JournalTOCs

ZDM
Journal Prestige (SJR): 0.781

Citation Impact (citeScore): 1
Number of Followers: 2

Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1863-9704 - ISSN (Online) 1863-9690
Published by Springer-Verlag

[2468 journals]

Mathematics education research on language and on communication including
some distinctions: Where are we now'
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  Abstract: In this article, we present a narrative review of mathematics education research on language and on communication over 2019–2022, but also look ahead by addressing challenges posed by the lack of distinction between language and communication. The persistence and significance of the problem of the distinction between language and communication are thus outlined in a historical moment of celebration of growth of research in the domain. Informed by the analysis of a selection of research journal articles and by our trajectories, we discuss influential topics in the recent discourse: multilingual mathematics classrooms; mathematics teacher education on language in mathematics teaching; multimodal mathematical communication; interaction and mathematics learning; mathematical language and discourse. We connect this with new emerging or old revisited concepts: instructional designing, gesturing, argumenting and languaging. We finish by further reflecting on multimodal mathematical communication and gesturing, and on the potential of expanding the notion of mathematics register towards a notion of mathematics communication register.
  PubDate: 2023-06-02
The use of Arabic language by mathematics teachers as a resource to
support teaching
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  Abstract: In the research described in this paper, we explored the way Palestinian teachers use the Arabic language to teach mathematics in Arabic. First, we address the issue from an historical overview of the context of study. The historical overview allows us to situate the current context of teaching mathematics in Arabic in Palestine. We rely on Halliday’s concept of register to define what we call “Mathematical Arabic For Teaching”. It allows us to focus our study, and to address the issue of combination between this register to be developed by the teachers and the Arabic textbook content. Our theoretical framework is based on a combination of the theories Documentational Approach to Didactics and Mathematical Discourse in Instruction, which allows us to discuss mathematical Arabic for teaching as a resource. We based our exploratory study on the case of three teachers, chosen according to well-defined criteria. We explored the issue through audio recordings of their lessons teaching tenth graders the signs of quadratic functions, and video recorded interviews on their reflections on those lessons. We identified three combinations between the teachers’ Mathematical Arabic For Teaching and the use of the mathematics textbook, namely, complementarity, tension and equivalence. We conclude with some implications of these forms of combination.
  PubDate: 2023-06-01
Resources in translation: towards a conceptual and technical apparatus
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  Abstract: In mathematics education, translation of resources from one language to another occurs in a wide range of situations. This paper explores how conceptual and technical apparatus from contemporary translation studies may be of use in guiding and analysing such translation. Key concepts—including those of source, target and intermediate text, of paradigms of equivalence, purpose, uncertainty and localisation, and of semantic, syntactic and epistemological equivalence—are introduced and illustrated, primarily with reference to translation of a series of school mathematics workbooks. Significant types of tool to assist translation—translation protocols and machine translation—are examined. A more detailed case study illustrates techniques (and associated tools) for analysing translation shifts and terminological translatability, applying them to examine translation of documentation of a framework for researching teachers’ interaction with resources—the Documentational Approach to Didactics. Specific insights that emerge are how translation is shaped by attention not just to fidelity to the source text but to the audience for, and function of, the target text; and how challenging it can be to formulate terms translatable across languages in such a way as to consistently anchor meaning in existing wordforms.
  PubDate: 2023-06-01
A dialogue between two theoretical perspectives on languages and resource
use in mathematics teaching and learning
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  Abstract: In this paper, we turn to the notion of networking theories with the aim of contrasting two theoretical mathematics education perspectives inspired by Vygotsky’s work, namely, the Theory of Objectification and the Documentational Approach to Didactics. We are interested in comparing/contrasting these theories in accordance with the following three main questions: (a) the role that the theories ascribe to language and resources; (b) the conceptions that the theories bring forward concerning the teacher, and (c) the understandings they offer of the mathematics classroom. In the first part of the paper, some basic concepts of each perspective are presented. The second part includes some episodes from a lesson on the teaching and learning of algebra in a Grade 1 class (6–7-year-old students). The episodes serve as background to carry out, in the third part of the paper, a dialogue between proponents of the theoretical perspectives around the identified main questions. The dialogue shows some theoretical complementarities and differences and reveals, in particular, different conceptions of the teacher and the limits and possibilities that language affords in teaching–learning mathematics.
