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No description available.

The performance of mathematics and physical science students are very low in South Africa. These students lack algebraic knowledge and skills in physics education. They tend to treat mathematics and science as separate entities; to them the two subjects are not related. Even the teachers seem not to realise the interrelationship of the two subjects, because according to the research, they perpetuate this attitude. A possible reason could be that they are unfamiliar with common objectives and applications. Knowledge of science is enhanced by the application of mathematics, but the role of mathematical knowledge and skills in the understanding of physical science is uncertain. Even in the new National Curriculum Statement (NCS) of South Africa the relationship between mathematics and physical science is not clearly indicated. Algebraic language is a main tool used in physics, but students still display a lack of understanding of mathematical concepts and problem solving skills. The study was aimed at identifying the mathematical knowledge and skills that would enable students to solve physics problems in grades 11 and 12. The aim was also to identify the specific problems experienced by students in applying these skills and knowledge in physics at grades 11 and 12 level. The empirical study was conducted amongst a group of 120 students in four schools in the Rustenburg Region, North- West Province, South Africa and 28 teachers of which 10 were from these schools and 18 were teachers participating in the Sediba project of the North-West University. The investigation was done by means of a self constructed test and questionnaires. The results indicate that the biggest problem lies with a lack of conceptual knowledge, especially with a basic understanding of proportional reasoning. Other problems were identified and possible remedies proposed. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2006.

SANTRAUKA Skirtingų kultūrų ir kalbų gausa sąlygoja būtinybę vienos tautos vertybes, mintis ir stilius perteikti kitai, taigi vertimas tampa kultūrinių kontaktų kūrimo ir plėtimo priemone. Kadangi vertimo svarba tarpkultūrinės komunikacijos raidoje nuolat auga, jis susilaukia vis daugiau lingvistų dėmesio. Gramatinė vertimo pusė sukelia eilę sunkumų, todėl geras vertėjas turi ne tik puikiai išmanyti gramatikos taisykles, bet ir gebėti jas taikyti praktiškai bei tinkamai atlikti įvairius pakeitimus, kurie neišvengiami vertimo procese. Šis darbas skirtas anglų kalbos gramatinės inkorporacijos proceso pristatymui ir jo perteikimo lietuvių kalboje būdų ir ypatumų analizei. Gramatinės inkorporacijos procesas, apibūdina konstrukcijas, kuriose pasak Farkas ir de Swart (2004:1), veiksmažodis ir vienas iš jo argumentų sudaro glaudžiai susietą junginį. Šis fenomenas neretai tampa vertimo sunkumų priežastimi, kadangi yra daug atvejų, kai inkorporacinių konstrukcijų pateikimas originalo ir vertimo kalbose skiriasi leksine ir semantine prasme. Tokie vertimo sunkumai bei jų analizė ir suteikia pagrindą šiam darbui, kuriame gramatinės inkorporacijos konstrukcijos analizuojamos gramatiniu ir vertimo aspektu. Darbe, naudojantis aprašomuoju, gretinamuoju ir statistiniu metodais, apžvelgta mokslinė literatūra, atskleidžiamos inkorporacinių konstrukcijų ypatybės, pateikiami ir aptariami pavyzdžiai bei analizuojami jų vertimo būdai. Atliktas tyrimas patvirtino hipotezę, kad ne visos... [to full text]

The performance of mathematics and physical science students are very low in South Africa. These students lack algebraic knowledge and skills in physics education. They tend to treat mathematics and science as separate entities; to them the two subjects are not related. Even the teachers seem not to realise the interrelationship of the two subjects, because according to the research, they perpetuate this attitude. A possible reason could be that they are unfamiliar with common objectives and applications. Knowledge of science is enhanced by the application of mathematics, but the role of mathematical knowledge and skills in the understanding of physical science is uncertain. Even in the new National Curriculum Statement (NCS) of South Africa the relationship between mathematics and physical science is not clearly indicated. Algebraic language is a main tool used in physics, but students still display a lack of understanding of mathematical concepts and problem solving skills. The study was aimed at identifying the mathematical knowledge and skills that would enable students to solve physics problems in grades 11 and 12. The aim was also to identify the specific problems experienced by students in applying these skills and knowledge in physics at grades 11 and 12 level. The empirical study was conducted amongst a group of 120 students in four schools in the Rustenburg Region, North- West Province, South Africa and 28 teachers of which 10 were from these schools and 18 were teachers participating in the Sediba project of the North-West University. The investigation was done by means of a self constructed test and questionnaires. The results indicate that the biggest problem lies with a lack of conceptual knowledge, especially with a basic understanding of proportional reasoning. Other problems were identified and possible remedies proposed. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2006.

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Hydraulic fracturing plays an important role in increasing production rate in tight reservoirs. The performance of the reservoir after fracturing can be observed from the productivity index. This parameter is dependent on the fracture geometry; height, length and width. Unified fracture design (UFD) offers a method to determine the fracture dimensions providing the maximum productivity index for a specific proppant amount. Then, in order to achieve the maximum productivity index, the treatment schedules including the amount of liquid and proppant used for each stage must be determined according to the fracture dimensions obtained from the UFD. The proppant number is necessary for determining the fracture geometry using the UFD. This number is used to find the maximum productivity index for a given proppant amount. Then, the dimensionless fracture conductivity index corresponding to the maximum productivity index can be computed. The penetration ration, the fracture length, and the propped fracture width can be computed from the dimensionless fracture conductivity. However, calculating the proppant number used in UFD requires the fracture height as an input. The most convenient way to estimate fracture height to input to the UFD is to assume that the fracture height is restricted by stress contrast between the pay zone and over and under-lying layers. In other words, the fracture height is assumed to be constant, independent of net pressure and equal to the thickness of the layer which has the least minimum principal stress. However, in reality, the fracture may grow out from the target formation and the height of fracture is dependent on the net pressure during the treatment. Therefore, it is necessary to couple determination of the fracture height with determination of the other fracture parameters. In this research, equilibrium height theory is applied to rigorously determine the height of fracture. Solving the problem iteratively, it is possible to incorporate the rigorous fracture height determination into the unified fracture design.

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