This study examines the validity of the measures obtained from a performance assessment of students' developing context in a numeracy context. The study was based on three premises: that teachers could make valid and reliable judgments about their students in regular classroom situations; that numeracy competence was developmental and involved higher order thinking; and that using different performance tasks could provide information about changes in students' performances over time. (For complete abstract open document)

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This study aimed at investigating the methods used by teachers to assist the acquisition of numeracy skills by Standard 10 Geography learners. The problem of high failure rate in these skills was considered in terms of Perkins' (1992) minimum conditions for learning which, according to him, could assist and improve learner performance. These are : clear information, thoughtful practice, informative feedback and strong motivation. This investigation also draws upon Gallimore and Tharp' s (1991) means of assisting performance in the zone of proximal development, which include modeling, contingency management, feeding back, instructing, questioning and cognitive structuring. Data was collected by means of a number of lesson observations in three senior secondary schools in the Eastern Cape Province. This data was analysed in terms of whether or not teachers included Perkins' (1992) minimum conditions for learning in their methods of teaching and whether or not teachers used Gallimore and Tharp's (1991) means of assisting performance in their teaching activities.The overall result of the investigation indicated the overuse of the lecture method and the "recitation script" which denied learners opportunities to participate actively in the lesson. This research indicated, therefore, that the methods used by teachers in teaching Geography numeracy skills did not contribute towards the improvement of the learners' performance. A number of suggestions are made regarding initial and in-service teacher education and the encouragement of research by teachers into their own professional practice. / Thesis (M.Ed.)-University of Natal, Pietermartizbrug, 1998.

