mathematics. They maintained expert readers actively construct meaning as they read, relating the text's ideas to their own knowledge. ...
... Textbooks play a significant role in shaping the curriculum and teaching practices in classrooms (Weinberg & Wiesner, 2011). It is important to investigate the similarities and differences between Turkish mathematics textbooks recommended by the Ministry of National Education's (MoNE) Middle School Mathematics Programme and the Middle Year Programme mathematics textbooks used in international schools following the International Baccalaureate (IB) programme. ...
It is imperative to explore the organization of contemporary teaching and learning methods in data analysis and probability within mathematics curricula, with a specific focus on comparing non-IB and IB approaches. This study analyzed how the contemporary teaching and learning of data analysis and probability was organized through an analysis of two textbooks as an intended mathematics curriculum (non-IB and IB respectively) by discussing similarities and differences between the two. It employed content analysis method to examine structural features, technology usage, and real-life connections by focusing on the topic in depth, exploring content, organization, and representation. This study results disclosed that both open-ended and closed-ended item formats were recommended, without clear superiority. Descriptive examples and percentages were provided to guide curriculum developers and support teachers in enhancing student learning outcomes. The study hopes to assist middle school students in achieving higher scores in international assessments such as PISA and TIMSS. It emphasizes the potential for revising mathematics curricula and textbooks to better meet students' needs, drawing inspiration from the success of the IB program.
... In addition, the Textbook is one of the main requirements in learning and is a medium that is a key element for increasing effectiveness in learning. In mathematics lessons, textbooks can help students build their understanding of mathematics and represent mathematics [17] [18]. Therefore, mathematics textbooks should support the achievement of competencies that students must master according to their class level. ...
... They express authors' interpretations of steering documents, and reflect views and beliefs involving mathematics and mathematics education. Their design depends on the image of the intended student (Weinberg & Wiesner, 2011) formed in the mind of the textbook author. In addition, they take into account teachers' expectations as well as publishers' views regarding what can be a successful product on the market. ...
... For quite an extended period of time, school textbooks have been a topic of international research (Fan, 2013;Fan et al., 2018). Textbooks have the potential to be a powerful instrument for assisting students in deepening their understanding of mathematics (Purnomo et al., 2019;Weinberg & Wiesner, 2011). According to Sievert et al. (2019), textbooks play a significant role in the teaching of mathematics because they have an impact on how teachers explain concepts and apply them in the classroom. ...
The objective of textbook study is to create high-quality textbooks. Analysis was done using a praxeological-didactical analysis (PDA) method. PDA offers space to analyze curriculum materials, such as math textbooks, which are the outcome of human action in the anthropology of a specific nation's society. There are 10 types of tasks given in the mathematics textbook on measurement of spatial figures and seven techniques are identified as possible ways to complete the tasks. The justification of praxis is that there are three emerging technologies and two theories that are used as the final direction of the given task type. There is a sequence of task composition at the start with loads at level 2 and level 3 that can affect student readiness. Psychologically, it is regarded as difficult at first, which can lead to students becoming disinterested as well as bored, thus experiencing difficulties, creating ontogenetic obstacles. The other predicted learning obstacles identified in this textbook are epistemological and didactic obstacles. All the findings from this analysis can be applied to continuously raise the standard of the currently available mathematics textbooks.
... The reading is written in a style that draws inspiration from the readings of mathematical texts that are found in Tymoczko (1993), Sinclair (2005), and Dietiker (2013) and also by considering the ideas of Rosenblatt (1988), namely to make explicit what the student knows and what one anticipates. When reading the textbook, I have imagined myself to be a student for whom the textbook is written (the intended reader according to Weinberg and Wiesner (2011)). More specifically, I have assumed that at that point of the textbook I: ...
Good stories, literary or mathematical, have the ability to keep the reader engaged and wanting for more. However, poorly designed stories may also elicit a negative aesthetic reaction and thereby reduce engagement. By drawing on literary theory and Dietiker’s (For the Learning of Mathematics 33(3):14–19, 2013; Educational Studies in Mathematics 90(3):285–302, 2015) theoretical framework of mathematical stories, this essay conceptualises two aspects of mathematical stories that are likely to be perceived by the readers as aesthetic deficiencies: mathematical cheap plot tricks and mathematical plot holes. Additionally, examples of them are proposed from various areas of mathematics curriculum and some ideas of how they can be avoided, so as not to hinder engagement, are offered.
... Based on text-reading theory, the "use" is understood as reading, a transaction between mathematics textbooks (written curriculum) and students (Berger, 2019). In reader-oriented theory, the student is viewed as actively constructing meaning from mathematics textbooks through the reading process, which is shaped and constrained by the intentions of the author, the beliefs of the reader, and the qualities the text requires the reader to possess (Weinberg and Wiesner, 2011). From the perspective of activity system, students' textbook use refers to the activities that are primarily associated with textbooks in students' mathematics learning, such as reading and practicing (Rezat and Sträßer, 2013;Wang and Fan, 2021). ...
Students’ use of textbooks is the key link of students engaged and learned curriculum and has received much attention recently. However, existing studies were mainly case studies or small-scale investigations and few addressed the context of China. Hence, this study provided a general overview of mathematics textbook use by Chinese secondary students through a large-scale investigation. Using a mixed-method approach, we collected the quantitative data from 2,145 students in eight provinces through a questionnaire survey and the qualitative data from 20 students and 8 teachers by the interviews. The results revealed that (1) Chinese students relied heavily on mathematics textbooks and pointedly used a portion of components in textbooks, mainly kernels, examples, and exercises; (2) Chinese students used mathematics textbooks for various but typical reasons, particularly to understand basic knowledge and skills, and showed self-regulation and teacher-mediation behind their use; and (3) Chinese students had a positive view about textbook use in mathematics learning, especially in developing mathematical knowledge, skills, and abilities. Furthermore, there were significant differences in mathematics textbook use among different students in terms of school regions, grade levels, and teachers’ demographic variables. Finally, explanations and implications of the results were discussed.
... Buku teks atau modul menjadi alternatif untuk membantu mahasiswa memahami materi matematika (Annisah, Zulela and Boeriswati, 2020). Namun, banyak mahasiswa yang kurang memperoleh manfaat dengan menggunakan buku teks ataupun modul sebagai sumber belajar (Weinberg and Wiesner, 2011). Oleh karena itu, diperlukan analisis yang tepat untuk menentukan modul yang akan dikembangkan sehingga modul tersebut dapat memberikan hasil yang optimal bagi pencapaian mahasiswa. ...