  PubDate: 2023-06-01
Navigating multiple languages and meanings in cross-cultural research on
teachers’ resource use
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  Abstract: Cross-cultural research covering multiple languages and cultures involves negotiating conceptual and linguistic challenges. This paper focuses on how researchers working across cultural and linguistic boundaries navigate the research process and negotiate a common understanding of the constructs under study. Working towards intersubjectivity within a cross-cultural research team is essential, as it deepens understanding of one another’s contexts and our own. We analyze our own research process, as a cross-cultural team studying elementary school teachers’ use of print and digital instructional resources in Finland, Flanders, Sweden, and the U.S. Recorded team conversations served as data to help us explore the way language and culture are intertwined and how these relationships surface when developing research instruments and conducting analysis of the interviews, in which language became a focal point. Challenges emerged particularly within three research aims, namely, naming and describing teaching practices, understanding teachers’ relationships with mathematics resources, and defining digital resources in a cross-cultural survey. Our systematic analysis of instances of conceptual and linguistic inequivalence prompted the team to make language explicit and revealed that these instances varied in several ways that had implications for how and whether they might be bridged. Thus, this paper contributes to understanding the methodological impact of using a shared language, acknowledging that researchers’ lexicons about mathematics teaching are closely linked to their own cultural knowledge and experience. Therefore, working explicitly across language and culture towards mutual understanding is a necessity and a way to reinforce the validity of research outcomes.
  PubDate: 2023-06-01
What is mathematics teaching talk for' A response based on three sites of
practice in mathematics education
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  Abstract: During the last decades, the study of how learners and teachers of mathematics use the resource of language has contributed to our understanding of mathematics teaching and learning in a variety of classrooms and cultures. Developmental work with mathematics teachers on the particular resource of mathematics teaching talk is more recent. In order to explore responses related to the importance of this talk, in this paper we consider three sites of practice in mathematics education—research, professional development and teaching—and illustrations of data from or about them, including studies from the literature, and work with secondary school mathematics teachers in Catalonia-Spain and Malawi around the teaching of angles. We argue that tensions permeate these sites of practice when a focus is placed on word use, specifically the practices of naming and explaining, in mathematics teaching talk. We conclude that the importance of mathematics teaching talk is construed through tensions with other resources in language and teaching. Tensions specifically appear in the realisation of mathematics teaching talk as mediational in the work with mathematics teachers on their classroom teaching.
  PubDate: 2023-06-01
Sourcing mathematical meaning as a dialogic process: meaning-focused and
language-focused repairs
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  Abstract: I report the results of an analysis of an episode of elementary school second language mathematics classroom talk focused on the classification of geometric forms, drawing on a dialogic, sources of meaning perspective. The episode was selected because participants make use of a variety of features of language, including vocabulary, gestures and diagrams. The analysis drew on methods and principles from conversation analysis and revealed that interactional repair was a key feature in the organisation of the episode. Repair sequences are stretches of interaction in which participants deal with explicitly signalled ‘trouble’ in participants’ working assumption of shared understanding. The results include a distinction between meaning-focused and language-focused repair, with some repair sequences embedded within others. This layered organisation is important in the emergence of meaning for participants’ utterances and mediates the tension between centripetal and centrifugal language forces. The findings highlight the complexity of mathematics classroom interaction and suggest possibilities for the careful management of focusing on language and on mathematical meaning in classroom interaction.
  PubDate: 2023-06-01
Using conceptual analyses to resolve the tension between advanced and
secondary mathematics: the cases of equivalence and inverse
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  Abstract: Advanced mathematics is seen as an integral component of secondary teacher preparation, and thus most secondary teacher preparation programs require their students to complete an array of advanced mathematics courses. In recent years, though, researchers have questioned the utility of proposed connections between advanced and secondary mathematics. It is simply not clear in many cases—to researchers, teacher educators, and teachers themselves—exactly how advanced mathematics content is related to secondary content. In this paper, we propose using a conceptual analysis—a form of theory in which one explicitly describes ways of reasoning about a particular mathematical idea—to address this issue. Specifically, we use conceptual analyses for the foundational notions of equivalence and inverse to illustrate how the ways of reasoning needed to support productive engagement with tasks in advanced mathematics can mirror and reinforce those that are similarly productive in school mathematics. To do so, we propose conceptual analyses for the key concepts of equivalence and inverse and show how researchers can use these conceptual analyses to identify connections to school mathematics in advanced mathematical tasks that might otherwise be obscured and overlooked. We conclude by suggesting ways in which conceptual analyses might be productively used by both teacher educators and future teachers.