Substantial sums of money are invested by governments in state, national and international testing programs. Australia in particular engages at all three levels. There are number of purposes served by these programs. One of these is to report student performance against standards. Standard setting exercises with respect to a particular assessment are commonly used by testing programs where there is a requirement to determine the point at which it can be said that students have demonstrated achievement of a standard. Several methodologies have been devised that use expert judgements to derive a numerical cut-score on an achievement scale. A commonly used standard setting methodology is one proposed by Angoff (1971). The kernel of the Angoff procedure is the independent judgement of the probability that a minimally competent person can or cannot answer a dichotomously scored item correctly. This methodology typically involves three stages: orientation and training, a first round of performance estimation followed by feedback, and then a second round of performance estimation. In the orientation session, judges are asked to define a hypothetical target group. This definition is dependent upon the judges’ tacit understanding of the standard. For example, in the context of a mathematics test, judges would be asked to agree the skills the students should be expected to have mastered. Then they would be asked to envisage a student with those skills and to estimate the proportion of a hypothetical group of equally competent students (as defined by the expected standard) who would answer each item correctly. This proportion is the estimate of the required probability. Then the sum of these probabilities is taken as the raw cut-score on a test composed of the items. Several studies, however, question the validity of the Angoff methodology because of the finding that judges were unable to perform the fundamental task required of them: to estimate the probability a student would answer an item correctly, (Shepard, 1995) even for groups of students who are well known to them (Impara and Blake, 1996). In addition, standard-setting exercises invariably take place in situations where the reporting of educational standards has a high profile and is of political importance. To address the accountability requirements that accompany such a task, a wide range of stakeholders are invited to act as judges in the exercises. Inevitably, however, variability between the judges conception of the standard, as represented by the cut-score set by each of them, causes concern. Can the public have confidence in the standard set if the judges themselves cannot agree? Several studies report the introduction of further rounds of performance estimation and more refined feedback in an attempt to obtain greater consistency between the judges’ ratings (Impara and Blake, 2000; McGinty and Neel, 1996; Reckase, 2000). In more recent studies Green, Trimble and Lewis (2003) report a study in which three standard setting procedures were implemented to set cut-scores and which required judges to synthesise the results to establish final cut-points. Green et al report studies such as Impara and Blake (2000) where convergence of results among multiple standard settings are used as evidence of validity of cut-scores, but note that while convergence may occur to a reasonable degree when variations of the same method are used, there are few reports of convergence when different procedures are used. The distinguishing factor between the standard-setting exercises reported in the literature, which rely on judges’ tacit understanding of the standard and this study, is the existence of an explicitly and operationally defined standard. In 1996 the Australian Ministers for Education agreed to a national framework for reporting of student achievement in literacy and numeracy and arising from this decision was the drafting of benchmark standards against which the achievement of students in years 3, 5, 7 and 9 could be reported. The benchmark standards are articulated in two components. Criteria describe the skills that students need to have acquired if it is to be said that they achieved the standard and sample work exemplify these criteria. The setting of standards independently of placing them on a scale permitted a more rigorous assessment of the effects of different designs on the setting of cut-scores. Two different standard-setting methodologies have been employed in this study to translate descriptions of the standards into cut-scores. One draws on the Angoff method and involves the use of a rating scale. Judges consider the items of a test and indicate the probability that a student at the cut-score will answer each item correctly. The probabilities are in increments of 0.10, ranging from 0.0 to 1.0. The sum of the probabilities that a judge gives to the items is taken as the raw score cut-score from that judge. The second study involves a method of pairwise comparison of the same items together with items that are operationalised to be benchmark items. The judge has to decide which of each pair of items is the more difficult. The results of the two benchmark setting designs appear to support findings from other standard-setting exercises reported in the literature. Namely, i. Judges were unable to estimate absolute item difficulty for a student of prescribed ability. ii. Where two different designs were used, there is no convergence in results. iii. Ratings from different judges within each design varied widely. To indicate the resultant discrepancy in setting the benchmark on the same test, the rating methodology gives a value of 16.08 and the pairwise a value of 7.10 on ostensibly the same scale. A closer examination of the judges’ ratings, however, suggests that despite the evidence of dramatically different cut scores between the two exercises, the judges were highly consistent in their interpretation of relative item difficulty. Two lines of evidence indicate this high level of internal consistency: (i) the reliability index for the pairwise data; and (ii) the correlation between the item estimates obtained from the rating and pairwise exercises, which was 0.95. In addition, the correlation of the relative item difficulties with those obtained from students responding to the same items was a satisfactory 0.80 and 0.74 for the ratings and for the pairwise designs, respectively. The high correlation between judgements across the two exercises, in conjunction with the relatively high correlation of the item difficulties from the judges’ data and from the student data, suggests that problems observed in the literature do not arise because judges cannot differentiate the relative difficulties of the items. Accordingly, the unit of scale as assessed by the standard deviations of the item difficulties were calculated and examined. The standard deviation of the items from judges in the likelihood design was half that of the item difficulties from the student responses, and the standard deviation of the items from the pairwise design was over twice that of the student scale. The substantial difference between the standard deviations suggests a difference between the units of scale, which presents a fundamental problem for common equating. In general, and in the literature, it seems that the unit of scale as evidenced from the standard deviations is not considered and it seems that it is simply assumed that the unit of scale produced by the students and the judges is the same and each design should be the same. Then if the results of different modes of the data collections do not arrive at the same or very similar cut-scores, it is not considered that this might be only a result of different units of scale. In retrospect, it is not surprising that different formats for data collection produce different units of scale, and that different cut-scores result. In addition, it is not surprising that these might also produce a different unit of scale from that produced by the responses of the students. The reasons that the different designs are likely to produce different units of scale are considered in the thesis. Differences in the unit of scale will inevitably have an impact on the location of the benchmark or cut-score. When the difference in standard deviation is accounted for, and the cut-scores are placed on the same scale as that produced by the students, the two exercises provide similar locations of the benchmark cut-score. Importantly, the thesis shows that these locations can be substantiated qualitatively as representing the defined standard. There are two main conclusions of the study. First, some of the problems reported in the literature in setting benchmarks can be attributed to difference in the units of scale in the various response formats of judges relative to those of students. Second, this difference in unit of scale needs to be taken into account when locating the standard on the student scale. This thesis describes in detail the two cut-score setting designs for the data collection, and the transformations that are necessary in order to locate the benchmark on the same scale as that produced by the responses of the students.

