This paper is great. It does some stuff with pronouns, which I was interested in last year. It’s based on social semiotics, specifically Halliday’s functional grammar:
The functional view of language – that people use language to achieve various different kinds of things – is widely accepted, but Halliday goes further than this, arguing that function is a fundamental property of the organisation of language itself, not just of its use (Halliday and Hasan 1989). His systemic-functional grammar (1985) indicates the ways in which grammatical features of language serve to perform ideational, interpersonal, and textual meta-functions and thus to embody the field of discourse (what the text is about), the tenor (the personal relationships involved) and the mode of discourse (the role that language itself is playing in theinteraction). p. 6
The paper’s great. I’m just going to pull out some useful quotes.
In mathematics, in particular, the public image of the subject is impersonal: mathematical knowledge is seen as abstract and separate from people, social issues and the real world (although it may be “applied” to these areas). The language in which mathematics is written is seen to be similarly abstract, with the extensive use of algebraic notation serving to distance mathematical texts from their readers. Of course, these two aspects inform and reinforce each other: belief in the ideal of objectivity and abstraction leads to valorisation of depersonalised and symbolic language, while the perception that mathematics is its symbol system contributes to its impersonal image – and to the consequent dislike and anxiety experienced by many (Buxton 1981). p. 1
This impersonal image is perpetuated in much research into mathematical language. For example, some analyses of mathematical language have focused on the structure of the notation, not only neglecting verbal aspects, but even dismissing them as merely
“connectives” (Ervinck 1992: 226) or as “semantically empty” (Roe 1977: 11). p. 1
In mathematics classrooms, interactions between students and teachers and among students themselves serve strong and readily identifiable interpersonal functions (Atweh, Bleicher, and Cooper 1998; Pimm 1984; Rowland 1995) that cannot be separated from the messages about mathematics. Thus, to use Atweh et al.’s example, a teacher’s utterance:
“So if we had 5 = x + 4 and worked that out, and then we had 5 < x + 4, I said
to you to solve these exactly the same way as [you would] with the equal sign.
So that is exactly the same procedure we are going to do in graphing
inequations” (Atweh et al. 1998: 74)
may be read simultaneously to convey a mathematical procedure to the students, to include them within a mathematical community (through the use of we), and to establish them as subordinate to the teacher’s authority (through the switch to using I and you). Equally, the practice of professional mathematicians is inextricably interpersonal. Surprisingly many work in collaboration with others (Burton and Morgan forthcoming) and, even where a mathematician works alone for much of the time, all must establish their personal identity and interpersonal relationships as members of a mathematical community (at both local and global levels). p. 2
The ways in which readers construct meanings from such texts, of course, depend not only on the intentions of the original authors but on the readers’ expectations and beliefs – both about the nature of the genre of the text and about the position that the author has within the community. The same text, presented as being by an expert or by a novice may be judged very differently… p. 4
It is thus important to recognise that semiotic activity in mathematical practices, as in other practices, is not just about communicating “content” but is also about the maintenance and contestation of power. p. 4
Who does mathematics and what sort of mathematics is it that they do? Is mathematics a human activity or is it an autonomous system that we merely observe and describe? An author’s identity as a mathematician and the identities constructed for her readers are related to the answers to these questions. In Halliday’s terms, the expression of agency is an ideational function in that it serves in constructing a picture of the world – that which exists, acts, causes. p. 7
The expression of agency in a mathematical text may be examined by using certain grammatical features as tools to interrogate the text. These linguistic features include the use of personal pronouns (I, you and we) indicating the author, the reader, and/or the broader community in which author and reader are positioned. p.7
In looking at the positioning of author and reader, one of the most obvious resources in any text is the use (or absence) of personal pronouns. At an initial level of analysis, the use of the first person singular may be taken to suggest the author’s personal involvement both in the activities, beliefs, or emotions reported in the text and in establishing a relationship with the readers. Of course, in academic texts the first person singular is precisely the resource that is not likely to be used – rupturing as it does the illusion of abstraction and objectivity. p. 7