  PubDate: 2023-05-28
Characterizing external visualization in mathematics education research: a
scoping review
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  Abstract: External visualization (i.e., physically embodied visualization) is central to the teaching and learning of mathematics. As external visualization is an important part of mathematics at all levels of education, it is diverse, and research on external visualization has become a wide and complex field. The aim of this scoping review is to characterize external visualizations in recent mathematics education research in order to develop a common ground and guide future research. A qualitative content analysis of the full texts of 130 studies published between 2018 and 2022 applied a deductive-inductive coding procedure to assess four dimensions: visualization product or process, type of visualization, media, and purpose. The analysis revealed different types of external visualizations including visualizations with physical resemblance ranging from pictorial to abstract visualizations as well as three types of visualizations with structural resemblance: length, area, and relational visualizations. Future research should include measures of visualization products or processes to help explain the demands and affordances that different types of visualizations present to learners and teachers.
  PubDate: 2023-05-25
Making university mathematics matter for secondary teacher preparation
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  Abstract: Internationally, questions about the perceived utility of university mathematics for teaching school mathematics pose an ongoing challenge for secondary mathematics teacher education. This special issue is dedicated to exploring this topic and related issues in the preparation of secondary mathematics teachers—by which we mean teachers of students with ages, approximately, of 12–18 years. This article introduces this theme and provides a semi-systematic survey of recent related literature, which we use to elaborate and situate important theoretical distinctions around the problems, challenges, and solutions of university mathematics in relation to teacher education. As part of the special issue, we have gathered articles from different countries that elaborate theoretical and empirical approaches, which, collectively, describe different ways to strengthen university mathematics with respect to the aims of secondary teacher education. This survey paper serves to lay out the theoretical groundwork for the collection of articles in the issue.
  PubDate: 2023-05-24
Preparing prospective secondary teachers to teach mathematical reasoning
and proof: the case of the role of examples in proving
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  Abstract: Mathematics teacher education programs in the United States are charged with preparing prospective secondary teachers (PSTs) to teach reasoning and proving across grade levels and mathematical topics. Although most programs require a course on proof, PSTs often perceive it as disconnected from their future classroom practice. Our design research project developed a capstone course Mathematical Reasoning and Proving for Secondary Teachers and systematically studied its effect on PSTs’ content and pedagogical knowledge specific to proof. This paper focuses on one course module—Quantification and the Role of Examples in Proving, a topic which poses persistent difficulties to students and teachers alike. The analysis suggests that after the course, PSTs’ content and pedagogical knowledge of the role of examples in proving increased. We provide evidence from multiple data sources: pre-and post-questionnaires, PSTs’ responses to the in-class activities, their lesson plans, reflections on lesson enactment, and self-report. We discuss design principles that supported PSTs’ learning and their applicability beyond the study context.
  PubDate: 2023-05-17
The mutual contribution between mathematics and other fields:
Mathematicians’ and teachers’ views
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  Abstract: This study focuses on the potential of university mathematics courses to advance teachers’ knowledge regarding an important component of knowledge about the nature of mathematics as a scientific discipline, namely the mutual contribution between mathematics and various fields: mathematics contributes to solving problems in different fields, and different fields contribute to the development of mathematics by raising new mathematical questions and motivating the development of new concepts, methods and research areas. The study investigates (1) what teachers may learn about the nature of the mutual contribution in an academic program that includes university level mathematics courses that offer teachers ample opportunities to learn contemporary and historical mathematical modeling and applications, and (2) what mathematicians, who teach in this program, want to teach teachers about the nature of the mutual contribution. The main data sources included interviews with five mathematicians and 14 secondary school teachers. The results indicate that the mathematicians viewed the mutual contribution between mathematics and other fields as an important component of teachers’ knowledge which they wished to advance, whereas the teachers reported only on considerably advancing their knowledge and appreciation regarding one direction: the contribution of mathematics to other fields. Interpretations of the results and future avenues to address this issue are discussed.