Thesis (Ph.D.(Education))-University of Pretoria, 2008. / Abstract in English. Includes bibliographical references. Available on the Internet via the World Wide Web.

Thesis (M.Ed. (Curriculum Studies))--University of Pretoria, 2008. / Includes bibliographical references.

To be numerate is to have the ability to understand numbers and be confident with numeric information presented in day-to-day situations. The way numeracy is defined varies between researchers; however, most agree that having skills in numeracy is essential to function in the world. In order to provide students with the opportunity for exposure to basic numeracy skills, McMaster University’s course Math 2UU3 – “Numbers for Life” is offered to non-mathematics major students in second year or above. To measure the effectiveness of this course, and to determine whether students retain the numeracy skills and knowledge acquired in the course, we developed a series of assessments with questions based on content learned throughout the semester. Students were tested three times – once before completing the course, once after completing the course, and once again a year later. This study focuses in on the logical reasoning aspect of numeracy which includes understanding logical structures and being able to work through problems rationally and systematically. The results from the study reveal that students who took the course and participated in completing the given assessments showed improvement with their logical reasoning skills significantly. / Thesis / Master of Science (MSc)

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Orientador: Deise Aparecida Peralta / Banca: Raul Aragão Martins / Banca: Fabiana Maris Versuti-Stoque / Resumo: No ambiente escolar, em referência à normas e legislações que regulamentam as necessidades educativas especiais, crianças com deficiências sensoriais são submetidas ao uso de tecnologias atuais, que não atendem ou não aprimoram requisitos-base de comunicação tanto pela interação, quanto pela implementação. Assim, a corrente pesquisa objetiva a parametrização e validação de características assistivas em dispositivos tecnológicos que viabilizem interações comunicativas na alfabetização matemática entre crianças com deficiências sensoriais distintas (auditiva e visual) na educação infantil, entre 3 e 5 anos. A metodologia baseia-se nas abordagens relacionadas ao construtivismo de Piaget no período pré-operatório e na teoria do agir comunicativo de Habermas, sendo dividida em três temáticas: a educação infantil e o ensino da matemática sob uma base construtivista; a educação inclusiva por meio de tecnologias assistivas (TA) pedagógicas; a perspectiva social e crítica da comunicação à efetiva inclusão. Ainda, é proposto, parametrizado e validado um protótipo referencial generalista em software que simula a comunicação direta entre crianças com deficiência auditiva (DA) e crianças com deficiência visual (DV), implementado em sistemas computacionais no processamento de imagens e reconhecimento de padrões de sinais gestuais-visuais na Língua Brasileira de Sinais e sistemas embarcados que traduzem tais sinais na linguagem tátil. Sob a perspectiva construtivista-crítica, defendeu-se... / Abstract: In school environment, in reference to norms and legislation which regulate special educational needs, children with sensory disabilities are subject to the use of current technologies that do not attend or improve basic communication requirements for both interaction and implementation. Thus, this current research aims at the parameterization and validation of assistive characteristics in technological devices which enable communication interactions in mathematical literacy among children with different sensory impairments (hearing and visual) in childhood education, between 3 and 5 years. The methodology is based on the approaches related to the constructivism of Piaget in the preoperative period and in the theory of communicative action of Habermas, being divided in three themes: the infantile education and the teaching of the mathematics on a constructivist basis; inclusive education through pedagogical assistive technologies (TA); the social and critical perspective of communication to effective inclusion. Also, it is proposed, parameterized and validated a generalist reference prototype in software that simulates direct communication between children with hearing impairment (HI) and children with visual impairment (VI), implemented in computer systems through image processing and visual-gesture signal pattern recognition in the Brazilian Sign Language and embedded systems that translate these signals in the tactile language. From a constructivist-critical perspective, it was defended in this research that the development of resources in assistive technology enables social interactions in various teaching and learning environments of children with different sensory disabilities (and different languages), since childhood education, an estimated margin of effective inclusion in society, initiating by insertion, interaction and mutual integration in respect to the diversity ... / Mestre