ZDM: the international journal on mathematics education

Publications in this journal

• Article: Connecting mathematical creativity to mathematical ability

  Maria Kattou, Katerina Kontoyianni, Demetra Pitta-Pantazi, Constantinos Christou
  ZDM: the international journal on mathematics education 01/2013; 45(2).
• Article: Researching young students’ mathematical world views

  Katrin Rolka, Stefan Halverscheid
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  ABSTRACT: As an alternative to questionnaires suitable for young students, pictures, texts and interviews are used as data sources for studying mathematical world views of fifth and sixth graders in a several-step design. The project was developed in three successive studies. In the first study, the approach of using pictures, texts and interviews for researching young students’ mathematical world views was investigated. Object of the second study was the development of an interrater-method for determining mathematical world views which delivered a satisfactory degree of reliability. The empirical results in the second study indicated as well that quite often mathematics courses were dominated by a view on mathematics emphasizing numbers or calculations. An analysis of students’ utterances suggests that some young students might have mixed world views. This motivates a modified rating approach in a third study in which raters can give weights to several world views. The procedure indicates that various mixed forms of the world views can be observed. This brings up the question as to whether this phenomenon is due to the methodology or whether it describes the formation of mathematical world views at that age. KeywordsMathematical beliefs–Mathematical world views–Lower secondary education–Pictures and texts–Inter-rater method
  ZDM: the international journal on mathematics education 05/2012; 43(4):521-533.
• Article: Handheld calculators between instrument and document

  Gilles Aldon
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  ABSTRACT: The new generations of handheld calculators can be considered either as mathematical tools with opportunities for calculation and representation or as a part of the teachers’ and students’ sets of resources. Framed by the Theory of Didactical Situations and the documentational approach, we take advantage of a particular experiment on introducing complex calculators in scientific classes to investigate the position and the role of this handheld technology both for students and teachers. The results show how different functionalities can be shared among teachers and students, but also how other functionalities remain private and may even conflict with the teacher’s intentions.
  ZDM: the international journal on mathematics education 05/2012; 42(7):733-745.
• Article: Imagining mathematics teaching practice: prospective teachers generate representations of a class discussion

  Sandra Crespo, Joy Ann Oslund, Amy Noelle Parks
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  ABSTRACT: Prospective teachers work with a variety of representations of mathematics teaching (i.e., narrative cases, transcripts, video clips) in teacher preparation courses. Generally, they are considered the audience, not producers, of those artifacts. In this article, however, we focus on representations produced by prospective teachers when they were asked to generate a hypothetical classroom dialogue for the equality task: “What goes in the box: 8+4=[]+5?” We discuss the nature and quality of the representations produced by four different cohorts of teacher preparation students—prior to admission, at the beginning, middle, and end of their program. Prospective teachers within and across all cohorts produced an unexpected diversity of representations of class discussions. Of special interest to us were their hybrid representations, those that combined multiple images of mathematics teaching practices. These representations not only provide a lens into prospective teachers’ development as mathematics teachers but could also become tools to support novices as they learn more complex forms of mathematics teaching. KeywordsMathematics classroom dialogues–Representations of teaching–Prospective elementary school teachers–Classroom discussion
  ZDM: the international journal on mathematics education 05/2012; 43(1):119-131.
• Article: Introduction: the transformative nature of “dynamic” educational technology

  Stephen J. Hegedus, Luis Moreno-Armella
  ZDM: the international journal on mathematics education 05/2012; 41(4):397-398.
• Article: Blömeke, Sigrid, Kaiser, Gabriele and Lehmann, Rainer (eds) (2008): Professionelle Kompetenz angehender Lehrerinnen und Lehrer. Wissen, Überzeugungen und Lerngelegenheiten deutscher Mathematikstudierender und -referendare. Erste Ergebnisse zur Wirksamkeit der Lehrerausbildung

  Annegret Helen Hilligus
  ZDM: the international journal on mathematics education 05/2012; 41(5):703-707.
• Article: Research on Dynamic Geometry Software (DGS)—an introduction