Perkembangan ilmu pengetahuan dan teknologi menuntut peningkatan kemampuan manusia salah satunya berpikir kreatif. Peningkatan kemampuan berpikir kreatif matematis ini salah satunya dapat diperoleh di Perguruan Tinggi melalui mata kuliah Kalkulus Integral. Untuk menunjang pembelajaran diperlukan suatu bahan ajar berupa modul. Penelitian ini bertujuan untuk mengetahui modul kalkulus integral yang bagaimana yang dibutuhkan mahasiswa untuk meningkatkan kemampuan berpikir kreatif matematis. Penelitian ini adalah penelitian kualitatif deskriptif menggunakan tes, observasi, angket, wawancara, dan analisis bahan ajar. Hasil penelitian menunjukkan bahwa mahasiswa Pendidikan matematika membutuhkan modul kalkulus integral yang mudah dipahami, memfasilitasi kemampuan bepikir kreatif matematis, memuat penjelasan dari konsep materi yang dipelajari, berbasis model pembelajaran inovatif, menggunakan teknologi sesuai perkembangan zaman, dan bisa digunakan secara mandiri. Kata kunci: analisis kebutuhan, berpikir kreatif matematis, kalkulus integral, modul
... Textbooks are considered to have the potential as a powerful tool to help students develop ideas and understanding of mathematical concepts. Reading textbooks provides opportunities for students to be involved in tasks that demand a high level of understanding, which is expected that students will have higher scores (Hadar, 2017;Weinberg & Wiesner, 2011). If the textbooks are different, students will get different learning opportunities, so learning opportunities affect student achievement (Yang & Sianturi, 2017). ...
Buku teks yang memiliki konten isi memiliki peranan yang sangat penting dalam menunjang proses pengetahuan siswa secara utuh. Fakta menunjukkan bahwa sebagian besar guru bergantung pada buku teks, hingga ada keluhan pada isi dan sajian buku teks. Penelitian ini bertujuan untuk mendeskripsikan karakteristik sajian buku teks kelas tujuh pada materi perbandingan berbalik nilai ditinjau dari teori prakseologi yang memiliki empat elemen analisis, yaitu tugas, teknik, teknologi, teori. Penelitian ini adalah penelitian deskriptif kualitatif dengan objek penelitian adalah buku teks siswa kelas VII terbitan Kemendikbud, serta subjek penelitian melibatkan guru kelas tujuh. Temuan penelitian menunjukkan bahwa sajian buku teks materi perbandingan berbalik nilai sudah cukup baik. Namun, ada beberapa sajian yang perlu dilengkapi. Materi perbandingan berbalik nilai sudah bersifat kontekstual, tetapi terdapat ilustrasi tidak sesuai perkembangan kognitif siswa. Sajian teknik kurang lengkap dan tidak memberikan ruang bagi siswa untuk memilih cara menyelesaikan kasus perbandingan berbalik nilai, tidak ada kesempatan bagi siswa untuk memberikan justifikasi terhadap teknik yang dilakukan, serta beberapa tidak ada situasi untuk membuat siswa menyimpulkan terhadap hasil justifikasi yang dilakukan. Textbooks with content are very important in supporting the students’ knowledge process. The facts show that most teachers depend on textbooks, so there are complaints about the content and presentation of textbooks. This study aims to describe the characteristics of a seventh-grade textbook presented on inverse proportion in terms of the praxeological theory, which has four elements of analysis, namely task, technique, technology, and theory. This research is a qualitative descriptive study with the object of research being a textbook of class VII students published by the Ministry of Education and Culture. The research subject involves seventh-grade teachers. The study results show that the presentation of inverse proportion in textbooks is good enough. However, there is some present that needs to be completed. The inverse proportion is already contextual, but some illustrations do not match students' cognitive development. The presentation of techniques is incomplete and does not provide space for students to choose how to solve cases of inverse proportion, there is no opportunity for students to justify the techniques used, and in some situations, there are no situations to make students conclude on the results of the justifications carried out.
... Though textbooks may have the potential to help students develop an understanding of mathematics, often many students are unable to read and hence use their textbooks effectively as learning tools. Teachers thus need to mediate their students' use of textbooks (Weinberg & Wiesner, 2011). Thompson's (2022) article iterates that reading mathematical texts is an essential component of developing deep mathematical understanding imperative for one's mathematical literacy. ...
This introductory paper to the special issue “Reading in Science and Mathematics” presents four major theoretical perspectives of reading, literacy, and language that underpin many studies in this area, including the nine articles selected for this issue. It first outlines several new developments and contemporary issues that drive the growing importance of reading in science and mathematics. It then presents the perspectives that inform and situate the authors’ research as reported in this special issue, followed by a brief introduction of their articles situated within each of the perspectives. The four perspectives are reading comprehension, scientific/mathematical literacy, disciplinary literacy, and linguistic/semiotic meaning-making. The purpose in discussing these perspectives is to map out the theoretical terrain in the field and connect the key ideas within the research on reading in science and mathematics.
... This is because subjects are abstract and require diversity in delivering their content (Gellert et al., 2013). Not all students have the same ability to understand the concepts of Mathematics based on textbook content (Weinberg and Wiesner, 2010). ...
... Education researchers could learn a lot about a country's teaching and learning environment by analyzing their textbooks (Sevimli & Kul, 2015). Therefore, several studies have focused on analyzing calculus textbooks to explore ways in which the teaching and learning of calculus could be improved (e.g., Artigue et al., 2007;Mesa, 2010;Mesa & Griffiths, 2012;Oehrtman et al., 2008;Weinberg & Wiesner, 2011). ...
Mathematical objects are the outcomes of human discourse and come to life through the process of objectification. Primary and concrete discursive objects (d-objects) play an important role in this process, forming different realizations through the objectification process. In the present study, we analyze the written discourses about the derivative at a point in fourteen Year 11 and Year 12 Iranian calculus textbooks over 42 years (1979–2020) in terms of primary objects, concrete d-objects, and the realizations used in them, here based on Sfard’s commognitive theory. The research method is a qualitative content analysis in which the analysis units were texts, examples, activities, and exercises in the textbooks. The results show that out of the 14 textbooks, only five included primary and concrete d-objects. The other textbooks only used abstract objects in their written discourse about the derivative. The pictures (visual mediators) that were used as primary objects gradually changed from schematic to real colored photos, and locally developed technologies and cultural elements were included in the new textbook editions. Additionally, the number of concrete d-objects increased in the new editions. In terms of the realizations, the number of roots also increased over time; however, none of the textbooks had all fve main realizations (i.e., symbolic, graphical, verbal, numerical, and physical) for the derivative at a point. The realization tree developed as part of this study can be used as an analytical framework to analyze calculus textbooks in other contexts and can be used by teachers and lecturers to help students have explorative participation in discourse on the derivative.
