M.Ed. / The object of this research project is to do an error analysis of standard five pupils' mathematics books and to to create guidelines for a mathematical programme, using direct instruction, learning strategies and problem solving skill ...

M.Ed. (Subject Didactics) / The ideal in education is that the curriculum provided (by the teacher) and the curriculum received (by the pupil), as originally drafted by the designers, should agree. However, there are indications that this ideal is often not achieved in the teaching of Mathematics, the reason being, inter alia, the backlog in the subject arising from inadequate knowledge as a result of misconceptions in regard to certain basic concepts. Misconceptions among pupils indicate that the shaping of understanding and mastering the concepts have been inadequate. It should be kept in mind that frame of reference and world view are peculiar to each pupil and will be utilized by him for interpreting and processing new concepts. It is therefore essential that the world view of the pupil should be investigated as being the factor which is probably basic to the problem of misconception. The point of departure is therefore that pupils have divergent world views, which invariably affect their understanding of Mathematics. Throughout the ages misconceptions were inextricably part of natural science in general and Mathematics in particular. During modern times, since the 1960s, Boyd has paved the way for reflection regarding misconceptions in natural scientific teaching by using the term "unfounded beliefs", and the attention was actively drawn to the problems surrounding misconceptions. Terms now mostly used as synonyms for misconceptions are conceptual framework, alternative frameworks, and alternative conceptions...

Afrikaans: Ontoereikende prestasie in wiskunde is ‘n verskynsel wat besonder algemeen voorkom en navorsers is dit eens dat die probleem veral by swart leerders kritieke afmetings aanneem. In die veranderende Suid-Afrika is een van die onderwysrealiteite dat 'n groot deel van die bevolking, vanweë verskeie faktore, steeds blootgestel word aan opvoedings- en omgewingsituasies wat nie bevorderlik is vir die optimale verwerkliking van die leerders se persoonsmoontlikhede nie, en tewens ook yan hierdie verwerklikingsgeleenthede weerhou. Die Tswanaleerders in die Mafikeng-area bevind hulle in ‘n opvoedingsituasie wat nie altyd vir optimale verwerkliking van hul persoonsmoontlikhede bevorderlik is nie. Een moontlike uitkoms van hierdie situasie is dan ook ontoereikende prestasie in wiskunde. Daar is veral gefokus op die taalaspek, waar die Tswanaleerders eendersyds probleme ondervind met die 'taal' van wiskunde, en andersyds dat hulle nie in hul moedertaal nie, maar wet in Engels onderrig word. Die doeI van hierdie studie is onder meer die verkenning van die Tswanaleerder in die Mafikeng-area se ontoereikende prestasie in wiskunde. Dit is gedoen deur die inskakeling van ‘n Diagnostiese Toets en ‘n Leerdersvraelys. Die kognitiewe en affektiewe fasette van die Tswanaleerder se prestasie in wiskunde is gemeet. Deur middel van assessering en evaluering is die huidige stand van die Tswanaleerder se prestasie in wiskunde onder die vergrootglas geplaas. 'n Remediëringstrategie wat spesifiek gerig is op die Tswanaleerder in die Mafikeng-area is saamgestel. Hierdie remediëringstrategie fokus op assessering en evaluering, deur gebruik te maak van die Diagnostiese Toets (Mafikeng-area) en die Leerdersvraelys. Daar is ook aangetoon in welke mate 'n wiskundeportefeulje in sodanige remedieringstrategie ingeskakel kan word. 'n Kontrolelys aan die hand waarvan wiskundefoute by die Tswanaleerder in die Mafikeng-area moontlik geidentifiseer kan word, is ook verskaf. 'n Bespreking van die diagnostiese ontleding van 'n Graad 4-groep se prestasie in die Diagnostiese Toets (Mafikeng-area) is ter iIIustrasie verskaf. Die voorgestelde remediëringstrategie is 'n potensiele hulpmiddel vir onderwysers/esse van die Tswanasprekende leerders in die Mafikeng-area om probleemareas in wiskunde te identifiseer en te hanteer. English: Inadequate achievement in mathematics frequently occurs especially amongst black learners where the problem is becoming critical. In a changing South Africa one of the realities in education is that a large part of the population, on account of various factors, is still being exposed to educational and environmental situations that do not promote the optimal realisation of the learners' personal potential, and also inhibit actualisation opportunities. The Tswana learners in the Mafikeng area find themselves in an educational situation that does not always promote optimal actualisation of their personal potential. One possible outcome of this situation is inadequate achievement in mathematics. Special attention was given to the language factor according to which learners experience problems with mathematical language on the one hand, and on the other, the problem that the learners are not being taught in their mother-tongue, but in English. The aim of this study is, inter alia, the exploration of the Tswana learner's inadequate achievement in mathemactis in the Mafikeng area. This was done by administering a Diagnostic Test and a Learner's Questionnaire. The cognitive and affective facets of the Tswana learner's achievement in mathematics was measured. The present state of the Tswana learners' achievement in mathematics was determined through assessment and evaluation. A remedial strategy specifically aimed at the Tswana learner in the Mafikeng area was devised. This strategy focused on assessment and evaluation by making use of the Diagnostic Test (Mafikeng area) and the Learner's Questionnaire. The relevant research also indicated to what extent a mathematics portfolio could be incorporated into such a remedial strategy. A check list according to which mathematical errors in the case of the Tswana learners in the Mafikeng area could possibly be identified was also compiled. A discussion of the diagnostic analysis of a Grade 4 group's achievement in the Diagnostic Test (Mafikeng area) is provided by way of illustration. The proposed remedial strategy is a potential aid for teachers of Tswana-speaking learners in the Mafikeng area to identify and deal with problem areas in mathematics. / Dissertation (MEd)--University of Pretoria, 2006. / Curriculum Studies / unrestricted

