ICMT3

Europe/Berlin
Paderborn University, Germany

Paderborn University, Germany

Warburger Straße 100 33098 Paderborn Germany
Sebastian Rezat (Chair), Lianghuo Fan (Co-Chair) (Co-Chair), Mathias Hattermann (Chair of LOC)
    • 08:30 10:00
      Others: Registration / Coffeebreak
    • 10:00 11:00
      Others: Opening Ceremony
    • 11:00 12:30
      Plenary: Plenary Jill Adler O1 (Paderborn University)

      O1

      Paderborn University

      • 11:00
        Revisiting resources as a theme in mathematics education 1h 30m O1

        O1

        Paderborn University

        The idea of interrogating resources and their use in school mathematics practice was mooted some twenty years ago, arguing for an extension of the notion of a resource beyond the physical and material, and examination of their use in practice (Adler, 2000). In this time extensive related work has evolved. In this presentation I will revisit the early work, the trajectory of selected related developments, including relevant work on textbooks, and reflect on its current salience

        Speaker: Jill Adler (University of the Witwatersrand, South Africa; King’s College London, UK)
    • 12:30 14:00
      Lunch 1h 30m
    • 14:00 16:00
      Oral Communications
    • 16:00 16:30
      Coffeebreak 30m
    • 16:30 18:30
      Symposia: Symposia I
    • 18:30 20:30
      Others: Postersession & Reception
      • 18:30
        A mathematics college textbook: design intentions and reading practice 2h

        Reading mathematics is difficult for many reasons such as dense text explaining abstract concepts. Many undergraduate mathematicians still struggle to read mathematics proficiently suggesting that not enough is being done at school or college to support learning this important skill. Although research in this area is increasing, research into the most widely used reading material in the mathematics classroom – the textbook – is relatively scarce. This project aimed to explore whether mathematics textbooks are fulfilling their potential by conducting two investigations into the design and use of a specific college-level textbook. Firstly, we interviewed authors of the textbook to investigate intentions behind design decisions and then we recorded students’ eye-movements as they read the textbook. We thematically analysed the interviews and the resultant themes helped to generate specific research questions for the eye-tracking investigation. Consequently, we found that authors tended to correctly predict how the textbook would be read even when the reading strategies were not representative of best practice. This poster recognises how better communication between educators, researchers, authors and publishers could improve a textbook’s potential as a facilitator of mathematical reading. Additionally, we explore differences between how students read and processed specific elements of the textbook’s design and discuss how better design might inspire more efficient reading.

        Speaker: Ms Bethany Woollacott (Loughborough University)
      • 18:30
        A qualitative study on the levels of mathematical explanation in Japanese elementary textbook 2h

        In Japan (maybe, also around other countries), one has pointed out that elementary students’ ability and skill for explanation in mathematics lacked. For this reason, we should analyze our own mathematics textbooks because it works as curriculum. (Notes: In Japan, all textbooks are authorized by the Ministry of Education).
        Our theoretical framework is framework for mathematical explanation in elementary school that is proposed by Miyazaki (1995). The purpose of Miyazaki(1995) is to improve teaching and learning proof and proving in junior high school students; for this purpose, he also construct the framework because explanation in elementary school will connect with proof. Miyazaki(1995) identify and distinguish 4 levels of explanation in elementary school mathematics; level 1 is lowest, and 4 is highest. Our methodology is qualitative analysis by the framework. Our object is “formula for the area of a parallelogram” in the fifth grade (Shimizu, Funakoshi, Negami, Teragaito et al., 2015, pp.124-125), because there are 4 explanations for one problem; since the number of explanations for one problem is most, it is expected that the intention of the textbook appears.
        As a result, we can pointed out there are explanation of level 2, 3, and 4 are written in it (there are two level 2); however, its order is not from 2 to 4, but from 4 to 2. Thus, we can say the textbook has not paid attention to level (or quality) of explanation.
        On the other hand, actual students may explain as it, level 2 or 3. Miyazaki’s (1995) framework does not refer how to improve it or reveal conception of students who explain as level 1, 2 or 3. Thus, we found necessity of another types of theoretical frameworks for it.