  PubDate: 2023-05-17
Teachers’ practices and resources in the Hungarian “Guided
Discovery” approach to teaching mathematics: presenting and representing
“series of problems”
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  Abstract: In the Hungarian “Guided Discovery” approach to teaching mathematics, teachers’ planning work plays a crucial role. Teachers following the approach develop teaching trajectories based on “series of problems”. This work includes the choice, creation, transformation, organization and networking of problems with regard to various teaching objectives. However, most of this planning work remains implicit; the structure and rationale of the teaching trajectories are often inaccessible for an external observer (including, for example, student teachers). An ongoing project based on teacher–researcher collaboration aims to reveal the hidden characteristics and principles of teachers’ work with series of problems through the creation of innovative resources for teachers. In this paper, we present the design of this collaborative work, a process we designate “reverse engineering”, and analyse the development process of resources, focusing particularly on the emergence of new vocabulary and representation tools serving as mediators in the communication between teachers and researchers.
  PubDate: 2023-05-05
Conceptualizing teachers’ interactions with resources in crossing
languages and cultures
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  Abstract: This paper introduces this special issue aiming to deepen and extend research on mathematics teachers’ work, from a resource perspective, by taking language and culture into account, and exploring two questions: How are teachers’ interactions with resources interpreted and modeled across contexts' And, What challenges and insights emerge through recent efforts to engage these models in cross-cultural (and linguistic) research' The fields of resources, language and culture in mathematics education are each extensive, and we do not attempt to survey comprehensively across them. We have chosen instead to propose three approaches on resources in mathematics teachers’ work that developed somewhat contemporaneously from three different countries with differing linguistic, curricular, and social contexts, corresponding to the work of the three guest editors. The models developed through these approaches are driven by the educational, and so cultural and material conditions of the time and the location of each author, and allow us to propose preliminary answers to our two guiding questions. We then move to pull the threads from these models together, and discuss the contributions to this Special Issue. This results in more robust and nuanced responses to our questions, and in identifying two themes that emerge from research that sit at the convergence of studies of teachers’ interactions with resources, languages, and cultures: an invisibility-visibility dialectic and a local-global tension. Finally, this study leads us to consider a new region of mathematics education research.
  PubDate: 2023-05-05
An anthropological point of view: exploring the Chinese and Japanese
issues of translation about teaching resources
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  Abstract: The aim of this study is to advance understading of teachers’ and researchers’ work, in particular its cultural specificities, from a resource perspective by exploring the issues and challenges faced during the translation of a theoretical framework, the Documentational Approach to Didactics (DAD), from Western (English and French) to East Asian languages (Chinese and Japanese). A basic assumption is that the challenges encountered while translating are driven by the cultural and linguistic differences that exist between the West and East. Adopting the perspective of the Anthropological Theory of the Didactic (ATD), we frame the translation work as a transposition process of research praxeology (a model of the researchers’ practices and knowledge) from a Western to an Eastern institution. We investigate this process to identify cultural elements at different levels (school, society, civilization, etc.) using the ATD framework. After translating a DAD article into Chinese and Japanese separately, we then worked collaboratively to identify similar or diverse translation issues and investigated their origins. Consequently, the results revealed a considerable difference between the West and East, and ample similarities between China and Japan, especially in terms of the researchers’ work and its relationship with the teachers’ work.
  PubDate: 2023-04-13
Deepening a conceptual framework in travelling between languages and
cultures: the case of the documentational approach to didactics
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  Abstract: Translation is a critical issue in international mathematics education studies but has seldom been carefully investigated. How can a theoretical approach be translated and subsequently used in different languages, and to what extent could the translation processes deepen the approach itself' This paper addresses such issues in the case of the Documentational Approach to Didactics (DAD). We explore possibilities of translating selected critical notions expressed in English terms into French, Arabic and Chinese, and developing insights from these possibilities. We further deal with the translation issues ‘in situ’, i.e. in an English mathematics teacher’s lesson where we can identify the embodiments of the DAD concepts. The most challenging part in the translation is the embedding of the English terms in the English cultural sphere, and ‘re-bedding’ them into another cultural sphere. It is claimed that examining the nuances between the different possibilities of translation for the same concept, in connection with their use ‘in situ’, and drawing inspiration from the educational, cultural and theoretical traditions in other cultural spheres, can help to deepen the theoretical constructs.
