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The self authors itself, and is thus made knowable, in the words of others. If, to be perceptible by others, we cast ourselves in terms of the other, then we do that by seeing ourselves from the outside. (Holland et al., 1998:173)

In the same way in which the other is always the-other-for-me, the I is always ‘I-for-the- other’. The I is always in a state of ‘addressing’ the others through whose eyes it sees itself as shown in Figure 7.

Figure 7: I-for-the-other.

‘There is no word directed to no one’ (Holquist, 2002:27), and this ‘addressing’ is central to the idea of self-authoring. As Bakhtin (1986) writes:

An essential (constitutive) marker of the utterance is its quality of being directed to someone, its addressivity … the utterance has both an author … and an addressee. This addressee can be an immediate participant-interlocutor in an everyday dialogue … And it can also be an indefinite, unconcretised other … Both the composition and, particularly, the style of the utterance depend on those to whom the utterance is addressed, how the speaker (or writer) senses and imagines his addressees, and the force of their effect on the utterance. (p95)

When we author ourselves, our words are directed to this other; we are addressing them and what we think they represent, and potentially what we think they want to hear as shown in Figure 8.

Figure 8: Addressivity.

As well being an addressee, every I is also addressed by others to whom it must respond: The world addresses us and we are alive and human to the degree that

we are answerable, i.e. to the degree that we can respond to addressivity. We are responsible in the sense that we are compelled to respond, we cannot choose but give the world an answer. (Holquist, 2002:30)

Thus, we are always ‘in a state of being ‘addressed’ and in the process of ‘answering’’ (Holland et al., 1998:169). This authoring or addressing takes into account what the I thinks it knows of these others – the details of their history-in-person lenses, their experiences and views – and the way in which they have seen themselves through the others’ eyes. Figure 9 shows how what the I knows of the others is present in the I’s authoring.

A central aspect of dialogism is the sense that when self-authoring, the I uses the words of others and is therefore inherently ‘multi-voiced’:

In the making of meaning, we “author” the world. But the “I” is by no means a freewheeling agent, authoring worlds from creative springs within. Rather, the “I” is more like Lévi-Strauss’s (1966) bricoleur, who builds with pre-existing materials. In authoring the world, in putting words to the world that addresses her, the “I” draws upon the languages, the dialects, the words of others to which she [sic] has been exposed. One is more or less condemned, in the work of expression, to choices because “heteroglossia,” the simultaneity of different languages and of their associated values and presuppositions, is the rule in social life. (p170)

‘The languages, the dialects, the words of others’ used by the I may not have ‘logical compatibility’ (p15) – they may not originate from speakers who hold similar perspectives – yet the I authors itself from this (potentially diverse) menu. Being heteroglossic is ‘the rule in social life’, it is normal. In the process of authoring, a speaker does not privilege each voice or discourse equally nor does s/he select voices at random. Authorship is a matter of choice and speakers choose to take on discourses as part of their identity work. However:

… not all words for just anyone submit equally easily to this appropriation, to this seizure and transformation into private property: many words stubbornly resist, others remain alien, sound foreign in the mouth of the one who appropriated them; they cannot be assimilated into his context and fall out of it; it is as if they put themselves in quotation marks against the will of the speaker. Language is not a neutral medium that passes freely and easily into the private property of the speaker’s intentions; it is populated – overpopulated – with the intentions of others. Expropriating it, forcing it to submit to one’s own intentions and accents, is a difficult and complicated process. (Bakhtin, 1981:294)

This ‘complicated process’ is termed ‘orchestration’. But orchestrating voices is not something that can happen freely, as orchestration happens in a context where restrictions, perhaps due to the positioning of the author or the nature of the addressee, impact on the way in which voices can be taken on:

In such a diverse and contentious social world, the author, in everyday life as in artistic work, creates by orchestration, by arranging overheard elements, themes, and forms, not by some outpouring of an ineffable and central source. That is, the author works within, or at least against,

a set of constraints that are also a set of possibilities for utterance. (Holland et al., 1998:171)

And yet, ‘Bakhtin resists the idea of an individual who is totally determined by social context’ (Solomon, 2012:175). Orchestration – the choosing of language – is a balance of context and self, of the ways in which the word has been used before and the ways the I wants and, through positioning, is able to take on the word.

All ‘utterances’, as well as having an author and an addressee, have an origin: The word in language is half someone else’s. It becomes “one’s own” only when the speaker populates it with his own intention, his own accent, when he appropriates the word, adapting it to his own semantic and expressive intention. Prior to this moment of appropriation, the word does not exist in a neutral and impersonal language (it is not, after all, out of a dictionary that the speaker gets his words!), but rather it exists in other people’s mouths, in other people’s contexts, serving other people’s intentions: it is from there that one must take the word, and make it one’s own. (Bakhtin, 1981:293-4)

And so one’s utterances reveal one’s influences. As Braathe and Solomon (2015) describe, the way in which we use the words of others, ‘brings tensions with it as we struggle to expropriate the others’ words’ (p154) and make them our own. In choosing among voices we establish an authorial stance and thereby assert some agency on the voices that surround us. For teachers of mathematics, working in a performative system which values results, these voices or discourses include those which promote different pedagogic approaches such as ‘instrumental’ or ‘relational’ teaching (Skemp, 1976) or ‘mastery’ approaches (NCETM, 2017a).