  Rudolf Sträßer
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  ABSTRACT: The introduction briefly describes the characteristic features of Dynamic Geometry Software (DGS) to give the main reasons for the selection of papers in this ZDM-volume. Research on every characteristic DGS-feature (dragmode, macro-constructions, locus of points) is presented in one paper from an author having done research on the feature. The last paper describes an example of classroom research on DGS. Die Einleitung beschreibt die Charakteristika (Zugmodus, Makro-Konstruktion, Ortslinie) des Software-Typs “Dynamische Geometrie Software (DGS)” und erklärt so die Konzeption dieses Heftes. Je ein Beitrag stellt nämlich Forschungen zu einem dieser Charakteristika dar, während der letzte Beitrag Ergebnisse einer Untersuchung zum unterrichtlichen Einsatz von DGS berichtet.
  ZDM: the international journal on mathematics education 05/2012; 34(3):65-65.
• Article: Dimensions of students’ views of themselves as learners of mathematics

  Bettina Roesken, Markku S. Hannula, Erkki Pehkonen
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  ABSTRACT: Students’ views of themselves as learners of mathematics are a decisive parameter for their engagement and success in school. We are interested in students’ experiences with mathematics encompassing cognitive, emotional and motivational aspects. In particular, we focus on capturing the structural properties of affect related to mathematics. Participants in our study were 1,436 randomized chosen students of secondary schools from overall Finland. In the Finnish upper secondary school, there are two different syllabi for mathematics: the general and the advanced one. Schools were invited to organize the survey by one of their year 2 general syllabus courses and one of their year 2 advanced syllabus courses in grade 11. By means of factor analysis, we obtained seven dimensions in which students’ hold beliefs and emotions about mathematics partly intertwined with their motivational orientations. These dimensions are described by reliable scales, which allow outlining an average image of Finnish students’ views of themselves as learners of mathematics. Moreover, we analyzed relations between the seven dimensions and what kind of structure they generate. Thereby, a core of three high correlating dimensions could be identified, yielding different accentuations with regard to course choice. KeywordsViews of mathematics–Affect and students’ beliefs–Beliefs structures
  ZDM: the international journal on mathematics education 05/2012; 43(4):497-506.
• Article: Learning, teaching, and using measurement: introduction to the issue

  John P. Smith, Marja van den Heuvel-Panhuizen, Anne R. Teppo
  ZDM: the international journal on mathematics education 05/2012; 43(5):617-620.
• Article: Advances in mathematics education: new book series connected to ZDM—The International Journal on Mathematics Education

  Gabriele Kaiser, Bharath Sriraman
  ZDM: the international journal on mathematics education 05/2012; 42(1):143-144.
• Article: Joan B. Garfield and Dani Ben-Zvi: Developing students’ statistical reasoning: connecting research and teaching practice

  Jane Watson
  ZDM: the international journal on mathematics education 05/2012; 41(3):393-395.
• Article: Characterizing exemplary mathematics instruction in Japanese classrooms from the learner’s perspective

  Yoshinori Shimizu
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  ABSTRACT: This paper aims to examine key characteristics of exemplary mathematics instruction in Japanese classrooms. The selected findings of large-scale international studies of classroom practices in mathematics are reviewed for discussing the uniqueness of how Japanese teachers structure and deliver their lessons and what Japanese teachers value in their instruction from a teacher’s perspective. Then an analysis of post-lesson video-stimulated interviews with 60 students in three “well-taught” eighth-grade mathematics classrooms in Tokyo is reported to explore the learners’ views on what constitutes a “good” mathematics lesson. The co-constructed nature of quality mathematics instruction that focus on the role of students’ thinking in the classroom is discussed by recasting the characteristics of how lessons are structured and delivered and what experienced teachers tend to value in their instruction from the learner’s perspective. Valuing students’ thinking as necessary elements to be incorporated into the development of a lesson is the key to the approach taken by Japanese teachers to develop and maintain quality mathematics instruction.
  ZDM: the international journal on mathematics education 05/2012; 41(3):311-318.
• Article: Mathematics as a constructive activity: Learners generating examples