One way in which human agency in mathematics is obscured is by a common feature of the mathematics register, the nominalisation of processes. This has the consequence of distancing author and reader from the activity. In the following example from a research paper, the use of nominalisation alienates the reader from the source of the “demand”:
The demand that the first vertex of (13) is polar to the other two gives
Aj + Bj2 – Cj3 = Aj2 – Bj3 + Cj = 0. p. 9
…the writer does not have the option of making agency explicit if he or she is to engage fully with mathematical ideas; the ability to represent processes as objects and hence to operate on the process-objects themselves is an integral part of the power of contemporary mathematics. p. 9
Studies of the language of academic scientific papers (for example, Master 1991) consistently show a high proportion of passive constructions. p. 10
The choice between passive and active forms, however, is not simply a matter of ease of reading. It again plays an ideational role, obscuring or constructing the presence of the human agent or agents who followed procedures, obtained solutions, found identities, replaced variables. In the example above, this obscuring of agency, together with the use of the present tense (rather than the past tense, which would construct a specific narrative about what was actually carried out on a particular occasion), contributes to a claim about the generalisability of the results: the procedures may be followed by anyone, at any time, with the same results. p. 10
the Mathematical Association of America advise:
The word “we” is often used to avoid passive voice . . . But this use of “we”
should be used in contexts where it means “you and me together”, not a formal
equivalent of “I”. Think of a dialogue between author and reader.
(Knuth et al. 1989: 2)
The advice that we should signal a dialogue between author and reader presents a rather simpler picture than that which we are likely to find in examining actual texts. It is easy to find cases where we is “a formal equivalent of ‘I’” – where the (sole) author describes her own actions or decisions in a way that logically cannot involve the reader…In other cases the logic of the situation is less clear cut and it is possible to read we in more than one way. For example, in the statement:
We determine V0 from the following relation…
it is unclear whether we is being used to refer to the author or whether the reader is being invited to participate in “determining”. p. 11
A further way in which the reader is positioned by the text is through the use of imperatives. p. 12
For the student and for the novice mathematical writer it is important to be aware of the judgements that readers may make about them on the basis of their writing; it may be important for writers to identify themselves as “thinkers” by claiming agency in high status mental processes and to distance themselves from low status “scribbling” by obscuring their agency in material processes. p. 13
Particularly common in academic mathematical writing is the use of terms such as clear, obvious, or trivial to describe intermediate stages of the work presented. Such terms appear to be used to indicate a gap in the rigour of the argument that is to be filled by appeal to a level of background knowledge and expertise that the author claims is trivial. p. 14
They thus act as a claim to authority on the part of the writer (I have deduced this readily and, if you cannot do so, that is your fault not mine). p. 15
In an analysis of a sample of 53 mathematics research papers (Burton and Morgan forthcoming), Leone Burton and I found that almost all the papers included some such claims to authority – some containing more than 20 indicators – while indicators of what we called “negative authority”, i.e. expressions of uncertainty or difficulty, were far less frequent – more than a quarter of the authors avoiding them altogether. Although this was a small and possibly atypical sample, it is interesting to note that the female authors were substantially less likely to include explicit indicators of a lack of authority. p. 15
Explicit attention to language in the mathematics classroom could enable more students, including those from less privileged backgrounds, to participate on an equal basis. p. 18
This one’s great:
The recognition that any text, however apparently abstract and formal, serves to construct the identities of both author and reader and to position them in relation to one another and in relation to broader social contexts provides writers with an important insight into the potential effects and effectiveness of their writing and provides readers with possibilities for adopting more powerful positions in relation to the texts they encounter. p. 20-21
I want to look up:
Atweh, Bill, Bleicher, Robert E., and Cooper, Tom J. (1998). The construction of the social
context of mathematics classrooms: A sociolinguistic analysis. Journal for Research in
Mathematics Education, 29(1), 63-82.
Master, Peter. (1991). Active verbs with inanimate subjects in scientific prose. English for
Specific Purposes, 10(1), 15-33.
Morgan, Candia. (1996a). “The language of mathematics”: towards a critical analysis of
mathematical text. For the Learning of Mathematics, 16(3), 2-10.
Rowland, Tim. (1995). Hedges in mathematical talk: linguistic pointers to uncertainty.
Educational Studies in Mathematics, 29(4), 327-353.