Geography

Within Geography, students were exposed to QM(s) through questionnaires, fieldwork, lab work, and maps and charts in GIS. Here QM(s) could be numerical representations of an environment, a mathematical model of a system, or outcomes of a statistical test. When stepping into Geography, the trends and patterns of crime seen in Criminology become trends and patterns across space, visualised, predominantly, through GIS. When exploring these trends and patterns, Geography had a similarly close relationship with secondary data as was observed in Criminology, with data sources including the

Ordinance Survey, Environmental Agency, or services such as EDINA Digimap Service, or Greenland and Antarctic Ice Sheet Model (GRANTISM). However, here the partiality and scepticism of QM(s), dominant in Criminology, was far less emphasised.

This lack of scepticism towards QM(s) is postulated to be a result of how QM(s) was positioned within the wider discipline. For many QM(s) was understood as being closely related to physical geography, as illustrated below:

So I guess yeah, I don’t know if I’d call myself a geographer any more […] I feel like, yeah, as I loose the quantitative and the physical side of my work, yeah, cus I’m drifting more.. more and more into this kind of social stuff then yeah, then I feel that that makes me less of a geographer and maybe more of a something else.

(PhD student, Geography – Laura)

(1st _{year UG student, Geography – Ella)}

While QM(s) were placed within a Human Geography context in the curriculum, many still tied QM(s) to a scientific approach, as discussed in Section 4.3, a legacy perhaps of the quantitative revolution of the 60s (see Sheppard (2001) for a description of the quantitative revolution within Geography). Within the literature, this division is commonly attributed to students seeing QM(s) being more widely used by Physical Geography staff members, which has thus resulted in a call for the promotion of Human Geography applications of QM(s) (Johnston et al., 2014). However, here, this link is thought to be also due to a difference in the nature of QM(s) uptake into each of the sub-disciplines.

Across much of Physical Geography, QM(s) were strongly tied to the measuring and estimation of physical parameters (speed, distance), as became apparent on a Physical Geography fieldtrip:

On arrival the whole group walked down to the first location, a bridge over a stream in the valley. Both lecturers gave a short introduction to the day and the context of the location in relation to the wider geography of the region. The group was then split into two, down the middle of the assembled students. For the first part of the day I was placed with the lecturer delivering the hydrology

content for the trip. We all walked along the path up to the first location. Here, next to the stream, the lecturer passed out his hand-outs, and gave an overview of the activity – which was to answer several questions about the processes occurring at the site and estimating the stream parameters.

Students were given a while to think and discuss the questions in smaller groups (twos or individually) before the group was brought back together. In talking through the question sheet a very physical approach was taken, students were asked to think about an individual raindrop falling into the valley and the path it would take through the valley. A numerical element was added in the estimation of the stream parameters, which included: width, depth, cross-

sectional area, velocity, discharge, and pH. Students were given no equipment to measure any of these elements. Instead the lecturer demonstrated how you could take a ballpark estimate using your body or foot, by first lying across the stream to estimate its width and then by putting his foot in the stream to estimate the depth. This provided a talking point for both students and demonstrators. He then asked the group what the cross-sectional area of the stream was, saying:

L: OK so what is 20cm in meters? S: 0.2

L: 0.2, that’s right, so 4 x 0.2 is? (The agreed upon estimated width multiplied by the depth)

S: 0.8

L: So that’s 0.8m2 _{is our cross sectional area.}

The lecturer moved onto the discharge of the river, asking what estimate of velocity the students thought the stream was moving at. To answer this the lecturer stood roughly a meter away and asked the students to think about how fast the stream was moving in that distance. They provided a guess, which was then used to estimate the discharge by multiplying by the cross-sectional area. There was a noticeable absence of calculators, with students calling out answers and the lecturer prompting “and what is that measured in? m3_/s”.

The session ended with the lecturer emphasising that it was important to have ballpark estimates as sometimes you did not have precise measurements to provide exact calculations of the stream dynamics.

As well as exemplifying QM(s) as a character of measures and estimates, in the above example the embodied nature of these numbers was drawn out. As measures embodied by either human bodies, or by tape measures or meters, numbers took on a kind of concrete quality that is hard obtain from the survey data of the Criminologists and, in some cases, Human Geographers. Given the apparent concreteness of these numbers, the scepticism of Criminology was hard to sustain, as one participant said:

Erm I suppose what I like about numbers is… erm, they’re definite lines in the sand, if that makes sense [mhm]. The, the number eight is not open to

interpretation, [yeah] erm, whereas almost anything written in language is open to interpretation, so I suppose, I suppose it, numbers provide anchors [mm] on which you can make decisions.

(Staff member, Geography - Aaron) With this self-assuredness, QM(s) became characterised as problem solvers, providing quantified solutions that were – at least theoretically – hard to argue against. This face of QM(s) as a problem solver was further foregrounded through module descriptions, which included phrases such as:

This module provides an introduction to the skills used by geographers to analyse problems in both human and physical geography.

(Geography, 1st _{year UG research methods module description)}

Apply industry standard flood estimation and modelling techniques to solve real problems in the context of flood risk management and the latest legislation and policy.

(Geography, PG content module description) At a generic level, the students will be able to critically appraise aspects of the scientific literature, formulating robust scientific arguments, using recent research data from the module convenor and others to design solutions to environmental problems.

As a problem solver, QM(s) was a powerful ally, providing answers to specific questions, the results of which were understood as (reasonably) stable and reliable. While these numbers were understood as having errors associated with them, these errors were understood as being able to be constrained and quantified, thus leaving the stability of the result intact. This was exemplified by one staff member – David - who explained his research process by using the following diagram, shown in Figure 6.1. Through this he explained how samples were collected, processed, analysed, and how the numbers generated were then transferred into models and interpreted at system and world scales:

Figure 6.1 Participant's (David) scale of thought diagram describing their research process.

He went onto explain that this process could be applied to the work of Human Geographers but that their work tended to be more qualitative explaining that in that context:

So in other words you don’t have a hard and fast number [mhm] on that, on that result. Erm, they may put it into some kind of conceptual model […] which is basically saying, erm, “OK we don’t put hard and fast numbers in and get hard and fast numbers out, we put ideas in, and we say how things are linked

together and how different things happen in the world through people’s perceptions”.

(Staff member, Geography – David) This infallibility of numbers in Physical Geography meant that QM(s) could acquire a strength and dominance, not only providing trends but reliable answers and predictions which were vital to solving the environmental questions and problems of interest to Physical Geographers. Valorising QM(s) for their fixity and robustness however becomes problematic when placing QM(s) within a Human Geography context. Where QM(s) has thrived in Human Geography it has been in areas where numbers can be rendered with this same fixity – i.e. Transport Geography or GIS. But for those fields where “hard and fast” numbers cannot be produced, or where the underlying phenomenon studied is understood as being inherently fluid – where the data that is available more closely resembles the survey’s found in Criminology – the power of QM(s) break down as a different kind of quantitative methods are employed (similar to that identified by Thrift (2002)). When compared to the highly prized fixed numbers – and world – of Physical Geography it is perhaps unsurprising that Human Geographers and Criminologists remain sceptical about QM(s) value. Overall, for Geography as a discipline this left a tension, as different kinds of data, methods, and epistemology overlaped, with QM(s) playing their part, but being kept in check by other approaches, as one student described:

I suppose, I think the focus has been too much on quantitative generally, erm, and I think sort of things like issues like climate change won’t be solved with quantitative methods. [mm] It’s er, you know working out how much carbon there is in a tree trunk or whatever is not going to sort of solve the issue. It’s humans living on the Earth, and the way humans live on the Earth which is the issue.