Elsevier

English for Specific Purposes

Volume 56, October 2019, Pages 50-67
English for Specific Purposes

“See Figure 1”: Visual moves in discrete mathematics research articles

https://doi.org/10.1016/j.esp.2019.08.001Get rights and content

Highlights

  • Visuals in discrete mathematics RAs perform three functions: ontological, argumentative, epistemological.

  • Visuals in discrete mathematics RAs support arguments by performing multiple functions.

  • Visuals in discrete math RAs initiate three moves: Define visually, Represent the operation outcome, Embody the operation.

  • Novice writers must understand how visuals in discrete mathematics RAs connect to rhetorical structure.

Abstract

This research is motivated by John Swales' genre analysis of academic texts and rhetorical studies of visuals in scientific texts. Swales' approach still generates insights into the rhetorical structure of research genres across disciplines, yet few studies explore their nonverbal aspects. Rhetorical studies of visuals examine images and ignore links with surrounding texts and may overlook ways that the nonverbal contributes to the discipline's intellectual project. ESP genre research has begun multimodal analysis of academic genres but its focus on conference presentations has left a gap in the study of verbal-visual links in other academic genres. This paper addresses this gap in multimodal genre scholarship. After analyzing a corpus of 30 RAs from discrete mathematics to identify the functions of visuals and possible visual–move associations, we found that visuals in two-thirds of the corpus perform three functions: ontological, argumentative, and epistemological. Our data also indicates three multimodal rhetorical moves initiated primarily by visuals. Implications of our findings are that visual moves go beyond textual considerations, they can disrupt the RA's chronological structure, and novice writers in the field would benefit from understanding the crucial associations between the visual representations, disciplinary knowledge, and the rhetorical structure of RAs in this field.

Introduction

Through more than three decades of research by applied linguists and rhetoricians, genre analysis has grown into an interdisciplinary field of study. The field integrates theories and analytical tools from both schools in the study and teaching of genres with an emphasis on the relationship between the context, linguistic, rhetorical, and social features of genres (Tardy & Swales, 2014, pp. 165–187). The integrated approach in genre analysis has shown increasing interest in academic discourses and genres of disciplines revealing disciplinarity in their discourses, rhetorical organization and argument (see for example Bazerman, 1988, Hyland, 2000; Prior, 1998, Swales, 1990, Swales, 2004).

From among the disciplinary genres, the research article (RA) has attracted much interest, being associated with Swales' CARS model (1990, 2004) and Hyland's corpus studies of disciplinary discourses. As “the pre-eminent genre of the academy” (Hyland, 2010, p. 117), the RA requires novice researchers and an increasing number of graduate students to master it to achieve academic success, making it a focus of research by scholars tasked with helping these populations. Since 2010, RA genre research has extended Swales' model of move structure in introductions to other sections or similar genres across disciplines. These studies have included genres in science and technology disciplines—traditionally known for their multimodal discourse—yet most researchers analyze the textual components in RAs and ignore the visual ones (Hyland, 2006, Johns, 2013, Tardy and Swales, 2014, pp. 165–187). Genre research pioneers have argued that visual components equally deserve attention because they contribute to the RA's rhetoric. Johns, for example, proposed research in multimodalities as a future ESP topic in 2013. She recalled her earlier work (Johns, 1998) on visual and verbal interactions in economics thus: “It is surprising that so little research has been completed either on the visual/verbal interaction in texts or on academic or nonacademic visual rhetoric” (Johns, 2013, p. 20).

Tardy and Swales (2014) also identify multimodal/visual genre analysis as a new direction. They argue that in some genres multimodal elements are “so essential that it would be impossible to overlook them in an analysis” (p. 173). In addition, Hyland (2006) points out, the fact that they “can occupy up to a half a science research article testifies to the significance of visuals in academic genres” (p. 53). Summarizing Miller, 1998, Hyland, 2006 also points out that “while arguments are based on plausible, and well-constructed, interpretations of data, they ultimately rest on findings, and these are often presented in visual form” (p. 54). Furthermore, many engineers and scientists assess the visual data first, when either reading an RA or writing one, to determine the argument and, in the latter case, distribute these data to structure their argument (Graves, 2014, Kresta et al., 2011). From a literacy perspective, ignoring the visual components of academic genres compromises student learning; hence EAP/ESP practitioners must attend to visual literacy and teach students, especially those in science and technical disciplines, “to read visuals as much as texts” (Hyland, 2006, p. 53).

As part of a larger study, this paper uses visual rhetoric (Gross & Harmon, 2014) to explore verbal-visual interaction in research articles in discrete mathematics. Unlike rhetorical analysis, which is mainly concerned with the verbal components of argument, visual rhetoric in science analyzes nonverbal displays to understand their role in scientific practices, knowledge creation, and communication. The discipline of study is discrete mathematics, a major sub-discipline in mathematics with inter- as well as cross-disciplinary links to other fields, e.g., optimization, computer sciences, and engineering. The generic structure of research articles in the discipline has already been examined (Moghaddasi and Graves, 2017, Graves et al., 2013, Graves et al., 2014). Based on the results from our analysis of the rhetorical structure from the larger project, we sought to answer the following questions:

  • 1.