        Speaker: Mr Takahiro Okubo
      • 18:30
        A Study of the Characteristic of Japanese Textbooks towards the Growth of Children's Mathematical Representation 2h

        The purpose of this research is to clarify the measures being used in Japanese elementary and junior high school’s textbooks to foster children’s understanding and usage of mathematical representations.
        First, a discussion were conducted on the kinds of representations required as well as the process of its development based on the national curriculum and achievement test. Both of them possess an explicit process of the continuity between elementary school and junior high school. As grade level increases, subject matter changes from arithmetic to mathematics as representations become more formal and mathematical, as well as more logical and systematic.
        Next, measures used by the textbooks were considered. As students progress through grade levels, their understanding and usage of representations, in the same manner as their textbooks, becoming more formal, for instance, from Manipulative Representation and Illustrative Representation to more Linguistic Representation, as well as the usage of more Symbolic Representation. Additionally, measures of representations are conducted not only through a textbook’s speech bubbles or comments, but also by preparation and usage of mathematical notes and reports that guide students in the development of their understanding and usage of representations. Certain textbook companies develop students’ representations by including content focused on knowledge and usage of vocabulary necessary for students to represent themselves logically.

        Speaker: kunihiko shimizu
      • 18:30
        A study on the educational ideology of modernization in the case of Japanese textbook 2h

        Purpose of this study is to describe an ideology of era of modernization in mathematics education by our theoretical framework. According to Chevallard (2015), our current ideology is ‘paradigm of visiting monuments’, on the other hand ‘paradigm of questioning the world’ should replace it. Here, we focus on the term ‘paradigm’ which is proposed by Kuhn (1970) because it was critiqued by Lakatos’s (1978) notion of ‘research program’. Base on it, we constructed our hypothetical framework which consists unseparatable three levels of ‘hard core’ and ‘protective belt’: ‘rational level’, ‘belief level’, and ‘society level’; ‘rational level’ is identical with Lakatos’s (1978) research program.
        Our methodology is philosophical consideration for mathematics textbook because it reflects social and ideological conditions and constraints in era of modernization. The reason for paying attention to modernization is that, it is one of most important educational movements and, in Japan, the curriculum clearly stated that the purpose is to foster students’ attitude for first time.
        As a result of consideration, we can describe that modernization attacked only protective belt in ‘belief level’ and ‘society level’; for example, it changed the contents and arrangement of mathematical knowledge in curriculum. Thus, modernization can not change hard core so it becomes new protective belt for monumentalism.

        Speaker: Takahiro Mabuchi
      • 18:30
        A study on the senior high school students’ algebraic activities and the digital tools in Japanese digital mathematics textbook 2h

        In this study, we analyse Japanese digital mathematics textbook in senior high school with focusing on students’ algebraic skills or notions. For learning algebra, generalization plays essential role; especially, Dörfler (1991) pointed out that to use algebraic letters relates with students’ activities.  For instance, according to Fujii (2000), when students can not consider about relationships between mathematical objects, they can not use algebraic letters well;  Dörfler (1991) said students abstract these relationships through their own activities.Thus, our theoretical framework is Dörfler (1991), and methodology is qualitative analyses of the digital textbook; we focus on unit of quadratic function because it is compulsory and core unit of learning algebra in senior high school. 
        As a result, we can point out the layout of digital textbook is same as paper textbooks; however, each problem has an icon to access the digital tools. From our theoretical view, almost of all these tools are for validating (and/or justifying) explanation by sentences.  In other words, we found that these tools do not allow students’ activities (in sense of Dörfler (1991)). Based on this result, we discuss nature of digital tools and propose concrete tools and theoretical perspective for digital tool which realize Dörfler's (1991) activities.

