<p>One of the key ideas in the research on mathematics education is that the mathematical knowledge that learners acquire is strongly tied to the particular situation in which it is learnt. This study investigated the contexts that learners in grades eight, nine and ten prefer to deal with in the learning of mathematics based on their personal, social, societal, cultural and contextual concerns or affinities. The study is situated in the large-scale project called the Relevance of School Mathematics Education II (ROSMEII), which is concerned with the application and the use of mathematical knowledge and processes in real life situations. It is based on a survey of learners from ten (10) secondary schools in the Oshana and Khomas regions of Namibia. The ten schools that were sampled represent the spectrum of schools in Namibia in both urban and semi-urban areas. The Rasch model of data analysis is employed to provide some insight into the contextual situations learners would like to deal with in their mathematical learning. The data obtained for this study was analysed using the WINSTEPS Version 3.65.0 suite of computer programs. The current study arises from a concern about the absence of the voices of learners in the contextual situations in mathematics selected by adults such as mathematics teachers, inspectorates and curriculum and materials developers. The assumption is that the inclusion of learners&rsquo / insights into mathematics curricular might enhance mathematical learning. The study reveals that school children have an intrinsic desire to learn about mathematical issues embedded in real-life contexts. Several items which Namibian learners have shown interest in are issues they experience in life out of school which are not directly dealt with in school, such as managing personal and financial affairs, health matters, technology, construction, engineering and government financial matters. However, learners indicated to have a low preference in contexts like lotteries and gambling, national and international politics, cultural products, all kinds of pop music and dancing. This thesis contends that the inclusion of contexts in the mathematics curriculum which are of interest to learners will go a long way in facilitating good performance of learners in mathematics.</p>

<p>One of the key ideas in the research on mathematics education is that the mathematical knowledge that learners acquire is strongly tied to the particular situation in which it is learnt. This study investigated the contexts that learners in grades eight, nine and ten prefer to deal with in the learning of mathematics based on their personal, social, societal, cultural and contextual concerns or affinities. The study is situated in the large-scale project called the Relevance of School Mathematics Education II (ROSMEII), which is concerned with the application and the use of mathematical knowledge and processes in real life situations. It is based on a survey of learners from ten (10) secondary schools in the Oshana and Khomas regions of Namibia. The ten schools that were sampled represent the spectrum of schools in Namibia in both urban and semi-urban areas. The Rasch model of data analysis is employed to provide some insight into the contextual situations learners would like to deal with in their mathematical learning. The data obtained for this study was analysed using the WINSTEPS Version 3.65.0 suite of computer programs. The current study arises from a concern about the absence of the voices of learners in the contextual situations in mathematics selected by adults such as mathematics teachers, inspectorates and curriculum and materials developers. The assumption is that the inclusion of learners&rsquo / insights into mathematics curricular might enhance mathematical learning. The study reveals that school children have an intrinsic desire to learn about mathematical issues embedded in real-life contexts. Several items which Namibian learners have shown interest in are issues they experience in life out of school which are not directly dealt with in school, such as managing personal and financial affairs, health matters, technology, construction, engineering and government financial matters. However, learners indicated to have a low preference in contexts like lotteries and gambling, national and international politics, cultural products, all kinds of pop music and dancing. This thesis contends that the inclusion of contexts in the mathematics curriculum which are of interest to learners will go a long way in facilitating good performance of learners in mathematics.</p>