... This is because subjects are abstract and require diversity in delivering their content (Gellert et al., 2013). Not all students have the same ability to understand the concepts of Mathematics based on textbook content (Weinberg and Wiesner, 2010). ...
... ▪ Actualmente, los marcos teóricos más prometedores para el estudio del libro de texto son aquellos que proponen un enfoque relacional, centrado en la comprensión del contexto donde el fenómeno tiene lugar: neo-institucionalismo, gramática de la escuela, y teoría del actor-red. Estos enfoques ponen el énfasis en la idea de que el significado del libro de texto se construye de forma activa, a través de las relaciones que se establecen con otros elementos contextuales (Hansen, 2018;Kolbeck y Röhl, 2018;Roldán, 2018;Weinberg y Wiesner, 2011). intermedia o problemas no rutinarios con un mayor nivel de complejidad cognitiva. ...
Los libros de texto son el tipo de material curricular más empleado en la educación obligatoria. El objetivo de este trabajo es analizar el tratamiento que reciben los problemas aritméticos verbales de estructura aditiva en estos materiales. Se llevó a cabo una revisión de estudios recientes que analizan la estructura semántica de los problemas en los libros de texto de diferentes sistemas educativos. Se concluye que los libros de texto no constituyen, por sí solos, herramientas eficaces para abordar el proceso de enseñanza-aprendizaje de la resolución de problemas. Además, es necesario tener en cuenta las carencias de estos materiales curriculares y utilizar problemas matemáticos que abarquen todas las estructuras semánticas.
... Content analysis is a research tool of qualitative research used to determine the presence and meaning of concepts, terms, or words in one or more pieces of recorded communication [38]. Mesa emphasized that analyzing the contents in textbooks could help one discover the authors' epistemological decisions while selecting specific content concerning what has led to the legitimization of a preferred piece of knowledge, what would students learn if they followed the text entirely, how would students construct meaning from the text in the textbooks, and what notions would the students develop by reading the text alone [39,40]. In Charalambous, Delaney, Hsu, and Mesa's comparative analysis of primary mathematics textbooks, they found three approaches to textbook analysis, which was classified as horizontal, vertical, and contextual analysis [41]. ...
The topic of similarity plays an essential role in developing students’ deductive reasoning. However, knowing how to teach similarity and understanding how to incorporate deductive reasoning and proof along with plane geometry remain a challenge to both school curriculum creators and teachers. This study identified the problems and characteristics regarding how similarity is treated in secondary mathematics textbooks in Hong Kong in the past half century. The content analysis method was used to analyze six secondary mathematics textbook series published in different periods. From the epistemological perspective of the textbook contents, our analysis shows the historical context and learning trajectories of how similarity was treated in school curriculum. The natural axiomatic geometry paradigm is not emphasized too much at different stages and most of the textbooks did not provide formal proofs of similarity. The intuitive idea was gradually consolidated into a formal definition of similarity. Furthermore, the way that rigorous geometric deduction can be performed from intuitive concepts and experimental geometry to the idea of proofs and formal proofs is also discussed.
... 705-706). Questioning in textbooks has a different character as they are meant to establish a personal relationship between the reader, the author, and the mathematics (Weinberg & Wiesner, 2011), a relationship that tends to be private. As the increased level of interactive technologies has also reached textbooks, it is now possible for students to type their responses directly in the textbook in response to a question, making those responses immediately available to instructors. ...
The goal of this study is to identify the multiple ways in which instructors take advantage of a feature designed into university textbooks that seeks to invite students to get acquainted with the content prior to attending the class in which such content will be discussed. We present an analysis of teacher instrumentation of this feature, which we call questioning devices, using data from 15 instructors who taught calculus, linear algebra, or abstract algebra over one semester. The instructors taught at 14 different universities in the United States. We identified four utilization schemes of the questioning devices in which instructors: completed questioning devices for pre-planning, required students to complete the questioning devices for the purpose of lesson planning, used the questioning devices for the purpose of instruction, and required students complete the questioning devices for the purpose of assessment. These schemes are supported by various operational invariants related to self-perception as competent instructors and implicit theories of teaching and learning. The identified utilization schemes inform textbook developers and author-designers, making them aware of whether these features fulfill their design purposes, and possibly think about changes that might be needed to support instructors in achieving their instructional goals and improve learning. We suggest some further areas of inquiry.
... Teachers commonly use textbooks as an instructional resource. Even though textbooks are meant to be read by students, and textbook authors often include messages to students about how to read the text (Weinberg & Wiesner, 2011), teachers lack a confidence and willingness to teach students how to read texts (Carter & Dean, 2006;Metsisto, 2005). However, teachers are willing to engage in vocabulary instruction to support students' understanding of mathematical concepts and procedures (Carter & Dean, 2006). ...
A survey of 80 United States middle and high school mathematics student teachers gathered data on availability and use of textbooks and traditional and technology-supported instructional strategies. Findings about textbooks include (1) most classrooms had one or more textbook formats (print, digital or e-textbook) available but did not necessarily expect students to use the textbook; (2) some differences were noted when comparisons were made based on school location, size, and grade level; and (3) student teachers preferred the digital textbook format but there was also support for the print format. Analysis of student teachers’ self-reported use of instructional strategies, including a principal component analysis, revealed use of traditional teaching strategies and student-centered teaching. Student teachers’ views about how best to teach mathematics centered on themes of active learning and ways to meet students’ needs.
... Researchers have studied the efficacy of the online homework systems, both quantitatively and qualitatively (e.g., Burch & Kuo, 2010;Halcrow & Dunnigan, 2012;Mathai & Olsen, 2013; Meletiou-Mavrotheris, Lee, & Fouladi, 2007;Smolinsky, Olafsson, Marx, & Wang, 2018;Zerr, 2007), but not how they are used by students. Traditionally, implementing an analysis of textbook use (e.g., Lithner, 2003;Weinberg & Wiesner, 2011) entails studying how the textbook is used. However, the shift brought on by online homework systems in what constitutes curriculum requires new studies. ...