  Michael N. Fried
  ZDM: the international journal on mathematics education 05/2012; 38(2):209-211.
• Article: Reflecting mathematics: an approach to achieve mathematical literacy

  Katja Lengnik
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  ABSTRACT: Mathematics plays a dominant role in today's world. Although not everyone will become a mathematical expert, from an educational point of view, it is key for everyone to acquire a certain level of mathematical literacy, which allows reflecting and assessing mathematical processes important in every day live. Therefore the goal has to be to open perspectives and experiences beyond a mechanical and tight appearance of the subject. In this article a framework for the integration of reflection and assessment in the teaching practice is developed. An illustration through concrete examples is given. Mathematik ist in unserer Welt auf vielfältige Weise präsent. Was an dieser Mathematik müssen allgemeingebildete Lai/inn/en verstehen, um mathematisch mundig zu sein. Aus der Bildungsperspektive mathematischer Mündigkeit werden Reflektieren und Beurteilen von Mathematik als wichtige Tätigkeiten im Unterricht begründet Es wird ein Rahmenkonzept für Reflexion im Unterricht ausgearbeitet und an Beispielen für den Unterricht konkretisiert. Mit dem Ansatz ist die Hoffnung verbunden, das oft starre und mechanistische Bild von Mathematik schrittweise in Richtung eines diskursiven Mathematikbildes wandeln zu können ZDM-ClassificationD20-D30-C20-C30-C60
  ZDM: the international journal on mathematics education 05/2012; 37(3):246-249.
• Article: Learning events in the life of a community of mathematics educators

  Orit Zaslavsky
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  ABSTRACT: The paper examines some characteristics of learning events of a community of mathematics educators. Participation in the community entailed gaining familiarity with agreed upon conventions, goals, and forms of communication. The case discussed herein is an attempt to convey the complexities underlying learning in such a community through (re)negotiation of practices and goals. The notion ofreflective discourse is borrowed to describe a group discussion involving collective reflection that constituted an occasion for meaningful learning. Im Beitrag werden einige Charakteristika von Lernereignissen in einer Gemeinschaft von Mathematiklehrer(inne)n untersucht. Die Arbeit in der Gemeinschaft unterstützt, mit vereinbarten Konventionen. Zielen und Kommunikationsformen vertraut zu werden. Die im Beitrag diskutierte Fallstudie versucht die Komplexität aufzuzeigen, die einem Lernen durch Aushandlungen von Praxis und Zielen in solch einer Gemeinschaft zugrundeliegt Mit Hilfe des Begriffs desreflektiven Diskurses soll eine Gruppendiskussion mit kollektiver Reflexion beschrieben werden, die Möglichkeiten für bedeutsames Lernen schafft. ZDM-ClassificationB50-C50-C69-C70-D20-D30
  ZDM: the international journal on mathematics education 05/2012; 36(1):20-26.
• Article: Vergleich grundlegender Konzeptionen der Mathematikdidaktik in der BRD und in der DDR

  Heinz Griesel
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  ABSTRACT: Der Vergleich erfolgt unter folgenden Aspekten 1. Genetische Wissenschaftsorientierung versus strenge Wissenschaftsorientierung, 2. Stellenwert des logischen Bereichs insbesondere des Beweisens. 3. Unterschiedliche Verteilung der Inhalte auf die Schuljahre, 4. Unterschiede im Praxisbezug und 5. Offene Mathematikdidaktik versus geschlossene Mathematikdidaktik. The developments of didactics of mathematics as a professional field in both German countries between 1945 and 1990 are compared. This is done under the following aspects: 1. Scientific methodology, 2. Importance of logic and proving, 3. Allocation of the contents to classes and school years, 4. Practical orientation of mathematical courses, 5.
  ZDM: the international journal on mathematics education 05/2012; 35(4):166-171.
• Article: Another approach to proof: Arguments from physics

