by Wong Yuen Ting. / Bibliography: leaves 38-41 / Thesis (M.A.)--Chinese University of Hong Kong, 1982

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Thesis (PhD)--Stellenbosch Universityh, 1995. / ENGLISH ABSTRACT: This study investigates the influence of readability of mathematics examination questions on achievement. The aim of any mathematics examination is to assess whether the aims of a specific mathematics programme have been realized. Readability factors that unnecessarily prevent a clear understanding of questions could jeopardize this aim. The important issue is, therefore, whether there are indeed readability factors in mathematics examination questions that cause comprehension problems for students and, if there are, do they hav~ any effect on test scores? The issue of readability is of even greater importance for second language readers. In the South Mrican context, the reading problems of second language readers are of particular importance as most students at school are second language learners. An important question would therefore be: What readability factors cause comprehension difficulties for second language students, especially those whose mother tongue is not kindred to English? Furthermore, what is the influence of cultural factors on readability? This study provides answers to these and other related questions for mathematics text at senior secondary school level. Protocol analysis was used to ascertain what readability problems are experienced by students when reading examination questions in mathematics. Three different language groups, comprising 17 -18-year-old students, were used in the study: English First Language students and two groups who had English as a second language. One second language group had Mrikaans as first language while the other group comprised Mrican students whose mother tongue is unrelated to English. A framework was developed to analyse the protocols and it comprised five categories: unfamiliar vocabulary structural problems obscure information visualization difficulties non-verbal factors Mter the protocol study, students were asked to adapt the examination questions to a more comprehensible form. Students' adaptations addressed lexical, syntactical, discourse and non-verbal factors. Most of the readability problems identified in the literature study were verified in the empirical study. However, the empirical study generated additional readability problems that are mainly restricted to mathematics text and relate to nonverbal factors like mathematical expressions. During the last phase of the empirical study a composite test was used to test the hypothesis that improved readability of the common language used in mathematics examination questions' will improve achievement. Nine socalled "word problems" from previous examination papers were set in three different versions: original, adapted and non-verbal. The hypothesis was confirmed in a number of important cases. A significant finding of the study was, therefore, that readability factors not only influence the comprehension of mathematics examination questions, but also have a marked influence on students' achievement levels. The results of the empirical study are reported quantitatively as well as qualitatively. Other results include the following: Not only second language students, but also first language students experienced a variety of readability problems. All three language groups demonstrated the same level of competency on the non-verbal versions. When comparing test scores of the verbal versions, differences in achievement levels between the different language groups were often caused by linguistic and cultural factors. Cultural thought patterns, typical of a mother tongue but absent in a second language, were often a source of comprehension difficulties for second language readers. This study has led to certain conclusions for teaching and examination practice. For example, factors influencing the readability of ordinary English should be considered with other factors when writing mathematics examination questions. Furthermore, the distinctly different reading needs of second language students suggest that examination papers be set, so that the language needs of second language learners are accommodated. Guidelines for writing more readable examination questions were developed and are presented as a readability