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

<p>This thesis describes the use of copper and palladium to mediate transformations of carboranes, especially <i>p</i>-carborane.</p><p>1-(1-<i>p</i>-carboranyl)-<i>N</i>-methyl-<i>N</i>-(2-butyl)-3-isoquinolinecarboxamide, a carborane containing analogue of the peripheral benzodiazepine receptor (PBR) ligand PK11195, has been synthesised. A key step in the reaction is the copper (I) mediated coupling of p-carborane with ethyl 1-bromo-isoquinoline-3-carboxylate. </p><p><i>p</i>-Carborane has been arylated on the 2-<i>B</i>-atom in high yields, using the Suzuki–Miyaura reaction. Thus the reaction between 2-I-<i>p</i>-carborane and various arylboronic acids [1-naphthyl-, phenyl-, 4-MeO-C₆H₄-, 3-CH₃CONH-C₆H₄-, 4-NC-C₆H₄-, 3-NO₂-C₆H₄-], gave the corresponding 2-aryl-<i>p</i>-carboranes in DME solution when reacted in the presence of cesium fluoride and the catalytic Pd₂(dba)₃–dppb system. Under the same conditions, the boron-boron bond forming reaction of two <i>p</i>-carboranylboronic esters (2-[(pinacolato)boron]-<i>p</i>-carborane and 2-[(neopentyl glycolato)boron]-p-carborane) was also shown feasible.</p><p><i>p</i>-Carborane has been vinylated on the 2-<i>B</i>-atom in high yields by use of the Heck reaction. The coupling between 2-I-<i>p</i>-carborane and various styrenes [4-H-, 4-C₆H₄-, 4-Cl , 4-Br-, 4-NO₂-, 4-CH3O- and 4 CH₃ ] resulted in the formation of the corresponding<i>trans</i>-β-(2-<i>B</i>-<i>p</i>-carboranyl) styrene in DMF solution when reacted in the presence of silver phosphate and the palladacycle Herrmann´s catalyst. The reaction was shown to proceed at higher rate with electron rich than with electron deficient olefins.</p><p>The feasibility of palladium-catalysed isotopic exchange of an iodinated closo-carborane with a radioisotope of iodine has been studied. 2-I-<i>p</i>-carborane was selected as a model compound. It was shown, that such isotopic exchange is possible and provides a high yield (83 ± 4.2 %) during 40 min long reaction. The reaction conditions were optimised, and it was demonstrated that presence of the tetra n-butylammonium hydrogensulphate is important in order to stabilise catalyst and provide reproducibility of labelling. In this work we have modified the methodology and extended the application to a wider range of iodinated carboranes. By the use of Herrmann’s catalyst in toluene at 100 °C this [¹²⁵I]-iodide labelling could be improved and extended. 2-I-<i>p</i>- 9-I-<i>m</i>-, 9-I-<i>o</i>-, 3-I-<i>o</i>-carborane, 1-phenyl-3-I-<i>o</i>-carborane and 1,2-diphenyl-3-I-<i>o</i>-carborane could be [¹²⁵I]-iodide labelled in high to excellent yields within 5 minutes.This reported palladium catalyzed radio-iodination of the uncharged closo-carboranes might find use in pharmacokinetic studies of carborane derivatives.</p>

This thesis describes the use of copper and palladium to mediate transformations of carboranes, especially p-carborane. 1-(1-p-carboranyl)-N-methyl-N-(2-butyl)-3-isoquinolinecarboxamide, a carborane containing analogue of the peripheral benzodiazepine receptor (PBR) ligand PK11195, has been synthesised. A key step in the reaction is the copper (I) mediated coupling of p-carborane with ethyl 1-bromo-isoquinoline-3-carboxylate. p-Carborane has been arylated on the 2-B-atom in high yields, using the Suzuki–Miyaura reaction. Thus the reaction between 2-I-p-carborane and various arylboronic acids [1-naphthyl-, phenyl-, 4-MeO-C6H4-, 3-CH3CONH-C6H4-, 4-NC-C6H4-, 3-NO2-C6H4-], gave the corresponding 2-aryl-p-carboranes in DME solution when reacted in the presence of cesium fluoride and the catalytic Pd2(dba)3–dppb system. Under the same conditions, the boron-boron bond forming reaction of two p-carboranylboronic esters (2-[(pinacolato)boron]-p-carborane and 2-[(neopentyl glycolato)boron]-p-carborane) was also shown feasible. p-Carborane has been vinylated on the 2-B-atom in high yields by use of the Heck reaction. The coupling between 2-I-p-carborane and various styrenes [4-H-, 4-C6H4-, 4-Cl , 4-Br-, 4-NO2-, 4-CH3O- and 4 CH3 ] resulted in the formation of the correspondingtrans-β-(2-B-p-carboranyl) styrene in DMF solution when reacted in the presence of silver phosphate and the palladacycle Herrmann´s catalyst. The reaction was shown to proceed at higher rate with electron rich than with electron deficient olefins. The feasibility of palladium-catalysed isotopic exchange of an iodinated closo-carborane with a radioisotope of iodine has been studied. 2-I-p-carborane was selected as a model compound. It was shown, that such isotopic exchange is possible and provides a high yield (83 ± 4.2 %) during 40 min long reaction. The reaction conditions were optimised, and it was demonstrated that presence of the tetra n-butylammonium hydrogensulphate is important in order to stabilise catalyst and provide reproducibility of labelling. In this work we have modified the methodology and extended the application to a wider range of iodinated carboranes. By the use of Herrmann’s catalyst in toluene at 100 °C this [125I]-iodide labelling could be improved and extended. 2-I-p- 9-I-m-, 9-I-o-, 3-I-o-carborane, 1-phenyl-3-I-o-carborane and 1,2-diphenyl-3-I-o-carborane could be [125I]-iodide labelled in high to excellent yields within 5 minutes.This reported palladium catalyzed radio-iodination of the uncharged closo-carboranes might find use in pharmacokinetic studies of carborane derivatives.