Article History The purpose of this mixed-methods study was to explore how undergraduate students in an applied calculus course used the written curriculum (i.e., textbook, online homework system, and previous exams). The study design included three phases: (a) an online survey, (b) individual observations, and (c) student interviews. Students' survey responses indicated that not many students referenced the required textbook, but all students accessed the online homework system, through which homework assignments were completed with immediate feedback available. A follow-up qualitative analysis of eight students revealed limitations of the usefulness of the feedback of this system.
... Tasks have been analysed from the perspective of the intended student (e.g. Weinberg & Wiesner, 2011). To accomplish this perspective, it has been assumed that the student has followed the textbook strictly, worked with all the preceding material, and comprehended it. ...
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.
... teachers, textbooks). However, if students encounter knowledge through an active meaning-making process (Weinberg & Wiesner, 2011), they can actively construct and regulate their understanding of mathematics. Where mathematics knowledge is constructed through inquiry (e.g. ...
Possessing the mathematical competence to encounter the challenges under globalisation and the ubiquity of digital technology is
an important goal of education. Herein, we propose a broad conceptual framework for understanding and developing mathematical competence. The framework comprises four non-overlapping
but interlinked cores: learning, knowing, applying, and viewing. Our
framework encompasses ontological, epistemological, and pedagogical dimensions based on a multi-dual perspective. The proposed
framework serves as a foundation for generating different learning
paths to develop mathematical competence. Examples of learning
paths are provided to illustrate the correlative and complementary
relationships among the cores of mathematical competence
Nos últimos anos, a produção acadêmica relacionada ao tema de livros didáticos de Matemática cresceu e vem se consolidando. O International Conference on Mathematics Textbook Research and Development (ICMT) é um evento específico, destinado a essa temática. Com o objetivo de mapear as perspectivas e possibilidades apresentadas na terceira edição do ICMT, especificamente aquelas sobre a análise de livros didáticos de Matemática, assumimos a abordagem qualitativa com a metodologia do tipo mapeamento. Assim, identificamos três perspectivas não disjuntas: quem são os sujeitos que analisam os livros didáticos; como esses livros são analisados; e o que é analisado neles. Como resultado, evidenciamos que a análise desses materiais possibilita revelar lacunas entre as prescrições oficiais e o que é proposto pelos autores de livros didáticos, além de salientar aspectos relacionados aos conteúdos e a procedimentos alusivos ao ensino e à aprendizagem da Matemática, no âmbito (ou não) das tendências em Educação Matemática. Abstract: In recent years, academic production related to Mathematics textbooks has grown and has been consolidating. The International Conference on Mathematics Textbook Research and Development (ICMT) is a specific event dedicated to this theme. In order to map the perspectives and possibilities presented in the third edition of the ICMT, specifically those about analysis of Mathematics textbooks, we take a qualitative approach with a mapping-type methodology. Thus, we identified three non-disjoint perspectives: who are the subjects which analyze textbooks; how these Esta obra foi licenciada com uma Licença Creative Commons Atribuição 4.0 Internacional 237 237
This work sets about understanding and modelling differences in look and feel between tertiary Abstract Algebra texts. We present a `proof-of-concept' stage model of this difference, in terms of a concept that we call the `terrain' of a text. Our model is influenced by our conceptual framework, which brings together `Reader Oriented Theory', and `Content Analysis'. We define `terrain' to be the proportion and arrangement of functionality within a text. The particular functionality that we explore in this article relates to four categories: `Facts', `Explanation', `Notation' and `Sign posting'. In particular, the modelling of the type and frequency of `Facts' in Abstract Algebra techniques appears to be novel; whereas `Explanation' has been considered in previous literature at least in the particular instance of proof. Utilising an acronym for the four categories, we call the resulting model the `FENS' model of Terrain. The FENS model has several different instantiations, each associated with a different type of theoretical reader, defined by a collection of reading characteristics. The differences depend on the kinds of Facts, Explanations etc. that different readers are likely to be sensitive to in their reading. For instance a reader who is interested only in technical mathematical facts will `see' a different book to one who is interested in big-picture ideas and historical origins. Our model indicates two results of interest: (i) different books have very different FENS even for the same reader, and (ii) different readers are likely to experience very different FENS for the same book.
Literacy, specifically reading mathematical text, is an essential component of developing deep mathematical understanding. Given the role that textbooks play in classroom instruction around the globe, it is useful to consider how features of curriculum design might influence classroom practice related to reading. Results from studies of a curriculum series in which reading mathematics is an embedded design feature provide insight on teachers’ and students’ perceptions on the importance and frequency of reading in mathematics and on the strategies used. The results have implications for curriculum developers as they design mathematics textbooks.
Bu çalışmada uluslararası sınavlarda başarı düzeyi yüksek olan Singapur ile başarı düzeyi orta sıralarda yer alan ABD’nin matematik ders kitapları ile Türkiye’nin 8. sınıf ders kitaplarının MEB Matematik Dersi Öğretim Programı (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar)’ında yer alan 8. sınıf kazanımları baz alınarak içerik ve görsellik açısından kıyaslanması amaçlanmıştır. Araştırma doküman analizi kullanılarak yapılmıştır. Çalışmada öncelikli olarak ülkelerin matematik öğretim programlarının uyumuna bakılmış, ABD ile Türkiye’nin öğretim programlarının daha uyumlu olduğu sonucu ortaya çıkmıştır. Kitapların organizasyonuna ilişkin öğrenme alanlarının sayfa sayıları karşılaştırılmış ve sayılar öğrenme alanına en fazla ABD’nin, Geometri ve ölçme alanına Türkiye’nin diğer iki ülkeden daha fazla yer verdiği, Cebir ile İstatistik ve Olasılık öğrenme alanlarına ise Singapur’un ABD ve Türkiye’den daha fazla yer ayırdığı sonuçlarına ulaşılmıştır. Her üç ülkenin de ders kitaplarının iç tasarımları ayrı ayrı incelenmiş, farklılık ve benzerlikler bulunmuştur. Sayılar öğrenme alanında Türkiye ve ABD çözümlü örneği diğer yaklaşımlardan fazla kullanırken, Singapur en çok keşfetmeyi kullanmıştır. Geometri ve ölçme alanında her üç ülke de çözümlü örneğe fazlaca yer verirken, Cebir ile İstatistik ve Olasılık öğrenme alanlarında Singapur keşfetme yaklaşımını daha fazla kullanmıştır. Türkiye matematik ders kitabında çözümlü örnek sayısı en fazla iken Singapur matematik ders kitabında çözümlü örnek sayısı en az, toplam gösterim sayılarına bakıldığında ise gösterimlerin en fazla Türkiye’de kullanıldığı görülmüştür. Ancak Türkiye matematik ders kitaplarında ilişkisiz gösterim sayısının da fazla olduğu görülmektedir. Bu durumun anlam karmaşasına ya da yersiz görsel yoğunluğa neden olabileceği düşünülmektedir. Ayrıca ilişkili gösterimlerin yoğunluklarına bakıldığında Singapur kitaplarının daha sade Türkiye ve ABD kitaplarında görsellerin daha yoğun olduğu görülmüştür.