Thesis (M. Ed. (Mathematics Education)) -- University of Limpopo, 2016. / The purpose of this study was to examine learners’ mathematical word problem solving skills and strategies in Intermediate Phase. The study was prompted by Grade 6 learners’ poor performance in the cognitive area, non-routine mathematical word problems, as revealed in Annual National Assessment reports of 2011, 2012, 2013 and 2014. The study followed action research collaborative method involving 26 Grade 6 learners and their mathematics educator. The school is a rural primary school categorised under quintile two. Problem solving theory by Polya (1957) guided the study in answering three research questions: What are the challenges faced by Grade 6 learners in solving word problems? What are Grade 6 learners’ strategies in solving word problems? How can learners’ problem solving skills and strategies focusing on word problems be improved? Data were collected in a routine structured process: pre-intervention phase, intervention phase and post-intervention phase. Analysis was made through the development of a system of categorisation of learners’ responses. The four principles of problem solving by Polya (1957) namely, the way learners understand the problem, how they devise the plan, how they carry out the plan and the manner in which they look back guided the analysis. The findings of the study revealed that the strategies introduced assisted learners in making sense of the word problems and finally proceeding towards an adequate solution. It was also found out that the learners lacked the ability to read with understanding; the problem being their lack of competence in the language of learning and teaching. The skills which learners also lacked when solving word problems were identified as arithmetic skills and reflective skills.

The purpose of this mixed method study was to determine if there is a relationship between characteristics of supplemental instructors’ personal traits, teaching skills, subject matter, constructive/active, collaborative learning, effective communication, and their practices (as judged by students) and student success in their remedial mathematics course. The college Provost was contacted by email to request an authorization to conduct this study in his college. Once approved, the investigator contacted face to face his colleagues to ask their students to participate in the study because they enrolled in a remedial algebra class where the instructor is assisted by a supplemental instructor (SI leader). Sixteen algebra classes were selected, and each were assisted by supplemental instructors. Students’ scores on the pre-test (at beginning of the semester) and post-test (at the end of the semester) were collected to gauge their achievement on both tests. Students completed a questionnaire that asked about their perceptions about their supplemental instructors’ personal traits, teaching skills, subject matter, constructive/active, collaborative learning, effective communication, and their practices throughout the semester. Students’ mean scores difference on the post-test were higher in 62.5% of the sections than on the pre-test. The evaluation of achievement on both tests, the responses to the questionnaire and comments from students showed that SI leader’s characteristics associated to effective communication/active learning, teaching skills, and personal traits could be contributor to score achievements. The linear regression in the study shows that the three factors did not significantly predict the post-test score. However, the pre-test did significantly predict the post-test score in a remedial Math 20 at the end of the semester (Beta = .47, t (197) = 6.56, p <.05). In addition, the comments in the questionnaire found that students acknowledged their supplemental instructor role in the classroom and during the SI’s weekly sessions.