checklist. Suggestions for further research include the investigation of the influence of readability on achievement in authentic examination conditions. / AFRIKAANSE OPSOMMING: Hierdie studie ondersoek die invloed van leesbaarheid van wiskunde eksamenvrae op prestasie. Die doel van enige wiskunde eksamen is om vas te stel of die doelwitte van 'n spesifieke wiskunde program bereik is. Leesbaarheidsfaktore wat die volledige begryp van vraestelle onnodig belemmer, kan die bereiking van hierdie doel verhinder. Dit is dus belangrik om vas te stel of daar wel leesbaarheidsfaktore in wiskunde eksamenvrae bestaan wat vir leerlinge begripsprobleme veroorsaak en, indien wel, of hulle enige effek op toetspunte het. Vir tweedetaallesers is die kwessie van leesbaarheid van nog groter belang. In die SuidAfrikaanse opset is die leesprobleme van tweedetaal lesers 'n uiters aktuele saak aangesien die meeste skoolleerlinge tweedetaal leerders is. Belangrike vrae is dus: Watter faktore veroorsaak leesbaarheidsprobleme vir tweedetaalleerlinge, veral diegene met 'n nie-verwante moedertaal en, watter invloed het kultuur op leesbaarheid? Hierdie ondersoek bied antwoorde op hierdie en ander verwante vrae ten opsigte van wiskunde eksamenvrae op senior sekondere vlak. Protokol analise is gebruik om vas te stel watter leesbaarheidsprobleme ondervind word wanneer leerlinge wiskunde eksamenvrae lees. Drie verskillende taalgroepe, bestaande uit 17 -18-jarige leerlinge, het aan die ondersoek deelgeneem: Engels Eerstetaalleerlinge en twee groepe wat Engels as tweede taal gehad het. Een van die tweedetaal groepe het Afrikaans as eerste taal gehad terwyl die ander groep bestaan het uit Afrikane wie se moedertaal nie aan Engels verwant is nie. 'n Raamwerk is ontwikkel om die protokolle te analiseer en het uit die volgende vyf kategoriee bestaan: onbekende woordeskat strukturele probleme onduidelike inligting visualiseringsprobleme nie-verbale probleme Gedurende die tweede fase van die ondersoek is leerlinge gevra om die vrae tot 'n meer verstaanbare vorm aan te pas. Leerlinge se aanpassings het leksikale, sintaktiese, diskoers en nie-verbale faktore aangespreek. Sommige leesbaarheidsprobleme wat in die literatuurstudie gei'dentifiseer is, is in die empiriese ondersoek geverifieer. Die empiriese ondersoek het egter addisionele leesbaarheidsprobleme uitgelig wat meerendeels wiskundig van aard is en verband hou met nie-verbale faktore soos wiskunde uitdrukkings. Gedurende die laaste deel van die empiriese ondersoek is 'n samegestelde toets gebruik om die volgende hipotese te toets: Verbeterde leesbaarheid van die gewone taal wat in wiskunde eksamenvrae gebruik word, sal die prestasie van leerlinge verb et er. N ege sogenaamde woordsomme is op verskillende maniere gestel: oorspronklik, aangepas en nie-verbaal. Die hipotese is in 'n hele aantal belangrike gevalle bevestig. Een van die bevindinge van die ondersoek was dus dat leesbaarheidsfaktore nie slegs be grip ten opsigte van wiskunde eksamenvrae bei:nvloed nie, maar ook 'n beduidende invloed op prestasie het. Die resultate van die empiriese ondersoek word kwalitatief sowel as kwantitatief weergegee. Ander resultate sluit die volgende in: Nie slegs tweedetaal leerlinge nie, maar ook eerstetaal leerlinge het 'n verskeidenhied van leesbaarheidsprobleme ondervind Al drie taalgroepe het op die nie-verbale weergawe dieselfde bekwaamheidsvlak getoon. Verskille in die prestasievlakke tussen die verskillende taalgroepe op die verbale weergawes is baiekeer deur taalkundige en kulturele faktore veroorsaak Kulturele denkpatrone wat tipies is van 'n leerling se moedertaal, maar nie in die tweedetaal voorkom nie, het dikwels tot begripsprobleme by tweedetaal lesers gelei. Hierdie ondersoek het sekere gevolgtrekkings v1r o~derrig- en eksamenpraktyk. Byvoorbeeld, faktore wat die leesbaarheid van gewone Engels bei:nvloed, behoort saam met ander faktore in ag geneem te word wanneer wiskunde eksamenvraestelle opgestel word. Verder is daar duidelike aanduidings dat aparte vraestelle vir eerste- en tweedetaal leerlinge opgestel moet word sodat die taalbehoeftes van tweedetaal leerlinge in ag geneem kan word. Riglyne vir die skryf van meer leesbare eksamenvrae is saamgestel en as 'n oorsiglys aangebied. Voorstelle vir verdere navorsing sluit in die ondersoek na die invloed van leesbaarheid op prestasie in ware eksamen omstandighede.