Recent research demonstrates that mathematics teachers rely on a variety of curriculum materials and must make meaning and synthesize these materials for use in a particular place with particular students. While there are multiple theories about the nature of this work and the factors which influence this work, the field continues to lack a theoretical basis with which to understand this multifaceted and complex work. This paper seeks to illuminate the process by which teachers come to make meaning from curriculum materials by the daily practices of one team of teachers. Findings supports a transactional view of curriculum in which students, teachers, curriculum materials, and contexts work with and on each other as curriculum emerges. Using this theory as a framework, multiple understandings of teachers’ work with curriculum can be synthesized as highlighting particular aspects of a larger curriculum system.
Textbooks are one of the most fundamental learning and teaching tools used in schools all around the world (Nicholls, 2003). Today's technology allows students to access a variety of textbook formats, including online textbooks that they may read from anywhere. This study looks into the style and arrangement of learning textbooks in Malaysia in order to make studying more convenient. The purpose of this research is to see if the dynamics of textbook layout affect students' desire to learn. Thirty Year 6 children from a primary school in the Selangor district of Hulu Langat participated in this study. Students' views of textbook design elements, such as paper quality, printing, colour, and pedagogical aspects, were determined using a quantitative survey. Print and colour were scored higher by the students than paper quality, artwork, and images, according to the data. Furthermore, the research discovered a link between the layout of a book and its actual use.
This article develops an analytical framework for analysing college (tertiary) statistics textbooks in terms of text accessibility by integrating the text, the reader, and the content into the framework. Five accessibility attributes of science texts were adapted to conceptualize the accessibility of statistics texts. For each accessibility attribute, two components were proposed by referring to the literature on the readability of mathematics texts as well as the characteristics of statistics. The feasibility of the framework is demonstrated by analysing sample statistics texts. The contributions and potential of the framework are discussed.
In global competition, Indonesian learners have not shown the intended achievement. PISA research reveals the lower mathematical literacy level of Indonesian learners. The Learners’ difficulty in mathematics is likely due to text-oriented learning and abstract object of mathematical analysis. This article particularly attempts to address the implementation of mathematic software toward the enhancement of learners’ ability of mathematical literacy. Based on the discussion, it can be concluded that mathematic software-based learning can be applied to enhance learners’ ability of mathematical literacy related to the exploration of a concept, reasoning, systematic-logic and analytical thinking as well as learning interest on mathematics
This questions the prevailing approach in the presentation of the concept of slope in teaching undergraduate in Turkey. For this purpose, five mathematics textbooks, were analyzed for problems related to slope, and similarities and differences were revealed. First, the subjects related to the slope in the textbooks were categorized and examined within the context in which they were handled. Therefore, this study is a qualitative study that adopts the interpretive paradigm. These categories are discussed in the form of connectivity, exploration, and purpose using the study for the context (Rezat, 2006). Stump (1999; 2001b) and Moore-Russo et al. (2011) studies were used for cognitive development. These are determined as geometric ratio, behavioral indicator, property determiner, algebraic ratio, parametric coefficient, functional property, linear constant, real life, physical property and trigonometry. Representations of the process skills were chosen as algebraic expressions, tables, and graphics. The concept is discussed in the form of calculus. In the use of technology (Akkoyunlu, 2002; Schware & Jaramillo, 1998), BCS, Scientific and Graphing Calculators, Internet are arranged. Definition, justification, and explanation for performance are arranged. When textbooks are compared, Turkey's textbooks contains more algebraic expressions, the use of the grounds and explanations and real-life connection, contains applications that use more formulas, the description is to use less highlighted is technology, other math they do not explicitly state their links with the subject areas. In general, it was seen that translated textbooks were mostly related to real life, equipped with explanations and justifications requiring cognitive competencies, and proceeded harmoniously between the subject area's main ideas and related ideas. These books use multi-step solved problems. Turkish textbooks need to be reviewed in terms of their functional areas in terms of context, cognitive need, representations, technology, and performance.
This study explores the disciplinary literacy perspectives of middle school students of color attending urban parochial schools and the reader subject positions they took up across content-area classrooms. Qualitative analysis of 19 student interviews and accompanying observations of subject-area classes revealed that students’ constructions of reading, circumscribed by classroom literacy activities, inhibited discipline-specific reading subject positions. In particular, this study highlights how teachers’ reading activities promoted reading as being about accomplishing a task rather than being apprenticed in ways of taking discipline-specific knowledge from text. When the boundaries between students’ home literacy experiences and school disciplinary literacy experiences were more contiguous, and when more meaningful, authentic literacy experiences were provided, students evidenced deeper disciplinary literacy engagement. Educational implications, including troubling disciplinary knowledge to open the disciplines to wider ways of knowing and learning for all learners, are discussed.
This research aims to describe students’ views in understanding mathematics by reading a mathematics textbook. The subjects of this research were 6 students on grade VI at Singapore International School (SIS) Palembang. This is descriptive research. The research instruments were interviews and questionnaires. Based on the results, 50% of students read a mathematics textbook by reading definitions or rules, learning examples of the problems and doing exercises. And 50% of students read a mathematics textbook by learning examples of the problems, reading definitions or rules and doing exercises. In understanding mathematics, 16.7% of students felt understood mathematics textbook after understood the definitions or rules, 33.3% of students felt understood mathematics textbook after doing the mathematics problems, 33.3% of students felt understood mathematics textbook after doing exercises and 16.7% of students felt understood mathematics textbook after doing mathematics problems and understanding definitions or rules.
