This research innovation reports on the application of Herrmann’s Whole Brain® theory in facilitating and assessing learning in Mathematics in the senior phase, Grades 7 - 9. It is a two-part interrelated initiative that seeks both to augment current Mathematics-specific educational theories to improve practice, as well as to reflect on ways that these theories impact on the teaching practice. The literature review synthesises existing educational theories in terms of Herrmann’s Whole Brain® model into a new proposed comprehensive Mathematics-specific Whole Brain® model. This synthesis of existing “good practices” in Mathematics education in terms of Herrmann’s Whole Brain® model, supports the need for a Whole Brain® approach to teaching Mathematics. Furthermore, it hopes to be a user-friendly model with which teachers can plan and facilitate learning and assessment opportunities in Mathematics. Data was collected on the thinking preferences of each Mathematics teacher participant, as well learners’ perception of their teachers’ thinking preferences. Both qualitative and quantitative data was used to report on the findings. Individual and collective reflective practices, situated in the framework of professional development and action research, were used to analyse and report on the findings. The reflective practice resulting from the initiative is in itself an outcome of the research, since “those teachers who are students of their own effects are the teachers who are the most influential in raising students’ achievement” (Hattie & Yates, 2014, p. 24). The degree to which the reflective process impacted on each participant’s practice appears to be dependent on each teacher’s level of professional development. Teacher participants engaging in post-graduate studies showed the ability to complement their “existing competencies with needed situational competencies” (Herrmann, 1996, p. 39), meaning that these teachers were not limited by their thinking preferences, but were able to employ lesser preferred preferences when needed. Each teacher participant’s unique set of thinking preferences was obtained using the Hermann Brain Dominance Instrument (HBDI®). When each of these unique profiles were combined, they produced a compound Whole Brain® profile. This supported Herrmann’s (1990, p. 10) notion that every sizeable group would consist of a “composite whole brain”, but also showed that there is no specific set of thinking preferences unique to a Mathematics teacher. The learner questionnaires also indicated a reasonably balanced Whole Brain® profile amongst learners, supporting the need for a Whole Brain® approach to facilitating learning and assessing in Mathematics. The reflective cyclic process of theory informing practice and practice in turn informing theory is at the core of this research innovation. This cyclic process has become my living theory from which I hope to inspire others to engage in similar initiatives. / Thesis (PhD)--University of Pretoria, 2019. / Humanities Education / PhD / Unrestricted

This dissertation concerns the location and nature of phenomenal qualities. Arguably, these qualities naively seem to belong to perceived external objects. However, we also seem to experience phenomenal qualities in hallucinations, and in hallucinations we do not perceive any external objects. I present and argue for a theory of the phenomenal qualities, "brain theory", which claims that all phenomenal qualities we experience are physical properties instantiated in the brain, regardless of whether they are experienced in veridical perceptions or in hallucinations. I begin by more carefully identifying the phenomenal qualities, discussing how they are related to "qualia" and "phenomenal character". Then I present brain theory, and investigate its implications for the perceptual relations we stand in to external objects, noting that it is mostly neutral. I also compare brain theory to a similar theory of perception advocated by Bertrand Russell. Next, I provide an overview over the competing theories of phenomenal qualities, and relate them to theories of perception, such as representationalism, qualia theory, sense data theory and disjunctivism. The majority of my argumentation for brain theory focuses on arguing that the phenomenal qualities are instantiated in the brain, rather than on arguing that they are physical properties. Instead, I largely assume physicalism. However, even independently of the physicalism assumption, I show that we have reason to believe that phenomenal qualities are experienced in hallucinations, and that qualities experienced in hallucinations are instantiated in internal objects, such as our brains or sense data. In the first step towards this conclusion I argue that theories which deny that phenomenal qualities are experienced in hallucinations face serious problems. In the next step I argue that theories which deny that phenomenal qualities experienced in hallucinations are instantiated in internal objects face serious problems. Finally, an important part of the argumentation is my replies to objections against brain theory, including common sense objections and the "observation objection". From these conclusions, together with the physicalism assumption, I infer that we have reason to believe that brain theory is true about hallucinations. On this basis, I then argue, through a generalizing argument, that the same is the case for veridical perceptions.