        Speaker: Mr Kazumichi Tanaka
      • 18:30
        ANALYSIS OF THE INTEGRATION OF TECHNOLOGIES IN TEXTBOOK GEOMETRY CONTENT 2h

        This paper is a result of an ongoing research, which among its objectives is the analysis of the integration of technologies in Mathematics textbooks. The research is qualitative and aims to instigate reflection on the contributions of different didactic resources (digital technologies in particular) to the practices of teachers with textbooks. In this conference the focus is to present part of the results, coming from the analysis of activities of five collections of textbooks of the High School in the ambit of the proposals of use of the technologies in the development of contents of Geometry. The results point to the low presence of digital technologies in high school books, with few research activities, visual exploration of geometric figures, and the use of dynamic geometry software, which address aspects of the dynamism of this resource. Most of them are limited to performing and checking calculations. It is expected that there will be a change of this framework, once since 2014 Digital Learning Objects have been incorporated into the textbooks, with the proposal of a greater integration of technologies to the traditional printed resource that the teacher uses to develop their classes.

        Speaker: Rúbia Amaral-Schio (UNESP)
      • 18:30
        ANALYSIS OF TYPES OF TASKS PROPOSED IN A TEXTBOOK: A COMPARATIVE APPROACH IN THE OPTICS OF PRAXEOLOGY AND PNLD/BRAZIL 2h

        This study is the result of an investigation conducted within a course in the Master's degree program of the Graduate Program in Mathematical and Technological Education - EDUMATEC/UFPE, whose objective was to analyze the approach for teaching areas of flat figures by comparing the types of tasks proposed in textbooks. In addition, we observed the changes in the textbooks with the recent regulations of the National Program of Didactic Book - PNLD/Brazil. The Anthropological Theory of the Didactic was used as theoretical reference of analysis to support the observation of the activities presented in the books. The ATD postulates that any human activity can be described by a praxeology, that is, a four-component model: [T / τ / θ / Θ], where T is a type of task, τ is the technique used to perform task, θ is a technology that justifies the technique and Θ is the theory that underlies the technologies. With this background, a comparative study was carried out between the two editions of the textbook “Vontade de saber Matemática” (“Will to know Mathematics”; 2009 – 1st ed.; 2015 – 3rd. ed.). The results of the study indicate that there are advances and evolution in the proposed approaches and activities consistent with the national official guidelines.

        Speaker: Rafael Marinho de Albuquerque (UFPE)
      • 18:30
        Analyzing Math Textbook in Elementary School Mathematics in Japan-Focusing on the explanation of multiply decimals- 2h

        The purpose of this paper is to analyze mathematics textbooks used in elementary school math classes in Japan. In Japan, textbooks are prepared based on the Course of Study prepared by the Ministry of Education (including guidelines). This study indents to analyze explanations of how to multiply decimals in the fifth grade of elementary school. In the Japanese calculation guidance, two explanations are recommended: one for writing expressions, and the other for calculating them. For these two kinds of explanations, two different publishers were compared and analyzed. The analysis was conducted using a modified and reinforced version of the TIMSS framework (Valverde et al. 2002). The results revealed that, while the subject being explained remained unchanged, there were differences in the following areas. First, in terms of the explanation of the grounds on which the formula was set up, Publisher T had an explicit activity explaining the process using a proportional relationship, while Publisher K did not use the proportional relationship. In addition, in the explanation regarding how to calculate, Publisher T used a number line, along with a verbal explanation of how to perform the calculation. Meanwhile, Publisher K used only a verbal explanation. Based on the above, it became clear that in the teaching of how expressions are written and calculated, the type of formula, and the content of the explanation differ, depending on the publisher.

        Speaker: Mr Shigetaro Sato (Matsumoto university)
      • 18:30
        CURRENT STATUS AND ISSUES OF DIGITAL TEACHING MATERIALS IN JAPAN 2h

        A considerable amount of time has elapsed since ICT was introduced into the class in Japan and it is recognized that it is comprehensively effective, but it is in progress in mathematics department. In this article, research trends related to mathematics education and technology are described as follows: (1) timing and scene of utilization in the class, (2) what kind of ability of the child to improve, (3) how to use commercial software, self-made software, (4) class design, The four points were organized. In classes, methods of using PCs in accordance with conventional learning processes are being studied, but research on the evaluation method is in short supply. It is not enough to clarify what kind of ability a child is able to develop, and it is necessary to combine the functions and properties of PC with self-made software after clarifying the aim and purpose of the lesson. As a future topic, I showed that desktop PC study from arithmetic education is desirable for PC to contribute to mathematics education.