Every year, thousands of Florida public high school graduates seek to enter Florida state colleges based on a single standardized placement test. This quantitative study sought to identify an actuarial model, based on multiple measures, as an alternative to standardized placement tests. The study, grounded on degree completion theories, examined high school students from the Miami-Dade metropolitan area and their performance in one first-year mathematics course in Miami Dade College during the Fall 2014 academic term. The study, using a sample size of 10,186 subjects, examined multiple predictor variables and one outcome variable to measure predictability of success in Intermediate Algebra. The study used descriptive statistics, multiple linear regression, and logistic regression to develop a multiple measure actuarial model. A quantitative analysis of archived student records was used in this study. The analysis revealed that the actuarial model, using gender, ethnicity, age, academic objective, academic load, high school GPA, high school mathematics gap, and high school mathematics curriculum composite score as predictor variables, was significant in predicting success in Intermediate Algebra. The actuarial model correctly classified 1,688 subjects who would fail Intermediate Algebra, achieving a hit rate of 75% in predicting failure in Intermediate Algebra. Similarly, the model achieved a hit rate of 54% when classifying subjects who would pass Intermediate Algebra. The improvement-over-chance index, I, was 44.8%, representing a 45% reduction in error when classifying subjects who would fail Intermediate Algebra. Thus, the actuarial model, with all its predictor variables, provides helpful guidance when advising incoming first-time-in-college (FTIC) students. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2016. / FAU Electronic Theses and Dissertations Collection

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With the introduction in 2006 of the school subject Mathematical Literacy (ML) in the further Education and Training band, there have been expectations that such a subject will develop responsible citizens, contributing workers and self-managing people. The extent to which the subject can meet these aims is dependent on the ways in which the subject is assessed which influences the focus of ML in the classrooms. With this in mind, this study set out to explore the ways in which a class of Grade 12 learners engaged with a preparatory examination designed and administered by the KZN Department of Education. This is a qualitative study carried out with seventy-three grade 12 mathematical literacy learners from an urban school in North Durban. The purpose of this research is to explore the learners’ engagement with the examination tasks, thereby identifying possible factors which influence learners’ success in these items. Data were gathered from a document analysis of the 2009 KZN Trial Examination question paper and marking memorandum; 73 learners’ written responses to the examination tasks, and interviews with ten of these learners. The purpose of the document analysis was to identify contexts in which learners performed well or poorly, as well as to assess the design of the instrument. Semi-structured interviews were conducted individually with ten learners and video recorded. The purpose of the interviews was to explore some of the factors which influenced their written responses. The findings revealed that the task design was problematic for learners in terms of the order of the questions and the placement of the crucial information necessary to answer the questions. Some tasks also contained errors. The complexity of the scenario in terms of the amount of information, the language used, and the presence of distracters further influenced the way in which learners responded to the task. Learners’ personal experience of the context also affected the way they interpreted and responded to the task. Factors that constrained learners’ success in the examination task included poor conceptual understanding, misconceptions and language-related misinterpretation. It was also found that learners did not consider it a priority to make sense of the context: they focused on identifying formulae or information that could be used to present answers with little concern about the reasonableness of their responses. Some strategies used by learners in responding to the task included number grabbing, guessing without checking, scanning for crucial information and assumption-making. The study recommends that provincial examination papers be subject to the same stringent moderation requirements of the national examinations. It also recommends that should diagrams be used, they must be relevant to the context and should not conflict with the subject matter. The use of contexts should cater for alternate answers and multiple approaches and the marking memorandum should be flexible to accommodate these multiple approaches. Care must be taken in the presentation and placement of crucial information, so that learners do not miss the information they need to answer the questions. When familiar contexts are being used, task designers should also consider whether learners’ everyday experiences may conflict with these scenarios. / Thesis (M.Ed.)-University of KwaZulu-Natal, Edgewood, 2011.

Thesis (M.A.T.S.)--University of Texas at El Paso, 2008. / Title from title screen. Vita. CD-ROM. Includes bibliographical references. Also available online.