  PubDate: 2023-04-03
The multimodality of lesson guides and the communication of social
relations
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  Abstract: Curriculum resources such as textbooks and lesson guides communicate messages about the social relations between the teacher, students, artefacts, and the mathematics. Because of their implicit nature, these messages can be hard to surface and perhaps therefore are not frequently covered in curriculum resource analysis. Tackling this shortcoming, we examine mathematics lesson guides or the daily lesson descriptions written for elementary teachers. Drawing on multimodality and activity theory, we characterize the social relations messaged in the lesson guides in terms of two constructs: authority and distance. We present and illustrate an analytical approach to uncovering these messages in lesson guides from Sweden, USA, and Flanders. Our analytical approach enabled us to distinguish configurations of social relations that vary primarily across the three educational contexts, which strengthens our argument for viewing the configuration of social relations as a cultural script.
  PubDate: 2023-04-03
Language as a resource for teachers describing mathematics classroom
teaching and learning: a comparative approach
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  Abstract: Describing mathematics classroom teaching and learning is part of a professional expertise. Comparing ‘our distinct stories’ and ‘our professional languages’ about teaching and learning in mathematics classes around the world, reveals cultural and linguistic underpinnings of our ‘stories’ and ‘languages’. Analysing and understanding these ‘stories’ and ‘languages’ in the form of narratives of classroom lessons, is a methodological approach that allows us to study and compare language as a resource across different cultural and linguistic contexts. We based our approach on results of the Lexicon Project, which set out to document the terms and the professional vocabulary that teachers use for describing the phenomena of middle school mathematics classrooms around the world, but enlarged this approach by narratives and a narrative methodology. Our cultural comparative approach based on these narratives revealed not only technical terms that define and make explicit didactical intentions, techniques and approaches, but also offered narrative descriptions of the enactment of the didactic intentions and techniques in situ. This approach provides a deeper understanding of the potential of language and turned out to be valuable for understanding how language orients teachers’ visions and analyses of mathematics classrooms.
  PubDate: 2023-03-28
Examining the key factors affecting teachers’ translation of a
theoretical framework from English into a native language: the Turkish
case
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  Abstract: This study was aimed at exploring the key factors affecting postgraduate students-teachers’ translation of a theoretical framework from English into their native language. The research was carried out with 21 Turkish postgraduate students who were also mathematics teachers, based on the theoretical framework of the documentational approach to didactics. The research was designed as a case study. The data were obtained from postgraduate students’ weekly translation papers, the recordings of collective translation sessions, and the researchers’ and the postgraduate students’ reflective notes over a period of 7 weeks. The data were analyzed using descriptive and content analysis in order to investigate the factors influencing difficulties the postgraduate students had while translating. The analyses showed that the task of translating a theoretical framework at the postgraduate level led student-teachers to work on the meaning of the concepts and the unity of the framework and to reinterpret the source text. The research showed that the translation of the theoretical framework was strongly influenced by syntactic, sociocultural, and academic/educational differences, and these factors were interrelated.
  PubDate: 2023-03-11
  DOI: 10.1007/s11858-023-01475-6
Teaching the concept of zero in a Malawi primary school: illuminating the
language and resource challenge
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  Abstract: In this paper we discuss findings of a study that investigated the resources and language that teachers in Malawi use to teach the concept of zero. In Malawi primary schools, textual resources available to teachers are mainly the curriculum materials in the form of syllabus, teacher guides and learner textbooks. The syllabus and teacher guides are in English while the learner textbooks are in Chichewa as teaching is in Chichewa or other local language in the first 4 years of primary school. We used the Mediating Primary Mathematics framework (Venkat and Askew in Educ Stud Math 97:71–92, 2018) and a qualitative case study of two teachers to explore the resources used, how the teachers interacted with the resources and how they moved between the two languages. Our findings include that the language and resources that the teachers used provided affordances as well as constraints for learning the concept of zero. We identified two types of challenges for the teachers; that of naming and that of representing the concept of zero. We discuss what the Malawi context illuminates about teaching zero in post-colonial multilingual settings.
  PubDate: 2023-03-07
  DOI: 10.1007/s11858-023-01473-8