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This study empirically compares the Classical Test Theory (CTT) and the Partial Credit Model (PCM) of Rasch focusing on the invariance of item parameters. The invariance concept which is the consequence of the principle of specific objectivity was tested in both CTT and PCM using the results of learners who wrote the National Senior Certificate (NSC) Mathematics examinations in 2010. The difficulty levels of the test items were estimated from the independent samples of learn- ers. The same sample of learners used in the calibration of the difficulty levels of the test items in the PCM model were also used in the calibration of the difficulty levels of the test items in CTT model. The estimates of the difficulty levels of the test items were done using RUMM2030 in the case of PCM while SAS was used in the case of CTT. RUMM2030 and SAS are both the statistical softwares. The analysis of variance (ANOVA) was used to compare the four different design groups of test takers. In cases where the ANOVA showed a significant difference between the means of the design groups, the Tukeys groupings was used to establish where the difference came from. The research findings were that the test items' difficulty parameter estimates based on the CTT theoretical framework were not invariant across the different independent sample groups. The over- all findings from this study were that the CTT theoretical framework was unable to produce item difficulty invariant parameter estimates. The PCM estimates were very stable in the sense that for most of the items, there was no significant difference between the means of at least three design groups and the one that deviated from the rest did not deviate that much. The item parameters of the group that was representative of the population (proportional allocation) and the one where the same number of learners (50 learners) was taken from different performance categories did not differ significantly for all the items except for item 6.6 in examination question paper 2. It is apparent that for the test item parameters to be invariant of the group of test takers in PCM, the group of test takers must be heterogeneous and each performance category needed to be big enough for the proper calibration of item parameters. The higher values of the estimated item parameters in CTT were consistently found in the sample that was dominated by the high proficient learners in Mathematics ("bad") and the lowest values were consistently calculated in the design group that was dominated by the less proficient learners. This phenomenon was not apparent in the Rasch model. / Mathematical Sciences / M.Sc. (Statistics)

A series of experiments was performed with the Texas A&M University Nuclear Science Center Reactor (NSCR) to verify ²³⁵U delayed neutron emission rates. A custom device was created to accurately measure a sample's pneumatic flight time and the Nuclear Science Center's (NSC's) pneumatic transfer system (PTS) was redesigned to reduce a sample's pneumatic flight time from over 1,600 milliseconds to less than 450 milliseconds. Four saturation irradiations were performed at reactor powers of 100 and 200 kW for 300 seconds and one burst irradiation was performed using a $1.61 pulse producing 19.11 MW-s of energy. Experimental results agreed extremely well with those of Keepin. By comparing the first ten seconds of collected data, the first saturation irradiation deviated ~1.869% with a dead time of 2 microseconds, while the burst irradiation deviated ~0.303% with a dead time of 5 microseconds. Saturation irradiations one, three and four were normalized to the initial count rate of saturation irradiation two to determine the system reproducibility, and deviated ~0.449%, ~0.343% and ~0.389%, respectively.

This study empirically compares the Classical Test Theory (CTT) and the Partial Credit Model (PCM) of Rasch focusing on the invariance of item parameters. The invariance concept which is the consequence of the principle of specific objectivity was tested in both CTT and PCM using the results of learners who wrote the National Senior Certificate (NSC) Mathematics examinations in 2010. The difficulty levels of the test items were estimated from the independent samples of learn- ers. The same sample of learners used in the calibration of the difficulty levels of the test items in the PCM model were also used in the calibration of the difficulty levels of the test items in CTT model. The estimates of the difficulty levels of the test items were done using RUMM2030 in the case of PCM while SAS was used in the case of CTT. RUMM2030 and SAS are both the statistical softwares. The analysis of variance (ANOVA) was used to compare the four different design groups of test takers. In cases where the ANOVA showed a significant difference between the means of the design groups, the Tukeys groupings was used to establish where the difference came from. The research findings were that the test items' difficulty parameter estimates based on the CTT theoretical framework were not invariant across the different independent sample groups. The over- all findings from this study were that the CTT theoretical framework was unable to produce item difficulty invariant parameter estimates. The PCM estimates were very stable in the sense that for most of the items, there was no significant difference between the means of at least three design groups and the one that deviated from the rest did not deviate that much. The item parameters of the group that was representative of the population (proportional allocation) and the one where the same number of learners (50 learners) was taken from different performance categories did not differ significantly for all the items except for item 6.6 in examination question paper 2. It is apparent that for the test item parameters to be invariant of the group of test takers in PCM, the group of test takers must be heterogeneous and each performance category needed to be big enough for the proper calibration of item parameters. The higher values of the estimated item parameters in CTT were consistently found in the sample that was dominated by the high proficient learners in Mathematics ("bad") and the lowest values were consistently calculated in the design group that was dominated by the less proficient learners. This phenomenon was not apparent in the Rasch model. / Mathematical Sciences / M.Sc. (Statistics)

The National Curriculum Statement (NCS) heralds the beginning of a new curriculum for Grades 10 to 12 in South Africa. Underpinned by the South African Constitution, and based on the tenets of Outcomes-based Education, the NCS seeks to provide contextually-relevant education for all South African learners, so that they are able to embrace inevitable change. Although the NCS highlights the importance of assessment, an analysis of the English Home Language (EHL) NCS reveals tensions between policy and practice. This study attempts to contextualise the role of relevant assessment for the 21st century. It then proceeds to engage in a historical evaluation of assessment within the NSC in terms of how assessment was conducted in the former Natal Education Department, a liberal education department within former apartheid South Africa. The conclusions drawn from the evaluation are used to provide recommendations to relieve the tensions identified within the EHL NSC. / Educational Studies / M.Ed.

The National Curriculum Statement (NCS) heralds the beginning of a new curriculum for Grades 10 to 12 in South Africa. Underpinned by the South African Constitution, and based on the tenets of Outcomes-based Education, the NCS seeks to provide contextually-relevant education for all South African learners, so that they are able to embrace inevitable change. Although the NCS highlights the importance of assessment, an analysis of the English Home Language (EHL) NCS reveals tensions between policy and practice. This study attempts to contextualise the role of relevant assessment for the 21st century. It then proceeds to engage in a historical evaluation of assessment within the NSC in terms of how assessment was conducted in the former Natal Education Department, a liberal education department within former apartheid South Africa. The conclusions drawn from the evaluation are used to provide recommendations to relieve the tensions identified within the EHL NSC. / Educational Studies / M.Ed.

Mathematics Education / M. Ed. (Mathematics Education)