        Speaker: MANABU GOTO (Sagami Women's University)
      • 18:30
        Exploratory Research on Understanding Proof by Coincidence: Building an Analytical Framework by Comparing Japanese Textbooks 2h

        This paper aims to create an analytical framework for empirical studies seeking to understand “proof by coincidence,” a type of indirect proof. Although little is known about teaching and learning proof by coincidence, all junior high school mathematics textbooks in Japan include this method of proof. To hypothesize the potential problems of teaching proof by coincidence, we investigated the variety of ways in which Japanese junior high school textbooks present the Converse of the Pythagorean Theorem (CPT), which is usually proven by coincidence. We found that the figures and emphatic points used to present the Pythagorean Theorem (PT) and its converse are often identical. It is noteworthy that we are not sure whether the differences in the ways textbooks present the PT and the CPT necessarily contributes to the resolution of students’ confusion, while we can conduct empirical research on students’ process of understanding of proof by coincidence from this point of view. Further research is therefore required to determine what influence this editing policy may have on students learning the proof by coincidence method.

        Speaker: Toru Hayata
      • 18:30
        Geometrical properties as assumptions in proofs in Japanese junior high school mathematics textbooks 2h

        Given the international evidence that students have trouble in understanding proof in mathematics (e.g. Hanna & de Villiers, 2012), the appropriateness of the content of textbooks is one crucial factor (Fan et al., 2018). Here, we focus on the introduction of proof in Japanese mathematics textbooks at the junior high school level. In one of these textbooks, authorized by the Ministry of Education in Japan, a proof is defined as ‘an explanation of a statement based on properties that we already know to be true’. If these ‘already known to be true statements’ are treated ambiguously or unclearly in the textbooks, this might underlie some of the difficulties in the teaching and learning of proofs. Hence our research question is: in Japanese junior high school mathematics textbooks, what is the relationship between the set of geometrical properties as assumptions in the definition of a proof, and the geometrical properties that appear in the proofs? For our analytic framework, we define ‘correspondence’ as the consistency between facts for students and geometrical properties, and ‘coherence’ as the deductive consistency between geometrical properties. We find that there is a ‘gap’ of adopting ‘correspondence’ and the ‘coherence’. One way to overcome this gap is to design textbooks for geometry that provide the sections for the proof structure, ‘justification’ and ‘systematization’ as the functions of proofs.

        Speaker: Prof. Mikio Miyazaki (Shinshu University)
      • 18:30
        LIMIT OF TEXTBOOK IN CONCEPTUAL UNDERSTANDING 2h

        In this paper, we consider the solution based on the universal mathematical idea in Japanese mathematics textbooks. We consider the conceptual understanding in the multiplication of the fraction. Teachers teach it in the fifth graders of elementary school. The conclusion is applying to numerators and denominators each other. It is the mere procedural understanding. In order to make this conceptual understanding, the area of the square is shown in the textbook. For example, the right figure illustrates 1/2×3/4. The Japanese fourth grader in elementary schools learn decimal × decimal. The teachers urge conceptual understanding based on the number line. However, that teachers do not use that number line in this scene. Because it is not used in textbooks. It can be expected that conceptual understanding is urged to examining the area of the square on the other hand. The relation of such Textbook and Student, Teacher, and Mathematical knowledge is as being shown in Rezat's model. So, in the multiplication of the decimal and fraction, it is concluded that the method of urging conceptual understanding is not related.

        Speaker: Tsutomu Ishii (Bunkyo University)
      • 18:30
        The Analysis of the Diagrams in the textbook of Arithmetic 2h

        It is useful and meaningful to used diagrams for making sense of calculation and solving word problems. But it is difficult for pupils to interpret and use the diagrams (NIER, 2014). In response to this situation in Japan, we need to reconsider using diagrams in teaching/leaning of calculations from the cross-sectional perspectives for the development of number concepts and meaning of calculation. So, the purpose of this study is to examine and consider the features and classification of diagrams in textbooks used in teaching/leaning of calculations in elementary school. As a method on this study, based on the theory of mathematical expressions by Nakahara (1995) and a process of solving word problems by Mayer (1992) as a theoretical framework, we are analysed and considered the diagrams used in textbooks. In this paper, we will cover teaching/leaning of addition and subtraction of integers of Japanese textbooks used from grade 1 to grade 3. As conclusions of this study, we have two points as below: (1) to suppose the new classification of the diagrams and (2) the difference of the quality of diagrams according to pupils’ development.

