"Strengthening Connections with the Audience: Reformation and Exemplification in Mathematics Research Articles"

Kristy Lesperance

Kristy was in her third year of undergraduate studies at the University of British Columbia when this essay was originally written, studying Mathematics under the faculty of Arts. The paper was written for an upper-level, intensive research and scholarly writing course using corpus analysis to investigate discursive features of literature from the student’s chosen major.

Contents

Introduction

Mathematics in Discourse Analysis

Method

Results & Discussions 

Results & Discussions Cont.

Conclusion

Works Cited

Mathematics in Discourse Analysis

Hyland (2009) highlights some distinctive differences between contrastive “hard” and “soft” disciplines, citing the “continuum of academic knowledge” which progresses from the sciences (hard) at one end, to the humanities (soft) at the other (p. 9). He suggests that broad clusters of scientific disciplines, such as biology, engineering, and physics, together occupy one end of the spectrum, whereas the humanities and social sciences (e.g., sociology, philosophy, applied linguistics) grouped together capture the other extremity. Owing to some fairly general epistemological, discursive, and practical similarities, these clusters of disciplines form the arguably stable and distinctive "hard" and "soft" categories referred to by numerous authors (such as Biglan, 1973; Hyland, 2007).

Becher (1994) originally had presented these "hard" and "soft" discipline categories by distinguishing between not two but four distinctive disciplinary groups: "hard pure," "hard applied," "soft pure" and "soft applied." In relation to the focus of the present paper, it is interesting to note that within these groupings, physics is assigned to epitomize the "hard pure" category, whereas "education" is assigned to epitomize "soft applied" (p. 154). Although Becher incorporates mathematics into his discussion of the disciplinary differences in academic writing, it seems to be a discipline that is particularly difficult to categorize definitively. On the one hand, it is set apart from both physics, by definition (p. 151), and chemistry (or presumably any science which involves expensive and elaborate lab equipment), in terms of academic activity (p.158). On the other hand, it is grouped together with both physics (in terms of a student’s entrance into the discipline and future employment) (p. 157) and philosophy (in terms of a reader’s approach to the subject) (p. 158).

It is difficult to find literature which explicitly examines the discursive style of mathematics, although Graves, Moghaddasi, and Hashim (2013) attempt to characterize some of the uniqueness of mathematics discourse in comparison to other academic disciplines. In their analysis of the organizational framework of academic research articles in pure and applied mathematics, Graves et al. show that mathematics articles tend to defy the traditional "hour-glass" structure defined by Swales (1990). That is, mathematics articles tend to transition from the Introduction directly into Results and omit a distinctive Conclusion. The rhetorical function of the mathematics Results section is similar to that of the Discussion and Conclusion sections in other disciplines. The title of their article notes that“Mathematics is [itself] the method” – a unifying feature of all mathematics articles. However, Graves et al. also make note of some distinctive discursive differences between the "pure" and "applied" sub-categories within mathematics, which suggests a potential for additional variation to be discovered between mathematics research articles on the basis of intended audience. The context under which an article is written (such as the author’s presumptions about future readers) can greatly affect the final product, and the goal of being understood by certain audiences, as well as to attract certain audiences, to a greater degree than others.

This is greatly elaborated upon by Van Dijk (2006), who asserts that contexts “directly interfere in the mental processes of discourse production and comprehension” (p. 163) in his socio-cognitive approach to the incorporation of context into textual analysis. Therefore, in order to truly understand a piece of discourse, it might be wise to consider the possible context surrounding its production, including any presumptions that the author may have held regarding his or her intended audience. 

This audience-sensitivity is also discussed by Hyland (2007) in relation to the use of exemplification and reformulation in academic research articles. He explains the use of "code glosses" (i.e., the incorporation of examples and reiterations) as a small gesture from authors to their intended audience, which creates “coherent, reader-friendly prose” (p. 266). Cuenca and Bach (2007) appear to agree, describing reformulation as beneficial to the author-reader relationship, insofar as it strengthens both a reader’s comprehension of an idea and the idea’s rhetorical force by increasing its intelligibility. Hyland also argues that, beyond enabling insight into the assumptions held by an author about his or her audience, reformulation can contribute to an argument’s effectiveness and persuasiveness, by increasing reader comprehension. It may, therefore, also increase the acceptance of an author and his or her ideas by the intended discourse community. To illustrate his ideas, Hyland chose to analyze the discourse of eight disciplines which ranged from  "hard" to "soft." While providing a useful starting point to code gloss analysis, his particular analysis does not specifically address the disciplines of mathematics or education.

I completed the present analysis to combine the ideas presented in Hyland (2007) and in Graves et al. (2013), in order to examine the frequency and particularity of exemplification and reformulation in academic discourse about geometry. Specifically, this study distinguishes styles of code gloss use between two supposedly contrasting "hard" and "soft" sub-disciplines within the single field of mathematics: theoretical mathematics and mathematics education. In sum, I would argue that although code gloss use may vary according to discipline, it can also vary within disciplines according to intended audience. Therefore, greater audience awareness may be of use to students seeking to gain acceptance into their chosen particular niches, within the more broad fields of research such as mathematics.