Having presented literature on both the obstacles to quantitative methods learning- teaching and the various solutions/strategies proposed to these obstacles we can now critically examine this literature identifying the assumptions made about quantitative methods learning-teaching. Given the role they play in shaping understandings of quantitative methods learning-teaching, the lack of research questioning these
assumptions represents a clear gap in the literature. By using alternative frameworks that challenge these assumptions, new understandings of quantitative methods learning- teaching may be produced that have hitherto been overlooked.
Firstly, across most – if not all – of the literature presented, attention is given to a limited number of actors involved in the learning-teaching environments. Frequently, students and teaching staff are the only actors considered – even here, discussion was centred around problems faced by students and staff and not other actors. For example, in Garfield’s (1995) principals, ‘students learn’ and ‘teachers often overestimate’ (p.30-32). Here we find ourselves back to an overly simplistic characterisation of the learning- teaching environment. In the few cases where other actors are mentioned – such as the course assessments, or technology (i.e. calculators, computer, and visual aids) – these actors are understood as having limited, or no, agency of their own – agency, here, is understood as an actor’s ability to create difference to another entity or network (Sayes, 2014; Latour, 2005) (see Section 2.3.3 for further discussion over the meaning of agency). These actors are instead presented as things to be used by the teacher to improve the student’s learning with little consideration given to how these technologies themselves have agency over the learning-teaching environments or how they shape understandings of QM(s). This is in sharp contrast to other research on technology and learning where attention is given to how these technologies change learning-teaching (e.g. Johannesen et al., 2012).
While this focus on students and teaching staff represents a simplification of the learning-teaching environment, it also can be understood as a consequence of a second common assumption made by this literature, namely, that the classroom/lecture
theatre/seminar room is the only scale at which learning-teaching can be understood. Much of the literature presents solutions for application within the classroom (Paxton, 2006; Lewis-Beck, 2001), for individual modules (Strangfeld, 2013; Becker et al., 2006; Folkard, 2004), or strips the learning-teaching from reference to any space. For example, work by Garfield (1995) and Onwuegbuzie & Wilson (2003) strip away the learning environment, reducing learning-teaching to the interaction between student and teacher – be that in person (Murtonen & Lehtinen, 2003), through an assessment (i.e. Hubbard, 1997) or via learning activities (i.e. Harlow et al., 2002). Where mentioned spaces are often simply described as a context for the activities – e.g. ‘The meetings took place in the computer lab’ (Meletiou-mavrotheris, 2004: p.274) – characterized as flat spaces onto/into which learning-teaching occurs. By conceptualizing space in this way, the literature fails to explore the interactions occurring across modules, and years, which are vital to students’ experiences of their degrees and to quantitative methods learning- teaching (Parker, 2011).
In addition, in understanding spaces as an abstract frame of reference, this literature overlooks space as a relational or relative construct, that our experiences of an
environment are also framed by (Harvey, 2004). Furthermore, this literature has given little attention to how learning-teaching may change across the different spaces(-times) quantitative methods learning-teaching occurs in, be these the formal spaces(-times) of the seminar room, computer lab, laboratory, or the field, or informal spaces of the library or study room.
Given this universal and homogeneous understanding of the learning-teaching spaces(- times) it is no surprise that this literature has a focus on generating universally applicable schemes of best practice, such as found within Garfield (1995). The quest for best practice is perhaps also linked to the popularity of quantitative methodologies being used to research quantitative methods learning-teaching, where extensive attention has been given to modelling/predicting student performance (e.g. Tempelaar et al., 2007;
Onwuegbuzie, 2003; Harlow et al., 2002). Garfield & Ben-Zvi (2007), themselves point towards the need for larger-scale quantitative research to further evaluate their guidelines and to strengthen the field. This dominance of the use of quantitative methods in
research on QM(s) learning-teaching research also reflects the wider quantitative turn within Educational Research, with random controlled trails being an increasingly popular
method to provide robust, scientifically-informed, best practice (Torgerson & Torgerson, 2011). While this approach is clearly of value, the quest for universal best practices undervalues the messy, everyday, lived performances of QM(s) learning-teaching. Through focusing on problems and solutions this literature overlooks, and undervalues, understanding the doings of QM(s).
Finally, while there are attempts to create research and guidelines published in specialist journals, such as the Journal for Research in Mathematics Teaching; the Journal for Mathematics Teacher Education; and the Journal of Statistics Education, much of the literature is published within discipline specific journals. While this acknowledges that teaching in different disciplines is different, it limits the amount of cross-disciplinary discussion about learning-teaching. In particular, Wagner et al. (2011) report that there is little cross-disciplinary discussion surrounding research methods teaching in the social sciences. They argue that while comparisons between Social Science and Science subjects have been made, further research is needed on the similarities and differences in research methods learning-teaching across, specifically, Social Science disciplines.