        Speaker: Haruka Kitabori (Faculty of Psychology Meiji Gakuin University)
      • 18:30
        The online platform Geogebrabooks as support of an electronic textbook: a study of potentialities and challenges. 2h

        In the context of digital inclusion, this research aims to find the possibilities and challenges that come from the use of digital media in the classroom, and also how they impact the school daily work. Through the discussion of a practice with the online platform “Geogebrabooks” in the teaching of quadratic functions, this work has the goal of defining an ETb and comparing it with the paper textbook.
        Naftaliev (2009) defines an Interactive Diagram (ID) as a relatively simple software application built around a visual example. The ETbs have the possibility of exploring IDs between conceptualization of mathematical objects, allowing a fluid visualization with movement. This brings lots of upsides for the education in general, making it more attractive for modern students. In addition, the use of IDs and other features of the ETbs might bring even bigger enhancements for the process of Reasoning-and-Proof (RP), theorized by Stylianides (2009).
        Since it’s an ongoing research, there are no conclusions yet, however we can look up to some expectations. In a recent brazilian paper, Madruga (2017) already noticed that the educational softwares are easy to learn, and that the students can use and play with them not only in school hours, but also in their free time too. This work also is looking for challenges, and it’s expected that some problems appear in the internet acces by the students, since not all of brazilian public schools have computers or tablets for them.

        Speaker: Mr Thor Franzen (Universidade Federal do Rio Grande do Sul (UFRGS))
      • 18:30
        THE PRESENCE OF GEOMETRY IN FRACTION TASKS: AN ANALYSIS OF TEXTBOOKS 2h

        This work presents results of a research, in development, which aims to investigate how Geometry is present in the other branches of Mathematics in some textbooks. We make a cut here, focusing on fraction tasks in textbooks destined to the Final Years of Elementary Education. We are looking at two books in the sixth year (because they contain most of the fraction content) of two different collections. First, we selected the chapters dealing with the fractions notions, and then separated the tasks in which Geometry appears. We analysed the tasks based on Arcavi (2003). The results show that Geometry appears in tasks that work the correspondence between fractional numbers and points of the numerical line and in the fraction representation through the decomposition of figures or geometric solids. Thus, the visual representations of Geometry can aid in the process of teaching and learning by making visible purely algebraic properties.

        Speakers: Prof. Liara Alves Gentil, Dr Rúbia Barcelos Amaral-Schio
      • 18:30
        The use of a digital textbook with integrated digital tools 2h

        The use of mathematics textbooks makes an impact on teaching and learning in the classroom. Because of the important role of textbooks, it can be presumed that digital mathematics textbook also have an effect on didactic aspects of the organisation of lessons and teaching. Since 2019, the project KomNetMath surveys the influence of a digital mathematic textbook regularly used by teachers and students in grade 10 and 11 at German schools. The goal is to examine the actual use of the digital textbook and the impact on teachers’ and students‘ attitude towards the use of digital textbooks as well as its influence on the progress of mathematical competencies. In this contribution, we present the concept of the digital textbook, the theoretical background, the research questions and the research design.

        Speaker: Mr Maxim Brnic (University of Münster)
    • 08:30 10:00
      Plenary: Plenary Birgit Pepin
      • 08:30
        Mathematics (E-)Textbooks: Help or Hindrance for Innovation? 1h 30m O1 (Paderborn University)

        O1

        Paderborn University

        Textbooks may help education innovation as they can efficiently steer and support many teachers to enact renewed curriculum intentions in classroom processes. At the same time textbooks may also hinder real innovation as they reduce the opportunities of teachers to (re)design the curriculum, or to develop curriculum design capacity, by an overdose of detailed scripts that reduce teachers to technical slaves. E-textbooks are heralded to be interactive and to support teachers in their everyday classroom practices, as well as in their curriculum (re-)design, and innovative and collaborative work with colleagues. However, access to useful subject-didactical resources does not always lead to curriculum renewal and innovative practices.

