Discusión y conclusiones

Throughout this thesis we have seen how QM(s) is itself inherently multiple, yet this begs the question: How can something multiple cultivate an appearance of singularity? After all, although the details of QM(s) character are varied, this shared thing, QM(s), still appears to exist across disciplines and sectors.

When embarking upon the project it was assumed that this unity was a product of similar techniques being included across all disciplines. However, after mapping the content of QM(s), included in Chapter 4, little evidence was found of this assumed corpus of unified QM(s) techniques. While – as seen in Chapter 5 – similar learning-teaching performances were observed across many of the disciplines these performances did not produce similar narratives of QM(s) across disciplines – as discussed in Chapter 6. Instead of being unified through similarities of techniques or performances, QM(s) appeared to unify itself, and be unified by others, through a process of othering (Said, 1985).

Across disciplines extensive boundary work was done to reinforce QM(s) as different to other kinds of knowledge. Most obvious to newcomers was the different language developed and spoken by QM(s). While regional dialects existed, the overarching mathematical language spoken was continually empahsised as different to common or even disciplinary languages used:

The seminar leader comments that, “The complete name is statistically

significantly different”, saying that “because in statistics” different has a special meaning. He reinforces this by writing up:

“X + Y are said to be statistically significantly different if !! is consistently bigger/smaller than !!”

He continues asking the group that as they have the “knowledge of statistically significant in statistics, should they replace the thermometers?”

S: No. SL: Why?

S: As there’s no difference. SL: Yes in statistics.

(Fieldnote: Economics, 1st _{year UG tutorial, QM(s) module)}

This special meaning of “significance” in QM(s) language, as exemplified in the above quote, was constantly repeated and reinforced across the disciplines observed. Alongside this, QM(s) also presented their own different framework for doing, through concepts such as representativeness or bias/impartiality - which students often easily translated to a qualitative methods context (a problem for qualitative methods learning-teaching as described in Glesne and Webb (1993)). For QM(s) results were evaluated using different mechanisms to those used in everyday logic or decision-making (Garfield & Ahlgren, 1998), with new rules developed and applied. This difference in language was reinforced through notation, which served as a means to both represent, and to communicate with, QM(s). Just as the spoken language of QM(s) must be learnt, so too must this notation, with both having to be translated into everyday language for students. Together this notation and language served as an obligatory passage point for those wishing to work with QM(s) independently, without the use of a translator.

As well as the different language serving to unify QM(s), when transferred into Higher Education learning-teaching environments QM(s’) difference was further magnified by curriculum and module structures. As presented in Chapter 4, in all disciplines QM(s) were boxed up in 15-20 credit modules separated from other disciplinary modules. While in all these modules QM(s) were presented through relevant disciplinary examples, the doing of these modules remained distinctly different to other forms of knowledge. As presented in Section 5.2.1, the doing of QM(s) through worksheets and exercises

reinforced QM(s) as a different kind of knowledge. This was knowledge that required the support of extra actors and learning-teaching environments, with workshops and

Furthermore, these modules adopted assessment methods and marking schemes that were strikingly different to those used in other modules. As explained in Section 5.2.2, while these assessments and mark schemes were enrolled to respond to QM(s) language and doing requirements, they served to translate QM(s) character, and distance QM(s) from wider disciplinary knowledge forms.

While this boxing up and othering of QM(s) serves to maintain QM(s) status as a single, unified actor, cultivating an identity based on difference creates difficulties when (re-)integrating QM(s) with disciplinary knowledges. As discussed in Chapter 4, when examining student concept maps, QM(s) was often represented as distanced and separated from the various theoretical contributions of their field. This separation of QM(s) mirrored not only the boxing up of QM(s) within methods modules, which is often emphasised within the literature (e.g. Williams et al., 2016; Buckley et al., 2015), but also the other boundary work described above which served to differentiate QM(s) from other kinds of knowledge.

Furthermore, for students the relationship of QM(s) to theory was often understood as one directional, as one student explained:

[Economics is] made up of the theory, but the theory must be confirmed through like statistics and research [mhm]. And basically erm, the only thing that came up in my mind for this is like er a weird ring, in the sense that theory is then confirmed by research, therefore theory again.

(2nd _{year UG student, Economics – Antonio)}

Although the student describes the relationship of QM(s) to theory as cyclical, this ring represents a linear sequence of steps followed to test theory and not a reciprocal relationship of influence from theory to method and method to theory. As one handbook summarised it, students should “understand the link between data and substantive psychological questions, and how one can answer such questions using statistical methods.” (Psychology, PG module information, QM(s) module description). This characterisation of the relationship between theory and methods can be understood as one directional/dimensional as here methods simply serve to passively generate or test theory, with little consideration given to how theories and methods actively influence one another.

In contrast, many staff included a representation of QM(s) (and research methods in general) link to theory, see Figure 8.1 for extract, full concept map show in Appendix 12.11. Although staff did not draw more links to QM(s) (average = 2) than students (undergraduate average = 2; postgraduate average = 2), Figure 8.1 illustrates that staff held a more complex understanding of QM(s) relationship to theory. As explained by the staff member, the cyclical nature of this link represented the following:

Figure 8.1 Extract of Psychology staff member’s concept map - Tristan

What tends to happen is the method takes priority over theory. So it’s certain advances in psychology, particularly neuro-scientific are primarily technological advances in terms of what it is we can detect. In terms of brain activation and in response to a particular stimuli without necessarily there being any er prior theory as to what those things might represent [mhm]. [...] Erm and you know if you read people like Danziger, erm Danziger will say actually it’s method that predominates and it’s particular forms of methods, primarily quantification, experimentation and measurement that predominate and that they are what now drives theory.

(Staff member, Psychology – Tristan) As such, instead of theoretical approaches guiding methodological choice – as often described by students – staff also acknowledged the role methods played in driving and shaping the kinds of theories that a discipline produced. For staff, QM(s) was not

characterised as distinctly different set of knowledge separate from the discipline. Instead QM(s) was understood as part of a collective of methods, which together formed a key

component of all knowledge. Here then, instead of an identity of difference, for staff QM(s) was understood through an identity of similarity.

These different understandings held by students and staff are represented in Figure 8.1.a) and b). Noticeably absent from both staff and students’ representations is the actor Data, whose relationship to QM(s) and theory is illustrated in Figure 8.1.c). When examining the actor-networks in the learning-teaching environments in Chapter 5, here too Data, as an actor, appeared to be silenced. Yet without data QM(s) is powerless. Moreover, as observed in Chapter 6, disciplinary differences in the character of QM(s) can be

understood as an effect of the different kinds of data used by, and available to, different disciplines. For those disciplines working with data in the form of absolute measures, QM(s) acquired a character of stability and reliability. Whereas for disciplines working with data in more complex forms the characterisation of QM(s) remained partial. Understood in this way it was the data type, not the techniques chosen that controlled the identities of QM(s) in disciplinary actor-networks.

a) b) c)

Figure 8.2 A figurative representation of student (a) and staff (b)

understandings of the relationship between theory and method, and a proposed alternative (c).