The purpose of this study is to determine the mathematics teaching materials needed by students to improve problem-solving skills. This research is a qualitative descriptive study. The subjects of this study were PGMI students in the Metro city, province of Lampung. Data collection uses a non-test method that uses a questionnaire. The questionnaire consisted of 16 questions, which included eight questions about the analysis of learning resources (teaching materials) and 8 questions about determining learning resources (teaching materials). The results of this study are 1) mathematics teaching materials that are used effectively help students understand mathematical material, but are not effective in helping students develop problem-solving skills, 2) students need mathematics teaching materials based on contextual approaches to improve problem-solving skills. Based on the results of this study, it is necessary to develop mathematics teaching materials based on a contextual approach to improve problem-solving skills.
Textbooks are a standard component of undergraduate mathematics courses, but research shows that students often do not view textbooks as productive resources to support learning. This article seeks to understand the factors affecting how individuals engage in reading a calculus textbook excerpt and what they learn from reading. To better understand the separate roles of background knowledge and other reading practices, we compare 2 readers: a 2nd-semester calculus student and a nonmathematics STEM professor. We employ the concepts of sense making and the implied reader to analyze each reader's experience and a disciplinary literacy perspective to explain the similarities and differences we find between the 2 readers. We propose the concept of didactical disciplinary literacy—an adaptation of disciplinary literacy applied to didactical texts—to describe the ways that the professor drew on his identity as a teacher to shape his reading practices.
Many active learning practices highly depend on students' advance preparation for the class. However, reading Calculus can be a challenging task to students. We address this concern by assigning targeted pre-class readings in multiple Calculus courses. We report on our implementations, provide students' feedback, and discuss the lessons learned from these implementations.
This study analyzed how the earliest teaching and learning of probability was organized in Singapore, the US, and Indonesia through an analysis of textbook as an intended mathematics curriculum. An analytical framework was developed comprising four perspectives: representational forms, cognitive demand levels, contextual features, and organization of topics and its uniqueness. This study disclosed that the organization of the earliest teaching and learning of probability in the three countries focused on approximately similar topics, such as basic concepts of probability and probability measurements, although they were intended for different educational levels. Nevertheless, the uniqueness of the organization indicated that students in the three countries may receive different opportunity-to-learn in the earliest teaching and learning of probability in schools. In addition, Singaporean textbook had more exposure to higher-cognitive demand levels and written forms, while the US textbook put more concerns on lower-level demands and visual forms, Indonesian textbook included more proportions of lower- cognitive demand levels and written forms. Moreover, the three textbooks provided considerable opportunity to engage in real-life situations. Considering these results, more studies analyzing other standards-based textbooks and teaching practices might be needed to have further understanding of the organization of probability teaching and learning in schools.
This is a review of research on thinking aloud in reading comprehension that considers thinking aloud as a method of inquiry, a mode of instruction, and a means for encouraging social interaction. As a method of inquiry, the analysis of verbal reports provided by readers thinking aloud revealed the flexible and goal-directed processing of expert readers. As a mode of instruction, thinking aloud was first employed by teachers who modeled their processing during reading, making overt the strategies they were using to comprehend text. Subsequently, instructional approaches were developed to engage students themselves in thinking aloud. Such endeavors revealed facilitation effects on text understanding. Current efforts to engage students in constructing meaning from text in collaborative discussions seem to indicate a new direction for thinking aloud research, one in which social interaction assumes increased importance.
In this paper, we analyze the way two groups of students—successful mathematics majors and less successful mathematics majors—attempted to learn a new mathematical concept. We presented both groups of students with a textbook-style presentation of the concept and then asked them to complete homework-type exercises. The successful mathematics students were more likely to reformulate the concept definition in their own words, connect the new concept to prior mathematical concepts that they had studied, try to understand what a theorem is asserting before reading its proof, and try to understand the statements in their exercises before attempting to prove them.
Textbook selection strongly influences on what students will learn and what the teachers will teach. Certain statements regarding the process of development and selecting mathematics textbooks are given and assessed.
This article establishes a broad framework from which to interpret and evaluate the reading–science learning–writing connection. The presentation of breakthroughs, barriers, and promises is intended to outline the established links between, to identify current bottlenecks in thinking about, and to highlight productive inquiries into, print-based languages and scientific understanding. The ideas presented come from various disciplines connected to science education. The ideas are meant to be informative, provocative, integrative, supportive, and without hidden agenda.
This study compares reading comprehension of three different texts: two mathematical texts and one historical text. The two
mathematical texts both present basic concepts of group theory, but one does it using mathematical symbols and the other only
uses natural language. A total of 95 upper secondary and university students read one of the mathematical texts and the historical
text. Before reading the texts, a test of prior knowledge for both mathematics and history was given and after reading each
text, a test of reading comprehension was given. The results reveal a similarity in reading comprehension between the mathematical
text without symbols and the historical text, and also a difference in reading comprehension between the two mathematical
texts. This result suggests that mathematics in itself is not the most dominant aspect affecting the reading comprehension
process, but the use of symbols in the text is a more relevant factor. Although the university students had studied more mathematics
courses than the upper secondary students, there was only a small and insignificant difference between these groups regarding
reading comprehension of the mathematical text with symbols. This finding suggests that there is a need for more explicit
teaching of reading comprehension for texts including symbols.
From a socio-cultural perspective it is argued that the modality of artefacts has, structuring effects on the activities in
which the artefact is involved. The mathematics textbook is an artefact that has a major influence on the activity of learning
mathematics. Against this setting, the structures of the units in German mathematics textbooks for different grades and ability
levels have been analysed. Firstly, the different structural elements have been examined with regard to: characteristics in
terms of content; linguistic characteristics; visual characteristics; their pedagogical functions within the learning process;
and situative conditions. Secondly, the orders of the structural elements within the units of the different textbooks have
been compared. The findings reveal that the structure of the units is very similar in different mathematics textbooks. The
units are not only composed of analogous structural elements, but these elements are also arranged in almost the same sequence.
In order to develop a deeper understanding of these findings the structure of the units has been compared to the influential
learning theories of J. F. Herbart and H. Roth. On this basis it is argued that the structure of the units seems to reflect
the phases of idealised learning processes in general. The issue is raised if this is an appropriate structure in order to
provide opportunities to learn mathematics.