Two particular types of voice are taken up by an authoring self: those which are authoritative and those which are internally persuasive.

3.4.1

Authoritative and internally persuasive

discourse

‘Authoritative discourses’ are dominant voices that are difficult to ignore and difficult to make one’s own:

The authoritative word demands that we acknowledge it, that we make it our own; it binds us, quite independent of any power it might have to persuade us internally; we encounter it with its authority already fused to it. The authoritative word is located in a distanced zone, organically

connected with a past that is felt to be hierarchically higher. It is, so to speak, the word of the fathers … It is therefore not a question of choosing it from among other possible discourses that are its equal. (Bakhtin, 1981:342)

Authoritative discourses come from ‘authority as such, or the authoritativeness of tradition, of generally acknowledged truths, of the official line and other similar authorities’ (p344). The words seem to demand ‘quotation marks’ (p343) and are ‘transmitted’ (p344). These are words that cannot be ignored and the term ‘ventriloquation’ is used by Bakhtin to describe the unthinking adoption of such discourses. This is what happens when the words of another are spoken without having been first populated ‘with [a speaker’s] own intention, his own accent’ or having been adapted to ‘his own semantic and expressive intention’ (p293). But this is hard to achieve with an authoritative discourse – such as the rhetoric of standards and testing – which:

… demands our unconditional allegiance. Therefore, authoritative discourse permits no play with the context framing it, no play with its borders, no gradual and flexible transitions, no spontaneously creative stylising variants on it. It enters our verbal consciousness as a compact and indivisible mass; one must either totally affirm it or totally reject it. It is indissolubly fused with its authority – with political power, an institution, a person – and it stands and falls together with that authority. One cannot divide it up – agree with one part, accept but not completely another part, reject utterly a third part. (p343)

Ventriloquation can only be avoided through the ‘adoption of stances toward these voices’ (Holland et al., 1998:185). Taking a stance is essential to the orchestration of authoritative discourses, something that Ball (2003) suggests is not possible for teachers working in a performative system where commitment to achieving results and compliance are highly valued (Reay, 1998) and conformity leads teachers to be ‘preferred’ (Smyth, 2001). For mathematics teachers, the authoritative discourse that producing results is of paramount importance ‘demands our unconditional allegiance’ and is imbued with ‘political power’.

In contrast, individuals are already aligned with discourses which could be described as internally persuasive:

Internally persuasive discourse—as opposed to one that is externally authoritative—is, as it is affirmed through assimilation, tightly interwoven with “one’s own word.” In the everyday rounds of our

consciousness, the internally persuasive word is half-ours and half- someone else’s. (Bakhtin, 1981:345)

If internally persuasive words are ‘half ours and half someone else’s’ then these are words that the I has taken on, approved of, perhaps combined with other discourses having read them through its history-in-person lens. These words somehow ‘fit’ with the I’s beliefs and values. In that sense, authoritative voices can shift to become internally persuasive when they become ‘half ours’ ‘without any imposition or violence (physical or psychological)’ (Matusov and von Duyke, 2010:176). And so an authoritative discourse that has been imposed cannot ever be considered internally persuasive.

Certain discourses and words are more attractive and can be said to have a ‘centripetal’ pull which makes them inescapable to some. In these cases, the discourses and words tempt the I to ‘unify’ or ‘conform’ and adopt them. As Morris (1994) writes:

… the centripetal forces of the life of language, embodied in a ‘unitary language’, operate in the midst of heteroglossia. At any given moment of its evolution, language is stratified not only into linguistic dialects … but also – and for us this is the essential point – into languages that are socio-ideological: languages of social groups, ‘professional’ and ‘generic’ languages, languages of generations and so forth. (p75).

Teachers have a shared professional ‘unitary’ language of educational bodies (e.g. Ofsted), terms (e.g. differentiation) and acronyms (e.g. SATs) which I also share, and which is used in conversations between teachers and in my research interviews. In recent years, the word and discourse ‘mastery’, has entered the ‘unitary’ language of mathematics education. Although ‘mastery’ has been defined by NCETM (2017a), it has remained nebulous, in part because it belongs to many different ‘languages’ and so while it is widely used, it is understood and adopted differently by teachers according to their previous meetings of the word and adherence to, or pressure from, other discourses (Duckworth et al., 2015; NAMA, 2015; Boylan et al., 2016; Townsend, 2016; Boylan et al., 2017; Boylan and Townsend, 2018).