The aim of this study was an exploration of the relationship between the use of an Integrated Learning System (ILS), entitled Master Maths, as a supplement to traditional mathematics instruction, and mathematics achievement as measured by the Paper 2 marks of the National Mathematics Examinations for standard grade learners in grade 12. The use of technology in education has increased over the past decade. One way of integrating technology into instructional programmes has been through the use of Integrated Learning Systems (ILSs). The review of the literature traces the history of computer-assisted instruction as conducted on ILSs. The review of recent research studies focuses on the impact of ILSs on learner achievement in mathematics internationally and in the South African context. This study used quantitative and qualitative methods to research the impact of the Master Maths programme on mathematics achievement. Twenty-six learners of the 133 standard grade learners from one high school in New Brighton, Port Elizabeth were selected for each of the experimental and control groups. The experimental group worked on the Master Maths programme for twelve sessions of three hours each. The results of the quantitative analysis show that the intervention did not make a significant difference to the experimental group. The Master Maths programme led to only a 0.56% increase in the marks of the experimental group. The qualitative analysis drew a comparison between the modules of the Master Maths programme and the relevant examination questions in terms of content covered and cognitive levels. The researcher used Bloom’s Cognitive Taxonomy to evaluate the cognitive levels. The data show that it was easier for the learners to obtain higher marks in the module tests than in the examination questions. The data indicate that the module tests were easier than the examination questions in that the cognitive levels of the module tests were lower. The data confirm that there is a gap between the acquisition and evaluation of core skills tested by the modules used in the intervention and the wider knowledge and skills tested in the examination.

M.Ed. (Mathematics in Education) / In spite of the efforts of the South African government, the Gauteng Department of Education and many business and private funders to place a high emphasis on mathematics performance, the mathematics achievement of South African learners is still less than desirable. In fact, the results of the three Third International Mathematics and Science Study (TIMSS) (Howie, 2001, 2003) reports in 1995, 1999 and 2003 reported South African learners as the lowest performing in those tests; performing well below the international average amongst the countries that participated. The Southern African Consortium for Monitoring Quality 2004 and Center for Development in Education 2004, 2010 and 2011 reports results show similar results (Moloi, 2005). The research study sought to get a deep understanding of why learners1 continue to perform poorly, and what the factors are which contribute to poor performance. While there are a number of factors responsible for the poor performance, one of the least researched areas is answered examination scripts. This research entailed a detailed error analysis of four items of the 2008 mathematics paper 1 senior certificate examination scripts, to see the trends and patterns of written responses with regards to the types of errors made by learners. The study was aimed at investigating South African Grade 12 learners‘ errors exhibited when solving quadratic equations, quadratic inequalities and simultaneous equations. Findings of this investigation shed light of the kind of knowledge learners bring into their learning experiences and this knowledge affects how they encode and later retrieve new information learned (Davis, 1984). While the study was not a mixed methods one, the data was analysed quantitatively using frequency counts and qualitatively by studying selected learners‘ solution of examination tasks. The study also identified common errors in the learners‘ work. The four items analysed in the study comprised of questions from three important areas of algebra namely: quadratic equations, quadratic inequalities and simultaneous equations. The scripts were analysed for carelessness, conceptual and procedural errors. The learner misconceptions were discovered in learners‘ work; v these comprised the notions of equality and inequality, the construct of the variable, order of operations, factorisation, and solution of equations instead of inequalities. From this, the researcher noted that learners' learning difficulties are usually presented in the form of errors they show. Not all the errors that learners had are the same; some errors in procedures can simply be due to learners' carelessness or overloading working memory (Davis, 1984). Some errors in procedures can be caused by faulty algorithms or "buggy algorithms". Other errors can have certain conceptual basis and can be termed as ‗misconceptions‘. The results obtained indicated a number of error categories under each conceptual area, namely, quadratic equations and inequalities and simultaneous equations. Some errors emanated from misconceptions. Under the conceptual areas indicated above, the main reason for misconceptions seemed to be the lack of understanding of the basic concepts including numbers and numerical operations; functions; the order of operations; equality; algebraic symbolism; algebraic equations, expressions and inequalities; and difference between equations, expressions and inequalities. The abstract nature of algebraic expressions posed many problems to learners such as understanding or manipulating them according to accepted rules, procedures, or algorithms. Inadequate understanding of the uses of the equal sign and its properties when it is used in an equation was a major problem that hindered learners from solving equations correctly. The main difficulty in inequalities was manipulating the inequalities correctly and converting the inequality to an equation. Recommendations to the mathematics educational community based on this research were made.