ZDM-ClassificationU20
Two experiments, theoretically motivated by the construction-integration model of text comprehension (Kintseh, 1988), investigated the role of text coherence in the comprehension of science texts. In Experiment 1, junior-high students' comprehension of one of three versions of a biology text was examined via free recall, written questions, and a keyword sorting task. This study demonstrates advantages for globally coherent text and for more explanato text. In Experiment 2, interactions between local and global text coherence, readers background knowledge, and levels of understanding were examined. Using the same methods as in Experiment 1, we examined students' comprehension of one of four versions of a text, orthogonally varying local and global coherence. We found that readers who know little about the domain of the text benefit from a coherent text, whereas high-knowledge readers benefit from a minimally coherent text. We argue that the poorly written text forces the knowledgeable readers to engage in compensatory processing to infer unstated relationships in the text. These findings, however, depended on the level of understanding, textbase or simational, being measured by the three comprehension tasks. Whereas the free-recall naeastne and text-based questions primarily tapped readers' superficial understanding of the text, the inference questions, problem solving questions, and sorting task relied on a situational understanding of the text. This study provides evidence that the rewards to be gained from active processing are primarily at the level of the situation model, rather than at the superficial level of textbase understanding. Interactions of text coherence, background knowledge, People learn a great deal from texts -- story books, textbooks, newspapers, or...
This article differentiates the usages of transaction and interaction as reflections of differing paradigms. The transactional theory of reading is dissociated from information-processing and interactive processing. The implications for research of various concepts basic to the total transactional theory of reading are discussed.
Concrete materials have a long history in the mathematics classroom, although they have not always been readily accepted or used appropriately. They disappeared when written computational methods arose and little premium was placed on understanding the algorithms being learned. Comenius and Pestalozzi began the process of reintroduction, with Montessori and many others in the present century providing new materials and new rationales for their use, so that today one finds hundreds of ‘manipulatives’ available. Arguments have persisted, however, as to whether common tools from daily life might be better than specially constructed educational materials and whether, in fact, all such materials might do more harm than good. Educational materials are not miracle drugs; their productive use requires planning and foresight.
The failure to distinguish between Iser's "implied" reader (analogous to Booth's implied author and referring to the reading behavior a text demands of us) and the "characterized" reader (referred to directly or indirectly in the text) has promoted a good deal of critical confusion. Although the work of Wolff, Iser, Ong, Link, and Prince, among others, is crucial to our understanding of how fictional readers function in texts, it generates certain misleading conceptual categories. In part this confusion is due to a gap between continental and American reader-response theory. The "implied reader" is not a philosopher's stone that will objectify criticism, but it can be a useful concept to the newer communication-oriented theories of criticism.
In this study we explore the potential for mathematics instruction of four reading strategies grounded in transactional reading theory. On the basis of the descriptive study of 18 instructional episodes developed in 4 secondary mathematics classes as a result of collaborative action research, we show that encouraging mathematics students to talk, write, draw, and enact texts can provide them with concrete ways to construct and negotiate interpretations of what they read. In addition to helping students better understand the text read, acting on and acting out a text allow students to use that text as a springboard for sense-making and discussion of important mathematical ideas and issues about the nature of mathematics, especially when these reading experiences are supported by compatible classroom norms and values.
In this paper I illustrate difficulties students have coordinating informal and formal aspects of mathematics. I also discuss two ways in which precalculus and calculus textbooks treat mathematics that may make this coordination difficult: emphasizing the informal at the expense of the formal and emphasizing the formal at the expense of the informal. By looking at student difficulties in light of textbook treatments, we see evidence that student difficulties are not merely developmental. Students are not given many opportunities to make the kinds of connections which, while difficult, are an essential component of mathematical thinking.
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Understanding Reading revolutionized reading research and theory when the first edition appeared in 1971 and continues to be a leader in the field. In the sixth edition of this classic text, Smith's purpose remains the same: to shed light on fundamental aspects of the complex human act of reading--linguistic, physiological, psychological, and social--and on what is involved in learning to read. The text critically examines current theories, instructional practices, and controversies, covering a wide range of disciplines but always remaining accessible to students and classroom teachers. Careful attention is given to the ideological clash that continues between whole language and direct instruction and currently permeates every aspect of theory and research into reading and reading instruction. To aid readers in making up their own minds, each chapter concludes with a brief statement of "Issues." Understanding Reading: A Psycholinguistic Analysis of Reading and Learning to Read, Sixth Edition is designed to serve as a handbook for language arts teachers, a college text for basic courses on the psychology of reading, a guide to relevant research on reading, and an introduction to reading as an aspect of thinking and learning. It is matchless in integrating a wide range of topics relative to reading while, at the same time, being highly readable and user-friendly for instructors, students, and practitioners.
This study investigated the incorporation of specific reading strategies in mathematics lessons. Fourteen students attended a three-week, individualized, summer intervention program provided by a large southern university for the purpose of increasing mathematical understanding. The frequency of reading-related instruction was documented from 72 audiotaped lessons and classified according to reading strategy. Although the purpose of the program was to improve mathematics functioning, findings indicated that teachers inherently instructed students in reading strategies while teaching mathematical concepts with: 1) vocabulary instruction the most prevalent reading strategy followed by 2) dense questioning and 3) anticipatory guide to improve reading comprehension of the mathematical text. Teachers also encouraged better mathematical reading comprehension by asking students to read aloud and discuss each passage.
Our goals in this study were to explore the type of written questions students ask after reading one or more chapters from their textbook, and to investigate the ability of students to improve their questions during the course of a single semester. In order to classify student's questions we used a taxonomy that we have developed specifically for this purpose. Two comparable populations were examined: Undergraduate students in a large, introductory biology class who were taught in traditional lecture format, and students in a similar class who were taught in cooperative/active learning style. After the taxonomy was presented to the active learning class, more students were able to pose better, written questions. Their questions became more insightful, thoughtful, and content-related, and were not easily answered by consulting the textbook or another readily available source. The best questions could be recast as scientific research questions (i.e., hypotheses). In contrast, when the taxonomy was presented to students in the traditionally taught class, the quality of student-posed questions was largely unchanged. Various explanations for the difference in outcomes are discussed, and methods are suggested about how generally to encourage students' questions and to improve their question-asking skills regardless of overall teaching style.