Objectives: To explore the prevalence and structure of self-reported disability after mild traumatic brain injury and the impact of traumatic brain pathology on such outcome. Material and methods: In study 1-3, symptoms data were collected by use of Rivermead Post-concussion Symptoms Questionnaire (RPQ) and data on global function by use of Glasgow Outcome Scale Extended (GOSE) from 2602 patients at 3 months after MTBI. RPQ data were subject to factor and Rasch-analyses Head CT data from 1262 patients were used in a prediction analysis that also included age and gender. In study 4, MRI and symptoms data were collected at 2-3 days and at 3-7 months follow-up after MTBI in 19 patients. Global function was assessed at follow-up by use of the Rivermead Head Injury Follow-Up Questionnaire (RHIFUQ) and GOSE. Results: I. Most respondents reported no remaining symptoms but 24% reported ≥3 and 10% ≥7 remaining symptoms. The factor analysis demonstrated that all symptoms are correlated but also identified subgroups of symptoms. II. Rasch-analysis of RPQ showed disordered category function, local dependency of items, poor targeting of persons to items and indications of 3 or more dimensions. There was no differential item functioning. III. Head CT pathology with no need for acute intervention was observed in 52 patients (4%) but was not associated with either frequency of remaining symptoms or global outcome at 3 months post injury. Female gender and age over 30 years were associated with less favourable outcome with respect to symptoms and GOSE. IV. Post-acute MRI indicated trauma-related pathology in one patient and follow-up MRI indicated loss of brain volume in 4 patients. Conclusions: A substantial proportion of patients with MTBI report remaining problems at three months after MTBI. RPQ is useful but not optimal to assess symptoms outcome after MTBI and calculation of a total sum score is not recommended. Female gender and older age are negative prognostic factors while brain pathology according to CT has no effect on self-reported outcome. Loss of brain volume after MTBI according to MRI may be a sensitive marker of traumatic brain pathology and deserves further studies.

This document is a supplementary text to "An Empirical Power Analysis of Quasi-Exact Tests for the Rasch Model: Measurement Invariance in Small Samples" by Koller, Maier, & Hatzinger (to be published in Methodology, ISSN-L 1614-1881), which covers all technical details regarding the simulation and its results. First, the simulation scenarios and the introduction of differential item functioning (DIF) are described. Next, the different populations' distributions that were investigated are discussed, and finally, actual type-I-error rates and empirical power are displayed for all simulated scenarios. (authors' abstract) / Series: Research Report Series / Department of Statistics and Mathematics

Magister Educationis - MEd / One of the key ideas in the research on mathematics education is that the mathematical knowledge that learners acquire is strongly tied to the particular situation in which it is learnt. This study investigated the contexts that learners in grades eight, nine and ten prefer to deal with in the learning of mathematics based on their personal, social, societal, cultural and contextual concerns or affinities. The study is situated in the large-scale project called the Relevance of School Mathematics Education II (ROSMEII), which is concerned with the application and the use of mathematical knowledge and processes in real life situations. It is based on a survey of learners from ten (10) secondary schools in the Oshana and Khomas regions of Namibia. The ten schools that were sampled represent the spectrum of schools in Namibia in both urban and semi-urban areas. The Rasch model of data analysis is employed to provide some insight into the contextual situations learners would like to deal with in their mathematical learning. The data obtained for this study was analysed using the WINSTEPS Version 3.65.0 suite of computer programs. The current study arises from a concern about the absence of the voices of learners in the contextual situations in mathematics selected by adults such as mathematics teachers, inspectorates and curriculum and materials developers. The assumption is that the inclusion of learners’ insights into mathematics curricular might enhance mathematical learning. The study reveals that school children have an intrinsic desire to learn about mathematical issues embedded in real-life contexts. Several items which Namibian learners have shown interest in are issues they experience in life out of school which are not directly dealt with in school, such as managing personal and financial affairs, health matters, technology, construction, engineering and government financial matters. However, learners indicated to have a low preference in contexts like lotteries and gambling, national and international politics, cultural products, all kinds of pop music and dancing. This thesis contends that the inclusion of contexts in the mathematics curriculum which are of interest to learners will go a long way in facilitating good performance of learners in mathematics. / South Africa