    What roles do visuals play in research articles in discrete mathematics?

  • 2.

    Which rhetorical structures in research articles in discrete mathematics rely more/less on visuals? Why?

  • 3.

    How can the results of the study be applied to the teaching of academic writing in mathematics and related disciplines?

To answer these questions, we used triangulation (Candlin & Hyland, 1999), which allows both collecting data from multiple sources and using multiple approaches to analyze the data (Hastings, 2012). Triangulation “provide[d] multiple lines of sight and multiple contexts” (Hastings, 2012) to examine and enrich our understanding of the move-visual interactions in research articles in discrete mathematics. Our results show notable associations between the move structure and the visuals used in the articles in ways that contribute to the central rhetorical purpose of the articles, namely establishing facts (i.e., new knowledge). Here we first summarize some existing research on visuals in academic genres. Next, we briefly describe the study design. We then present results including the roles that visuals play in RAs in discrete mathematics as well as examples of move-visual associations in their rhetorical structure. Lastly, we discuss the implications of our findings, including the pedagogical implications for academic writing classes in mathematics and related disciplines.

Section snippets

Studies of visuals in academic genres

The study of visuals in multimodal genres has a tradition in linguistic-oriented ESP research. In 1980 Dubois studied presentation slides in biomedical speeches (Dubois, 1980), becoming probably the first ESP researcher to demonstrate the potential of visuals to make meaning. Other researchers followed thereafter, mainly drawing on Halliday's Systemic Functional Linguistics in their analyses (Morell, 2015, O'Halloran, 2005, Rowley-Jolivet, 2002, Rowley-Jolivet, 2004). Rowley-Jolivet (2002), for

Research design and methodology

This research builds on earlier research analyzing the move structure of discrete mathematics RAs (Graves et al., 2013, Graves et al., 2014, Moghaddasi and Graves, 2017). Our corpus comprises five high impact discrete mathematics journals. Journal selection criteria included their being listed in two prestigious citation indexing service platforms (Thomson Reuters Web of Science and Scopus); their high impact factors; their coverage of a wide range of topics from both pure and applied

Results and discussion

Seventy percent (70%) of our corpus contains visuals, suggesting they are conventional in RAs in discrete mathematics. However, in 8 RAs (DAM3, DM3, G&C2, JCO5, SIAM1, 2, 3, 4), they are absent. Our informants suggested that the mathematical problems addressed in these RAs either are supported by existing objects or deal with simpler abstract objects, making visuals inessential. However, where present, the visuals project both disciplinarity and specificity.

Conclusion

In this study, we have examined how mathematical argument initiates, develops, and establishes new knowledge through structuring the verbal and visual rhetoric in interactive ways. We showed how the visuals collaborate rhetorically with the verbal to create tangible objects from abstract concepts (ontological function), supply the reasoning behind mathematical relations (argumentative function), and integrate to create and support arguments for new knowledge (epistemological function). One

Acknowledgements

We would like to acknowledge our anonymous reviewers who helped improve this work. We would also like to thank the mathematicians who generously gave their time to participate in this study and provide insider data and insights about our findings. The first author would like to thank the WAC Program at the University of Alberta for its financial support while she worked on this project. We would also like to thank Shahnaz Shahtoosi for designing Figure 1 and Lily Lai for creating an earlier

Shahin Moghaddasi is a PhD candidate in applied linguistics at the University of Alberta in Edmonton, AB, Canada. She teaches writing for the Writing Studies Program, with an emphasis on international students. She is also a researcher with the Writing Across the Curriculum Program. Her research interests include genre analysis, EAP, and blended learning.

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    Shahin Moghaddasi is a PhD candidate in applied linguistics at the University of Alberta in Edmonton, AB, Canada. She teaches writing for the Writing Studies Program, with an emphasis on international students. She is also a researcher with the Writing Across the Curriculum Program. Her research interests include genre analysis, EAP, and blended learning.

    Heather Graves is Professor in the Department of English and Film Studies and the Director of Writing Studies at the University of Alberta. She has recently published articles in POROI, Rhetor, and English for Specific Purposes journal. Her research interests include the rhetoric of science, visual rhetoric, argument in academic discourse, and gamification in writing pedagogy.

    Roger Graves is Professor in the Department of English and Film Studies, Director of Writing Across the Curriculum, and Associate Director of the Centre for Teaching and Learning at the University of Alberta. His current research interests include writing assignments across disciplinary fields and the gamification of peer response systems in writing classrooms.

    Xavier Gutiérrez is an Associate Professor in Applied Linguistics and Spanish in the Department of Modern Languages and Cultural Studies at the University of Alberta. His research interests are knowledge representations of language, teaching and learning L2 grammar, task-based language teaching, and learners' perceptions about their learning experiences.

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