School of Science
http://hdl.handle.net/10500/2736
2017-09-20T07:16:30ZMathematical symbolisation: challenges and instructional strategies for Limpopo Province secondary school learners
http://hdl.handle.net/10500/23154
Mathematical symbolisation: challenges and instructional strategies for Limpopo Province secondary school learners
Mutodi, Paul
This study reports on an investigation into the manner in which mathematical symbols influence learners’ understanding of mathematical concepts. The study was conducted in Greater Sekhukhune and Capricorn districts of Limpopo Province, South Africa. Multistage sampling (for the district), simple random sampling (for the schools), purposive sampling (for the teachers) and stratified random sampling with proportional allocation (for the learners) were used. The study was conducted in six schools randomly selected from rural, semi-urban and urban settings. A sample of 565 FET learners and 15 FET band mathematics teachers participated in the study. This study is guided by four interrelated constructivist theories: symbol sense, algebraic insight, APOS and procept theories. The research instruments for the study consist of questionnaires and interviews. A mixed method approach that was predominantly qualitative was employed. An analysis of learners’ difficulties with mathematical symbols produced three (3) clusters. The main cluster consists of 236 (41.6%) learners who indicate that they experience severe challenges with mathematical symbols compared to 108 (19.1%) learners who indicated that they could confidently handle and manipulate mathematical symbols with understanding. Six (6) categories of challenges with mathematical symbols emerged from learners’ encounters with mathematical symbols: reading mathematical text and symbols, prior knowledge, time allocated for mathematical classes and activities, lack of symbol sense and problem contexts and pedagogical approaches to mathematical symbolisation. Two sets of theme classes related to learners’ difficulties with mathematical symbols and instructional strategies emerged. Learners lack symbol sense for mathematical concepts and algebraic insight for problem solving. Learners stick to procedurally driven symbols at the expense of conceptual and contextual understanding. From a pedagogical perspective teachers indicated that they face the following difficulties when teaching: the challenge of introducing unfamiliar notation in a new topic; reading, writing and verbalising symbols; signifier and signified connections; and teaching both symbolisation and conceptual understanding simultaneously. The study recommends teachers to use strategies such as informed choice of subject matter and a pedagogical approach in which concepts are understood before they are symbolised.
2016-09-01T00:00:00ZBoundary current response in Ba0.34K0.64Fe2As2 superconducting single crystal probed by non-resonant microwave absorption technique
http://hdl.handle.net/10500/22966
Boundary current response in Ba0.34K0.64Fe2As2 superconducting single crystal probed by non-resonant microwave absorption technique
Ramashitja, Tshiwela Caroline
Non-resonant microwave absorption (NRMA) in superconducting materials has become a new experimental technique to probe and understand superconducting materials. For example cuprate superconductors are well studied with this technique. At the same time the technique is also evolving. This technique (NRMA) has been used to study magnetic shielding effects/boundary current in Ba0.34K0.64Fe2As2 (BaK122) single crystals of iron pnictides superconducting sample measured at 9.4 GHz below TC (4.2K-32K). It has been observed that a small modulation field used in NRMA experiment yield the boundary current response. We have established that the boundary current response depends on both modulation amplitude and the temperature. At high modulation field amplitudes and temperatures close to Tc the boundary current response gets suppressed and flux modulated response dominates. At low temperatures far away from Tc, only the boundary current response dominates.
2016-06-01T00:00:00ZStructure and spin dynamics in Cr Doped ZnO
http://hdl.handle.net/10500/22833
Structure and spin dynamics in Cr Doped ZnO
Amami, Paul Erhire
Polycrystalline Zn1-xCrxO (0.01 ≤ x ≤ 0.09) samples synthesized by solid state reaction technique were sintered at different temperatures following slow step sintering schedule. Structural, micro-structural, optical, magnetic properties and homogeneity were investigated using suitable characterisation techniques. Cr2O3 and CrO2 phases have been detected in the XRD patterns and Raman spectra of Zn1-xCrxO samples with x ≥ 0.05. Photoluminescence study has indicated improved optical property of the samples compared to undoped ZnO. While low percentage Cr doped samples showed diamagnetic behaviour, higher percentage doped samples (≥ 5%) exhibited ferromagnetic, paramagnetic and anti-ferromagnetic behaviours depending upon the sintering temperatures. The magnetic properties have been analysed through Electron Spin Resonance study. A g-value of 1.97 indicates Cr in +3
valence state in doped ZnO system. Presence of Cr3+ and Cr4+ in ZnO is understood to facilitate super exchange interactions to promote ferromagnetism at room temperature. ESR study shows improved magnetic homogeneity achieved by slow step sintering process.
2016-06-01T00:00:00ZSynthesis, characterization and biological activity of some cluster and mononuclear osimium complexes with P- donor ligandds
http://hdl.handle.net/10500/22823
Synthesis, characterization and biological activity of some cluster and mononuclear osimium complexes with P- donor ligandds
Monareng, Jubrey Mosima
Routes to mononuclear Os(II) and Os(0) cluster complexes containing P-donor ligands (PR3, PP) were studied using the osmium salts Y2[OsX6] (Y = NH4, K; X = Cl, Br, I) as precursors. Carbonylation of the precursors and then subsequent reaction with tertiary phosphines afford neutral complexes of the type cis,cis,trans-[OsX2(CO)2(PR3)2] (X = Cl, Br, I, PR3 = tertiary phosphine), which were characterized by combination of infrared and Raman spectroscopy, NMR (1H, 13C, 31P) spectroscopy and elemental analysis. The compounds cis,cis,trans-[OsBr2(CO)2{Ph2P(CH2C6H5)}2] (2b), cis,cis,trans-[OsBr2(CO)2{P(CH2C6H5)}3] (3b) and cis,cis,trans-[OsBr2(CO)2{P(C6H11)}2] (4b) have been further characterized by single crystal X-ray diffraction. Thermogravimetric analysis of these complexes shows multiple stages of decomposition that can be directly related to the loss of ligands.Microwave-promoted reaction of the osmium salt precursor with bidentate phosphine ligands affords the neutral complexes [OsX2(PP)2] (X = Cl, Br, I; PP = bidentate phosphine ligand). A stepwise substitution pathway has been suggested resulting in the formation of compounds cis/trans-[OsX2(PP)2] in which the ligands display different reactivity. The size of the bidentate phosphine ligand determines the stereochemistry of the product complex. Reaction with short ligands such as dppm selectively yield the cis-[OsX2(PP)2] isomers. Whilst reaction with dppe and dppp under the same conditions gives the trans-[OsX2(PP)2] isomers. Steric bulkiness of the ligands influences the stereochemistry. The cis-[OsX2(PP)2] isomers are thermally stable with onset of decomposition at temperatures above 300 °C. In contrast, the trans-[OsX2(PP)2] isomers were found to be thermally less stable and found to decompose in the range 195 – 251 °C. Microwave irradiation of [Os3(CO)12] in the presence of PPh3 in acetonitrile solution gave a mixture of disubstituted and trisubstituted phosphine cluster complexes which have been characterized by IR, Raman, 1H and 31P (where applicable) NMR spectroscopies. Variation of solvents influences substitution and give a mixture of monosubstituted and disubstituted phosphine cluster.
Complexes of the type [OsX2(PP)2] exhibited both anticancer and antimicrobial activity. In some instances the activity was comparable to that of the reference drugs. The complexes cis,cis,trans-[OsX2(CO)2(PR3)2] and phosphine substituted derivatives of [Os3(CO)12] exhibited moderate antibacterial activity against Gram-negative bacterial strains and some fungal strains under study.
2017-02-01T00:00:00Z