This paper reviews the literature on reading and mathematics and calls for a new synthesis which views reading as a mode of learning. This synthesis focuses not on the acquisition of techniques but on the process of doing mathematics and the more humanistic aspects of the discipline. Four alternative frameworks for the problem of "reading mathematics" are identified: (1) extracting information from technically oriented mathematics texts; (2) reading to learn so as to achieve the goal of a technically oriented mathematics curriculum; (3) introducing rich mathematical texts to provide students with information on important aspects of mathematics typically excluded from the mathematics curriculum; and (4) shaping a new synthesis in which reading to learn mathematics so as to understand mathematics becomes a "way of knowing." The literature for each of the frameworks is reviewed; most of the existing literature belongs to the first framework. (A figure provides a theoretical grid of the four frameworks; 46 references are attached.) (RS)
College science teachers know that students get the most out of class if they have completed the assigned reading. To reinforce this expectation, we ask our introductory physics students to submit a question they had about the reading. In this paper we describe the rationale and logistics of this assignment. (Contains 2 tables and 2 figures.)
Textbooks play an important role in undergraduate mathematics courses and have the potential to impact student learning. However, there have been few studies that describe students' textbook use in detail. In this study, 1156 undergraduate students in introductory mathematics classes were surveyed to describe how they used their textbook. The results indicate that students tend to use examples instead of the expository text to build their mathematical understanding, which instructors may view as problematic. This way of using the textbook may be the result of the textbook structure itself as well as students' beliefs about reading and the nature of mathematics. Although many instructors may not clearly convey how they want their students to use the textbook, students do report using it more productively when they believe they are asked to do so. This suggests that instructors should carefully choose text materials to promote mathematical reasoning and actively encourage their students to read the text in a way that supports the development of this reasoning.
College students responding to the Preferred Method of Study (PMOS) questionnaire explained how they approach reading a new textbook chapter for comprehension. Results indicated that a significant positive correlation exists between the number of passes a student makes at new textbook material and his/her college grade-point average. Women showed a significant preference for adopting a single method of study. Less than half of the students queried construct “organizational tools” such as outlines or diagrams as they study a textbook. Students said they would alter their textbook strategies in response to the type of test they expected significantly more often than they would for the type of subject matter being studied. Only 6% of the students said they make a conscious effort to link the new concepts in the text to prior knowledge. There was no discernable relationship between the study strategies undergraduate college students employ and their college grade level (freshman through senior).
Investigations of the actual reading process and of the structure of a mathematical text are important for elaborating didactical methods for teaching reading a mathematical text. The article reports on a broader project concerning the structure of a mathematical text. The structure of several hundred texts has been analyzed. Academic textbooks and mathematical monographs (especially in Polish) written by mathematicians have been used as a source. Characteristic features of proof construction, that may influence the course of the reading process, have been isolated. For instance, transmission means have been investigated such as text segmentation which uses delimiters and so called procedure schemes.
The teaching-learning process is considered as a social interaction. In this microethno-graphical case study an elementary teacher and first graders are observed when they ascribe mathematical meanings of numbers and of numerical operations to empirical phenomena. Because of the differences of their ascriptions, the teacher and the students negotiate mathematical meanings. Also interactional regularities help the participants to cope with ambiguity. According to different theoretical approaches, the text discusses some indirect relations between social interaction and mathematics learning. Several classrooms episodes are interpreted to illustrate specific theoretical concepts.
Video recordings of three undergraduate students' textbook-based homework are analysed. A focus is on the ways their exercise reasoning is mathematically well-founded or superficial. Most strategy choices and implementations are carried out without considering the intrinsic mathematical properties of the components involved in their work. It is essential in their strategies to find procedures to mimick and few constructive reasoning attempts are made.
The article examines mathematics textbooks and their use in lower secondary classrooms in England, France and Germany. In particular, it looks at popular selling textbooks in each country and their treatment of 'angle', and examines teachers' mediation of those books based on observation and interview of a small sample of teachers in those countries. An analysis of the data suggests that learners in the different countries are offered different mathematics and given different opportunities to learn that mathematics, both of which are influenced by textbook and teacher. In addition, it identifies pupil access to textbooks in England as a cause for concern. It is argued that mathematics classroom cultures need to be understood in terms of a wider cultural and systemic context, in order for shared understandings, principles and meanings to be established.
Reading and writing in science have been frequently maligned but infrequently studied since the 1960s move toward hands-on science. Current interest in the printed-based language arts in science is supported by contemporary educational reforms and the realization that simply doing more hands-on activities may not improve meaningful learning. Students need opportunities to consolidate their science experiences and to contrast their understandings with the interpretations of the science establishment. Science literacy means that students learn about the "big" ideas of science and how to inform and persuade others about these ideas. This article attempts to sketch a substantive framework for using science reading and science writing with deaf students based on research and informed practice with hearing students.
The foundations of mathematical competence laid by primary schools in Germany and Switzerland are compared with Britain on the basis of the main textbooks used in the three countries, supported by observations of classroom practice. The study forms part of the National Institute's wider research programme into comparative productivity, education and training which has repeatedly noted the mathematical deficiencies of British school-leavers. The study examines, among other matters, the greater emphasis given to mental calculation in Continental schools, the more detailed gradation of successive learning-steps, greater number of practice-exercises at each step, and greater continuity in the teaching of each topic. British pupils' attainments could be improved by textbooks which gave more attention to these aspects but, the author stresses, classroom organisation and teaching methods in Britain would also benefit from closer attention to Continental practices.
Toward a semiotics of mathematics How implicit models of reading affect motivation to read and reading engagement
- B Rotman
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Epistemological assumptions in the study of response Reader-response criticism: From formalism to post-structuralism (pp
- D Bleich
Reading to learn mathematics: New connections, new questions, new challenges
- R Borasi
- M Siegel
An examination of textbook “voice”: How might discursive choices undermine some goals of the reform?
- B A Herbel-Eisenmann
Didactic transposition in mathematics textbooks
- W Kang
- J Kilpatrick
Rezeptionsforschung: Eine einführung in methoden und probleme [Reception Research: An introduction to methods and problems]
- H Link
Lebensweltliche inszenierungen. Die aushandlung schulmathematischer bedeutungen an sachaufgaben [Real-world Role Plays: The negotiation of school-related mathematical meanings through assigned tasks
- A Neth
- J Voigt
Textual strategies. For the Learning of
- M Otte
The implied reader in calculus textbooks
- A Weinberg
Der intendierte leser [The Intended Reader]. Poetica
- E Wolff