Theoretical lineage and applications of the Threshold Concepts Framework

knowledge construction in a social context (Meyer & Timmermans, 2016). The framework prompts thinking and discussion about the mastery of disciplinary threshold concepts, whilst insisting that learning is as much about identity formation and disturbance as it is about cognition; this all the while weaving together insights from a range of learning theories and disciplines (Cousin, 2007; Rattray, 2014).

3.3.1 Theoretical lineage and leanings

In describing threshold concepts as the bedrock to attaining disciplinary mastery, the threshold concepts analytic framework to learning builds on the idea of learning for mastery initially proposed by Bloom (1968) – that is, to be deemed proficient in key disciplinary concepts, students need to display both the surface order levels of cognition exhibited by memorisation, understanding and application, as well as deep cognitive levels of analysis, evaluation, and creativity. Thus, the threshold concepts approach suggests that the student on the edge of understanding takes a surface approach to learning, whereas a student in the throes of acquiring mastery of a concept is likely to be taking a deep approach, following in the phenomenographic research tradition (Bhola & Parchoma, 2016; Marton & Saljo, 1976).

The transformative nature of threshold concepts implies that once a student has grasped the concept, her relation to the subject changes, representing a moment of deep learning, which in turn encourages even greater depth of learning. On the other hand, lack of mastery invites mimicry,

54

which can be understood as a form of surface learning (Cousin, 2007). This view of a transformative learning journey also resonates with other learning perspectives, including Vosniadou’s conceptual change process (2008), and Perry’s views on changing epistemological beliefs (1970). These views parallels Talanquer’s proposal of the terms conceptual threshold and crossing a conceptual threshold (2015). The former refers to the cognitive aspects that support the construction of a threshold concept, while the latter requires learners to “dismantle, set aside, coalesce, or separate existing assumptions, concepts, and ideas while building new ones”, thus, portraying threshold concepts as complex cognitive constructs comprised of conceptual, epistemological, and ontological elements (Talanquer, 2015, p. 4).

Threshold concepts interrogation of sources of disciplinary difficulty links to Perkins’s ideas of “troublesome knowledge” (2006) and, in terms of the threshold concepts framework’s acknowledgement that letting go of an old world view and embracing new ideas is also troubling, the threshold concepts approach links to Dewey’s observation that it is troublesome work to alter old beliefs (Dewey, 1986; Land & Rattray, 2017). In its focus on the liminal space as an unstable space in which the learner oscillates between old and emergent ideas, Meyer and Land (2003) borrow from anthropologist Turner’s work on rites of passage (1969, cited in Cousin, 2007). Additionally, the metaphor of a liminal space has been likened to Vygotsky’s (1978a) zone of proximal development (Cousin, 2008).

The role of discipline-specific orientation and context in the threshold concepts approach to learning, where learning includes participation processes of enculturation, links well with social learning theories and communities of practice (Cousin, 2007). Thus, threshold concepts can be said to echo aspects of “acquisition” and “participation” metaphors of learning (Sfard, 2009, cited in Goebel, 2017).

3.3.2 Scope and recent trends

Over the last decade, the threshold concepts analytic framework has “proved influential around the world as a powerful means of exploring and discussing the key points of transformation that students experience in their higher education courses and the ‘troublesome knowledge’ that these often present” (Perkins, 2010 , par 1). Early threshold concepts studies in diverse disciplines

55

focused on identifying, interrogating and acquiring disciplinary threshold concepts (Flanagan, 2018). These early research activities have expanded and evolved to an extent that the latest volume of research into threshold concepts, Threshold Concepts in Practice (Land et al., 2016), the fourth volume in a tetralogy on threshold concepts discussing students experiences and curriculum interventions in a range of disciplines and professional practices and contexts, includes the doctoral research process (Keefer, 2013; Maistry, 2017).

A threshold concepts framework to teaching and learning has not been widely applied in statistics education research (Wills, 2017), where a majority of the statistical education literature on threshold concepts tends to focus on the identification of statistical threshold concepts (Bulmer et al., 2007; Dunne et al., 2003; Khan, 2014); with the list of statistical topics considered to be threshold concepts being: confidence intervals, randomness or variation, sampling distribution, the Central Limit Theorem, linear regression, Bayes’ theorem, interval estimation, hypothesis testing, Analysis of Variance (ANOVA), the understanding of statistics and how it relates to understanding scientific articles, and identifying which tests to use for various data sets (Bulmer et al., 2007; Dunne et al., 2003; Norton, 2015).

Recent research suggests that there are many troublesome concepts in statistics that are not threshold, such as deriving estimators, and that there are three potential areas in statistics where threshold concepts may exist: (i) the nature of statistical inference and uncertainty; (ii) probability; and (iii) descriptive statistics (Wills, 2017). In statistics education research studies, application of the threshold concepts framework as an analytical tool to understanding students learning resulted in the promotion and adoption of various pedagogical and curricular reforms. For example, the use of online discussion boards generally enhanced medical statistics students learning of threshold concepts (MacDougall, 2010). Also advocated for was clear explanations and concise instructions on how to solve statistical problems, with a focus on the basics and opportunities to practice these (Bulmer et al., 2007). The general consensus was that the statistics curriculum is enriched by using

visual,narrative and mathematical approaches with detailed examples, quizzes and exercises to assist learning by application (Thompson, 2008). In South Africa, the threshold concepts approach to learning remains largely unexplored in statistics higher education research and I was only able to find one research paper based on the identification of statistical threshold

56 concepts by Dunne et al. (2003).

Recent trends in the application of threshold concepts has seen them being applied beyond the narrow confines of disciplinary conceptual focus to the liminal-esque space that is student-hood (Berg, Erichsen, & Hokstad, 2016). The transition into student hood, draws on one’s “emotional capital” while attempting to master perceived “rules of engagement”, and this may be especially difficult for non-traditional students, where context influences conceptual mastery, as is the case in South Africa (Goebel, 2017). Providing a supportive learning environment for students is critical (Cousin, 2014), and this view aligns with work relating to epistemological access in South Africa.

Although liminality (with its cognitive and affective connotations) is central to the threshold concepts view of learning, the focus has not generally been placed on students’ experiences of learning threshold concepts within the liminal space and “quite what supports or facilitates this passage has not been clear” (Rattray, 2016, p. 71). Thus, an emergent focal area of research within the threshold concepts framework is a consideration of the psychological and affective aspects of student learning, in an attempt to understand how students cope with the demands of the journey through the liminal space (Land & Rattray, 2017; Rattray, 2014, 2016).