Theses and Dissertations (Mathematical Sciences)
http://hdl.handle.net/10500/3017
2014-10-22T10:48:37ZGrade 10 physical science students' reasoning about basic chemical phenomena at submicroscopic level
http://hdl.handle.net/10500/14145
Grade 10 physical science students' reasoning about basic chemical phenomena at submicroscopic level
Nyanhi, Musekiwa Gift
The study investigated South African Grade 10 Physical science learners’ reasoning about basic chemical phenomena at sub-microscopic level. The study adopted a non-experimental, exploratory and descriptive method and was principally guided by the ex-post facto research design using a concurrent embedded strategy of mixed qualitative and qualitative approach. A total of 280 grade 10 physical science learners in their intact classes and six of their teachers participated in the study. The 280 physical science learners comprised of 100 students from two top performing schools, 100 learners from two middle performing schools and the last 80 learners were drawn from two poor performing schools in Gauteng Department of Education’s Tshwane North District.
A two-tier multiple-choice paper and pencil Test of Basic Chemistry Knowledge (TBCK) based on the three levels of chemical representation of matter was administered to the 280 physical science learners in their Grade 11 first term to collect both quantitative and qualitative data. In addition to the TBCK, focus group discussions (FGDs) with learners, teacher interviews and document analysis were used to triangulate data.
The results revealed that most Grade 10 learners find it easy to identify pure elements and the solid state but find it difficult to negotiate between the three levels (macroscopic, sub-microscopic and symbolic) of chemical representation of matter. It became clear that learners experienced more difficulties in the concepts of basic solutions, acidic solutions, concentration and ionic compounds in solution. It also became apparent that some learners could not tell differences between a diatomic element and a compound indicating conceptual problems when they reason at particle level, and as a result they could not identify a mixture of elements. The results also indicated that the concepts of pure compounds and mixtures of compounds were not easy to comprehend as most learners took a pure compound for a mixture of atoms and a mixture of compounds for a mixture of elements. It is therefore concluded that learners find it difficult negotiating the three levels of chemical representation of matter. However, it is not clear whether the misconceptions the learners showed could be completely attributable to the concepts involved or the nature of the sub-microscopic models that were used in the test as it was also revealed that most teachers were not using sub-microscopic representations during instruction to enable learners to think at particle level. Furthermore, justifications to the multiple-choice tasks revealed lack of understanding of basic chemical concepts as well as language problems amongst learners as they could not clearly express their reasoning. Based on the results, some recommendations to educators, chemistry curriculum planners, teacher education and the chemistry education research field are suggested.
2013-10-01T00:00:00ZAn investigation of the use of computers in the teaching and learning of hyperbolic graphs in grades 10 to 12 mathematics
http://hdl.handle.net/10500/13694
An investigation of the use of computers in the teaching and learning of hyperbolic graphs in grades 10 to 12 mathematics
Mavhungu, Lavhelani Emily
In this investigation an attempt was made to determine how learners and teachers use
computers in the teaching and learning of hyperbolic graphs in Mathematics. A
comprehensive literature study showed that there are many benefits in using computers
to study Mathematics. The investigation was done in two phases. In the first phase, a
questionnaire was given to learners. The second phase involved interviewing learners
and teachers. Findings indicate that learners and teachers enjoy using computers in the
teaching and learning of Mathematics. Analysis of the results shows that the use of
computers in teaching and learning of Mathematics, in particular the teaching and
learning of hyperbolic graphs is beneficial.
2013-11-01T00:00:00ZPricing European and American bond options under the Hull-White extended Vasicek Model
http://hdl.handle.net/10500/13346
Pricing European and American bond options under the Hull-White extended Vasicek Model
Mpanda, Marc Mukendi
In this dissertation, we consider the Hull-White term structure problem with the boundary value condition given as the payoff of a European bond option. We restrict ourselves to the case where the parameters of the Hull-White model are strictly positive constants and from the risk neutral valuation formula, we first derive simple closed–form expression for pricing European bond option in the Hull-White extended Vasicek model framework. As the European option can be exercised only on the maturity date, we then examine the case of early exercise opportunity commonly called American option. With the analytic representation of American bond option being very hard to handle, we are forced to resort to numerical experiments. To do it excellently, we transform the Hull-White term structure equation into the diffusion equation and we first solve it through implicit, explicit and Crank-Nicolson (CN) difference methods. As these standard finite difference methods (FDMs) require truncation of the domain from infinite to finite one, which may deteriorate the computational efficiency for American bond option, we try to build a CN method over an unbounded domain. We introduce an exact artificial boundary condition in the pricing boundary value problem to reduce the original to an initial boundary problem. Then, the CN method is used to solve the reduced problem. We compare our performance with standard FDMs and the results through illustration show that our method is more efficient and accurate than standard FDMs when we price American bond option.
2013-01-01T00:00:00ZConcerning ideals of pointfree function rings
http://hdl.handle.net/10500/13342
Concerning ideals of pointfree function rings
Ighedo, Oghenetega
We study ideals of pointfree function rings. In particular, we study the lattices of z-ideals
and d-ideals of the ring RL of continuous real-valued functions on a completely regular
frame L. We show that the lattice of z-ideals is a coherently normal Yosida frame; and
the lattice of d-ideals is a coherently normal frame. The lattice of z-ideals is demonstrated
to be
atly projectable if and only if the ring RL is feebly Baer. On the other hand, the
frame of d-ideals is projectable precisely when the frame is cozero-complemented.
These ideals give rise to two functors as follows: Sending a frame to the lattice of
these ideals is a functorial assignment. We construct a natural transformation between the
functors that arise from these assignments. We show that, for a certain collection of frame
maps, the functor associated with z-ideals preserves and re
ects the property of having a
left adjoint.
A ring is called a UMP-ring if every maximal ideal in it is the union of the minimal
prime ideals it contains. In the penultimate chapter we give several characterisations for
the ring RL to be a UMP-ring. We observe, in passing, that if a UMP ring is a Q-algebra,
then each of its ideals when viewed as a ring in its own right is a UMP-ring. An example
is provided to show that the converse fails.
Finally, piggybacking on results in classical rings of continuous functions, we show that,
exactly as in C(X), nth roots exist in RL. This is a consequence of an earlier proposition
that every reduced f-ring with bounded inversion is the ring of fractions of its bounded
part relative to those elements in the bounded part which are units in the bigger ring. We
close with a result showing that the frame of open sets of the structure space of RL is isomorphic to L.
2013-11-01T00:00:00Z