        In this presentation I suggest a promising middle road: educative materials, focusing on a limited number of essential characteristics for curriculum renewal. Such materials may:

        • help teachers to orientate on and practice with new elements in their teaching repertoire;
        • guide teachers in role taking experiences that exemplify new pedagogical approaches;
        • create opportunities for shared reflection by teachers that may challenge also their beliefs about appropriate teaching.

        It is argued that such educative materials are best designed and piloted by small teams of mixed composition: teachers, teacher educators, curriculum designers, and researchers. The development process is said to be iterative, with gradually shifting emphasis in quality criteria: from relevance, to consistency, practicality, and effectiveness.

        Speaker: Birgit Pepin (Eindhoven University of Technology, The Netherlands)
    • 10:00 10:30
      Coffeebreak 30m
    • 10:30 12:30
      Oral Communications
    • 12:30 14:00
      Lunch 1h 30m
    • 14:00 16:00
      Symposia: Symposia II
    • 16:00 16:30
      Coffeebreak 30m
    • 16:30 18:30
      Workshops
    • 08:30 10:00
      Plenary: Plenary Susanne Prediger O1 (Paderborn University)

      O1

      Paderborn University

      • 08:30
        Enhancing and understanding students’ processes of mathematization and active knowledge organization - Didactical Design Research for and with textbooks in the KOSIMA-Project 1h 30m

        When textbook research is conducted as design research, two aims are systematically combined: (a) research-based design of teaching-learning arrangements and (b) design-based research for a deeper understanding of the initiated learning processes. In the Kosima-project, 14 years were spent on enhancing and understanding students’ learning processes, with a specific focus on mathematization and active knowledge organization. Initiating rich processes of mathematization is a central aim for all mathematics education. However, many obstacles appear for these processes to generate solid and sustainable mathematical knowledge. By Didactical Design Research, obstacles in students’ learning pathways can be systematically identified in the Kosima-project and then overcome.

        Speaker: Susanne Prediger (TU Dortmund)
    • 10:00 10:30
      Coffeebreak 30m
    • 10:30 12:30
      Oral Communications
    • 12:30 14:00
      Lunch 1h 30m
    • 14:00 18:00
      Others: Excursion
    • 20:00 22:00
      Others: Conference Dinner
    • 08:30 10:00
      Plenary: Plenary Jinfa Cai O1 (Paderborn University)

      O1

      Paderborn University

      • 08:30
        Mathematical Problem Posing, Curriculum Development, and Professional Learning 1h 30m O1

        O1

        Paderborn University

        Recent years have seen an increased effort to incorporate problem posing into school mathematics at different educational levels around the world. Curriculum has historically been viewed as a powerful agent for instructional change. Given the potential positive impact of including problem-posing activities in mathematics classrooms, it is useful to consider how curriculum might support such activities. In this plenary, I will first present a historical analysis of mathematical problem-posing activities in both China and the United States over the past several decades. Unfortunately, this analysis shows that only a very small proportion of the mathematical activities included in Chinese and U.S. curricula were problem-posing activities. Thus, the call to integrate problem-posing activities in mathematics classrooms is not well aligned with existing curricular resources and there is a need to help teachers develop problem-posing resources and implement problem posing in mathematics classrooms. I will then present findings from a longitudinal study investigating the impact of teachers’ learning to teach mathematics using problem posing on students’ thinking and affect. I will end by discussing methodological issues related to historical analyses of curricula and a longitudinal study of teachers’ professional learning.

        Speaker: Jinfa Cai (Changjiang Scholar, China Ministry of Education, Southwest University; University of Delaware, US)
    • 10:00 10:30
      Coffeebreak 30m
    • 10:30 12:30
      Oral Communications
    • 12:30 14:00
      Lunch 1h 30m
    • 14:00 16:00
      Symposia: Symposia III
    • 16:00 17:00
      Others: Closing Ceremony
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