  Gila Hanna, Hans Niels Jahnke
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  ABSTRACT: In the first part of the paper we will explore the use of arguments from physics in mathematical proof and give some reasons why this approach might be worthwhile. In the second part we will relate this idea to Freudenthal's concept of local organization. The third part of the paper will present the results of an empirical study conducted in Canada on the classroom use of arguments from physics in mathematical proof. Im ersten Teil diskutieren wir den Gebrauch physikalischer Argumente in mathematischen Beweisen und begründen, warum dieser Zugang im Unterricht sinnvoll sein kann. Im zweiten Teil stellen wir eine Verbindung zu Freudenthals Begriff des lokalen Ordnens her. Der dritte Teil enthält Ergebnisse eines in Canada durchgeführten Unterrichtsversuchs zur Anwendung physikalischer Argumente bei mathematischen Beweisen.
  ZDM: the international journal on mathematics education 05/2012; 34(1):1-8.
• Article: Students’ self-regulation of emotions in mathematics: an analysis of meta-emotional knowledge and skills

  Erik De Corte, Fien Depaepe, Peter Op ’t Eynde, Lieven Verschaffel
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  ABSTRACT: Over the past decade, the concept of self-regulated learning has broadened to include motivational, volitional, and emotional components next to (meta-)cognitive ones. In this article, we present a meta-emotion perspective as an essential component of a conceptual framework on self-regulation that fully acknowledges the role of emotions. Against this background, a study is presented that attempts to contribute to the clarification of the relevance and the functioning of students’ meta-emotional knowledge and emotional regulation skills in school-related mathematical activities. It investigates the coping strategies that 393 students of the second (age 14) and fourth (age 16) year of secondary school report to use to regulate their emotions in three different mathematical school settings (i.e., a mathematics test, a difficult mathematics homework, and a difficult mathematics lesson). More specifically, it aims (1) to document the nature and frequency of the reported coping strategies, and (2) to explore—for the three different mathematical school settings—relationships between these reported coping strategies and personal characteristics (i.e., students’ familiarity with the particular school settings, their track in secondary education, their achievement level, their age, and gender). The results indicate that students report to know and to make use of several coping strategies in school-related mathematical activities, and reveal that the use of these strategies is related to specific person-related characteristics. In conclusion, we elaborate on how schools and teachers can stimulate students to acquire appropriate strategies and skills to self-regulate their emotions. KeywordsSelf-regulation–Emotions–Meta-emotional knowledge–Meta-emotional self-regulation skills–Mathematics education
  ZDM: the international journal on mathematics education 05/2012; 43(4):483-495.
• Article: How can teachers’ beliefs affect their professional development?

  Katja Maass
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  ABSTRACT: This paper describes a qualitative study that examines in more detail the question of how teachers’ beliefs may influence the intention to implement change as suggested by a professional development initiative. Several teachers in Germany took part in a professional development initiative for modelling. The course comprised five workshops spread over 2008. A part of our evaluation of the course involved interviewing six teachers after they had taken part. Teachers were interviewed about the impact the course had had on them, the opportunities and any related impediments they saw for modelling, and the way in which they typically taught. The interviews were evaluated using codes. Although the sample is very small, the cases allow for interesting insights, and for the hypotheses that teachers’ beliefs about effective teaching seem to have a major impact on whether or not they intend to change their classroom practice, as suggested by the professional development initiative, and on whether or not teachers perceive the context in which they are teaching (school head, parents, students, etc.) as supportive.
  ZDM: the international journal on mathematics education 05/2012; 43(4):573-586.
• Article: Who does what? A linguistic approach to analyzing teachers’ reactions to videos

  Gloriana González
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  ABSTRACT: This paper describes a technique for analyzing teachers’ reactions to videos. The technique uses Halliday’s systemic functional linguistics to identify teachers’ perceptions of the division of labor between teachers and students when working on a mathematical task. The author uses the technique to analyze data from focus group sessions where teachers reacted to a video episode. The author argues that the technique could be particularly useful for studying teachers’ perspectives about novel teaching activities, such as problem-based instruction in mathematics. KeywordsDiscourse analysis–Teacher thinking–Teacher decision making–Systemic functional linguistics–Geometry–Representations of teaching–Video–Focus groups–Theory–Instructional situations
  ZDM: the international journal on mathematics education 05/2012; 43(1):65-80.