Browsing by Author "Gumedze, Freedom Nkhululeko"

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    An investigation of mathematical misconceptions through an analysis of Grade 7 learners' responses to test items on decimals, percentages and measuremnt
    (2001) Tawodzera, George; Ensor, Paula; Gumedze, Freedom Nkhululeko
    This research dissertation emerges as a component of a broader research study, which sought to determine the impact of a mathematics textbook, Maths for all (Mfa) on teaching and learning, in general, and on learners' performance, in particular. The impact evaluation study focused on Grade 7 learners, from a sample of formerly DET primary classrooms in townships near Cape Town. It focused particularly on the teaching of decimals, percentages and measurment which 14 teachers in these schools agreed to teach in the second term of 2000. The 538 learners, from 10 experimental classrooms (with access to Mfa) and 4 control classrooms (with no access to Mfa), were given a pre-test at the beginning of the second term, and the same test as a post-test towards the end of the same term of the year 2000. The present study aims to analyse possible patterns of error in learners' responses to the test and investigate whether these patterns suggest underlying misconceptions held by the learners on decimals, percentages and measurement. As a secondary aspect, the study also set out to evaluate the test instrument as a measure of achievement and of potential misconceptions.
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    A variance shilf model for outlier detection and estimation in linear and linear mixed models
    (2008) Gumedze, Freedom Nkhululeko
    Outliers are data observations that fall outside the usual conditional ranges of the response data.They are common in experimental research data, for example, due to transcription errors or faulty experimental equipment. Often outliers are quickly identified and addressed, that is, corrected, removed from the data, or retained for subsequent analysis. However, in many cases they are completely anomalous and it is unclear how to treat them. Case deletion techniques are established methods in detecting outliers in linear fixed effects analysis. The extension of these methods to detecting outliers in linear mixed models has not been entirely successful, in the literature. This thesis focuses on a variance shift outlier model as an approach to detecting and assessing outliers in both linear fixed effects and linear mixed effects analysis. A variance shift outlier model assumes a variance shift parameter, wi, for the ith observation, where wi is unknown and estimated from the data. Estimated values of wi indicate observations with possibly inflated variances relative to the remainder of the observations in the data set and hence outliers. When outliers lurk within anomalous elements in the data set, a variance shift outlier model offers an opportunity to include anomalies in the analysis, but down-weighted using the variance shift estimate wi. This down-weighting might be considered preferable to omitting data points (as in case-deletion methods). For very large values of wi a variance shift outlier model is approximately equivalent to the case deletion approach.