The problem of this study was performance on selected mathematics and reading assessment tests as predictors of achievement in remedial mathematics. The purpose of the study was twofold. The first was to determine the internal consistency of a locally developed remedial mathematics placement test and the mathematics section of the Pre-TASP Test. The second was to determine the predictive validity of performance on (a) the local remedial mathematics placement test, (b) the mathematics section of the Pre-TASP Test, and (c) the Descriptive Tests of Language Skills, Reading Comprehension Test in combination with demographic variables for mid-semester achievement, end-of-semester achievement, and course success in three levels of remedial mathematics at Richland College, Dallas, Texas.

Mathematics can be a difficult topic both to teach and to learn. Word problems specifically can be difficult for students with disabilities because they have to conceptualize what the problem is asking for, and they must perform the correct operation accurately. Current trends in mathematics instruction stem from the National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics that call for an inquiry learning model (NCTM, 2000). Unfortunately, this model may not be sufficient to meet the needs of students with disabilities. Researchers are currently looking at what elements will assist students with disabilities to learn mathematics both conceptually and procedurally. Explicit direct instruction, modeling, guided and independent practice, and providing advanced organizers have been found to help students with disabilities to be successful. Results indicated that students with mild disabilities were able to use the strategy independently to accurately solve the training word problems using division or multiplication. Also, students were able to generalize both the strategy use as well as the word problem accuracy to the measurement of area problems. Additionally, two of the three students continued to use the strategy appropriately to accurately solve word problems in the 6-week follow-up phase. Suggestions for future studies are provided as well as educational implications. / by Mary R. Taber. / Thesis (Ed.D.)--Florida Atlantic University, 2013. / Includes bibliography. / Mode of access: World Wide Web. / System requirements: Adobe Reader.

The current study seeks to investigate pre-service elementary mathematics teachers&rsquo / (PEMTs&rsquo / ) self-regulated learning (SRL) strategies within the context of their teaching practices in the field work. It was aimed to explore the SRL processes and strategies of four PEMTs while preparing mathematics lessons at their practice schools. In addition to PEMTs&rsquo / SRL strategies, the changes and adaptations through their teaching practices and reasons of those changes were also examined in the study. In total 22 pre-interviews and 22 post-interviews were made through the study. Observations were also performed for each teaching practice. Besides observations, PEMTs&rsquo / end of semester reflection papers in the context of Teaching Practice course were examined in the study. In addition to those multiple data sources, initial interviews representing detailed information about the participants were also analyzed. The overall data were analyzed by using the SRL framework combined and adapted from Zimmerman&rsquo / s and Pintrich&rsquo / s SRL models. The findings of the pre-interviews revealed that PEMTs began with a &lsquo / lesson planning process&rsquo / reflecting the forethought phase. This phase included searching resources, arranging and organizing the available sources, asking for help and feedback when needed, mental planning of the lesson, and setting goals for the teaching session. These strategies were considered as cognitive self-regulation strategies. In addition to cognitive SRL strategies, motivational factors such as self-efficacy, perception of task, and intrinsic interest were appeared in the study. Post-interviews reflecting the self-reflection phase revealed that PEMTs had a self-evaluation process covering various issues for their teaching sessions as a final step through the study. Finally, it was seen that contextual issues related to teaching practice played a substantial role in PEMTs&rsquo / SRL strategies.

M. Tech. Education / Given the challenges of shortage of skills as informed by low performance in Grade 12 Mathematics, it seemed appropriate that a study on factors behind poor performance in Mathematics amongst grade 12 learners be undertaken. The study explored various factors that contribute to poor performance of learners in Mathematics in grade 12.

Thesis (Ph.D.) -- Mississippi State University. Department of Curriculum and Instruction. / Title from title screen. Includes bibliographical references.