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The ceiling and basal rules of the Wechsler Adult Intelligence Scale – Fourth Edition (WAIS-IV; Wechsler, 2008) only function as intended if subtest items proceed in order of difficulty. While many aspects of the WAIS-IV have been researched, there is no literature about subtest item difficulty and precise item difficulty values are not available. The WAIS-IV was developed within the framework of Classical Test Theory (CTT) and item difficulty was most often determined using p-values. One limitation of this method is that item difficulty values are sample dependent. Both standard error of measurement, an important indicator of reliability, and p-values change when the sample changes. A different framework within which psychological tests can be created, analyzed and refined is called Item Response Theory (IRT). IRT places items and person ability onto the same scale using linear transformations and links item difficulty level to person ability. As a result, IRT is said to be produce sample-independent statistics. Rasch modeling, a form of IRT, is one parameter logistic model that is appropriate for items with only two response options and assumes that the only factors affecting test performance are characteristics of items, such as their difficulty level or their relationship to the construct being measured by the test, and characteristics of participants, such as their ability levels. The partial credit model is similar to the standard dichotomous Rasch model, except that it is appropriate for items with more than two response options. Proponents of standard dichotomous Rasch model argue that it has distinct advantages above both CTT-based methods as well as other IRT models (Bond & Fox, 2007; Embretson & Reise, 2000; Furr & Bacharach, 2013; Hambleton & Jones, 1993) because of the principle of monotonicity, also referred to as specific objectivity, the principle of additivity or double cancellation, which “establishes that two parameters are additively related to a third variable” (Embretson & Reise, 2000, p. 148). In other words, because of the principle of monotonicity, in Rasch modeling, probability of correctly answering an item is the additive function of individuals’ ability, or trait level, and the item’s degree of difficulty. As ability increases, so does an individual’s probability of answering that item. Because only item difficulty and person ability affect an individual’s chance of correctly answering an item, inter-individual comparisons can be made even if individuals did not receive identical items or items of the same difficulty level. This is why Rasch modeling is referred to as a test-free measurement. The purpose of this study was to apply a standard dichotomous Rasch model or partial credit model to the individual items of seven core perceptual, verbal and working memory subtests of the WAIS-IV: Block Design, Matrix Reasoning, Visual Puzzles, Similarities, Vocabulary, Information, Arithmetic Digits Forward, Digits Backward and Digit Sequencing. Results revealed that WAIS-IV subtests fall into one of three categories: optimally ordered, near optimally ordered and sub-optimally ordered. Optimally ordered subtests, Digits Forward and Digits Backward, had no disordered items. Near optimally ordered subtests were those with one to three disordered items and included Digit Sequencing, Arithmetic, Similarities and Block Design. Sub-optimally ordered subtests consisted of Matrix Reasoning, Visual Puzzles, Information and Vocabulary, with the number of disordered items ranging from six to 16. Two major implications of the result of this study were considered: the impact on individuals’ scores and the impact on overall test administration time. While the number of disordered items ranged from 0 to 16, the overall impact on raw scores was deemed minimal. Because of where the disordered items occur in the subtest, most individuals are administered all the items that they would be expected to answer correctly. A one-point reduction in any one subtest is unlikely to significantly affect overall index scores, which are the scores most commonly interpreted in the WAIS-IV. However, if an individual received a one-point reduction across all subtests, this may have a more noticeable impact on index scores. In cases where individuals discontinue before having a chance to answer items that were easier, clinicians may consider testing the limits. While this would have no impact on raw scores, it may provide clinicians with a better understanding of individuals’ true abilities. Based on the findings of this study, clinicians may consider administering only certain items in order to test the limits, based on the items’ difficulty value. This study found that the start point for most subtests is too easy for most individuals. For some subtests, most individuals may be administered more than 10 items that are too easy for them. Other than increasing overall administration time, it is not clear what impact, of any, this has. However, it does suggest the need to reevaluate current start items so that they are the true basal for most people. Future studies should break standard test administration by ignoring basal and ceiling rules to collect data on more items. In order to help clarify why some items are more or less difficult than would be expected given their ordinal rank, future studies should include a qualitative aspect, where, after each subtest, individuals are asked describe what they found easy and difficult about each item. Finally, future research should examine the effects of item ordering on participant performance. While this study revealed that only minimal reductions in index scores likely result from the prematurely stopping test administration, it is not known if disordering has other impacts on performance, perhaps by increasing or decreasing an individual’s confidence.

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