6 research outputs found
Critical reflective teaching practice in three mathematics teachers
No full textThis qualitative study reports on critical reflective teaching by three mathematics teachers and how it shapes their classroom practice. The study was carried out in three secondary schools in Rundu in northern Namibia. The study employed a case study method. The selection of teachers was based on their rich practical professional knowledge and exemplary teaching practices. Data collection and analysis was done through an interpretive approach. Interviews and document analyses were the two research tools used, not only for the collection of data but for triangulation also. Interpretations of the findings were validated through member checking. Critical reflective teaching involves thought and action, and it raises teachers’ consciousness of what they do. Through critical reflective practice, teachers scrutinize their beliefs and knowledge of the subject and their practice. Furthermore critical reflective practice may get teachers into a disposition to find alternatives to improve their teaching. In this study, the findings are that participants reflect extensively on their classroom practice. The teachers pointed out that reflection on practice enables them to analyse and evaluate their teaching in line with effective mathematics teaching. They emphasised that critical reflection leads to the identification of weaknesses in teachers’ classroom practice. This culminates in better planning whereby alternative approaches to teaching are exercised. Because of its potential to improve teaching and enhance professional development it is therefore recommended that mathematics teachers be exposed to skills that enhance critical reflective teaching practice. Teachers need to familiarise themselves with the concept of critical reflective teaching in mathematics to meet the demands of superior quality teaching
The development of pre-service teachers mathematical knowledge for teaching flexible mental computation
No full textThesis (PhD)--Stellenbosch University, 2020.ENGLISH SUMMARY : This empirical study explored an approach to develop elementary pre-service teachers’ mathematical knowledge for teaching flexible mental computation skills in school. The study began by determining pre-service teachers’ existing knowledge, beliefs and experience pertaining to how they learned flexible mental computation skills at school. Ways pre-service teachers learned flexible mental computation skills in school shape their beliefs about learning and teaching. Currently, research indicates that pre-service teachers continue to graduate with inadequate skills to do flexible mental computation, and overreliance on calculators and the standard method is prevalent among pre-service teachers. Since teacher knowledge affects learning directly, developing pre-service teachers’ mathematical knowledge for teaching flexible mental computation of whole numbers would break the cycle of innumeracy. Whole number computation forms the basis of learning different mathematical topics at school, and most professions and activities in society involve the calculation of whole numbers. To achieve the objective of this study, a purposive sample of 51 pre-service elementary mathematics teachers participated in the study. Both quantitative and qualitative research methods were used to collect data using questionnaires, pre- and post-intervention tests, intervention cycles and interviews. This study used the realistic mathematics education (RME) instructional theory with the backing of design-based research (DBR) to design problems that translated into a hypothetical learning trajectory (HLT) to contribute to the knowledge of how to prepare teachers to teach flexible mental computation. The nature of the HLT makes it suitable for teacher educators to adopt it to develop pre-service teachers for effective teaching. This study found that most pre-service teachers believe that flexible mental computation is important and that concrete objects and the use of the pencil-and-paper method underpins its development. Pre-intervention interviews indicated that PSTs developed flexible mental computation skills through problem solving or memorisation of the multiplication table. Pre-service teachers also indicated that at school they had done mental calculations using strategies prescribed by their teacher. Consequently, during the intervention some PSTs expected a prescription of strategies and had to be persuaded to develop the necessary habits of mind to invent strategies. In the pre-intervention test, 49% of the PSTs’ scored above 50% whereas in the post-intervention test 53% scored above 50%. Pre-intervention interviews revealed that although correct answers were provided for specific items, not all answers were calculated in a flexible manner. Interviews revealed the use of fingers and standard algorithms to compute mentally. This occurred during and after the intervention process, and these existing methods were hard to change. Findings confirmed that the invention of flexible strategies demanded considerable effort on the part of the pre-service teachers to solve context-rich problems, discuss, think, imagine reason and justify invented strategies. It was, however, demonstrated that all pre-service teachers could develop fluency and flexibility with mental calculation, provided their knowledge of numbers and operations, ability to generalise patterns, and knowledge of relationships between numbers had improved through practice. Ultimately, a problem solving approach is recommended as it fosters critical and strategic thinking to re-invent calculation strategies and develop the desire to teach constructively.AFRIKAANSE OPSOMMING : Hierdie empiriese studie ondersoek ’n benadering tot die ontwikkeling van voordiensonderwysers in aanvangsonderwys se wiskundige kennis van die onderrig van buigsame hoofrekenevaardighede in die skool. Die studie begin met die bepaling van voordiensonderwysers se bestaande kennis, oortuigings en ondervinding wat betref die aanleer van buigsame hoofrekenevaardighede op skool. Maniere waarop voordiensonderwysers buigsame hoofrekenevaardighede aangeleer het op skool vorm hul oortuigings oor leer en onderrig. Tans dui navorsing daarop dat voordiensonderwysers steeds hul studie voltooi met onvoldoende vaardighede om buigsame hoofrekene te kan doen, en dat voordiensonderwysers te veel op sakrekenaars en die standaardmetode vertrou. Aangesien die kennis van onderwysers ’n direkte invloed op leer het, kan die ontwikkeling van voordiensonderwysers se wiskundekennis met die oog op die onderrig van buigsame hoofrekene van heelgetalle die siklus van ongesyferdheid verbreek. Die berekening van heelgetalle vorm die grondslag vir die aanleer van verskillende wiskundige onderwerpe op skool, terwyl die meeste beroepe en aktiwiteite in die samelewing die berekening van heelgetalle verg. Om die doelstelling van hierdie studie te bereik, is ’n doelgerigte steekproefneming uitgevoer waaraan 51 voordienswiskunde-onderwysers in aanvangsonderwys deelgeneem het. Sowel kwantitatiewe as kwalitatiewe navorsingsmetodes is gebruik om data te versamel met behulp van vraelyste, voor- en ná-intervensietoetse, intervensiesiklusse, en onderhoude. Hierdie studie gebruik die realistiese wiskunde-opvoeding (realisticmathematicseducation=RME)-teorie vir onderrig, gesteun deur ontwerp-gebaseerde navorsing (design-basedresearch=DBR) om probleme te ontwerp wat tot ’n hipotetiese leerbaan (hypotheticallearningtrajectory=HLT) verwerk word, om by te dra tot die kennis oor hoe onderwysers voorberei moet word om buigsame hoofrekene te gee. Die aard van die HLT maak dit geskik dat onderwyseropvoeders die HLT kan aanpas by die ontwikkeling van voordiensonderwysers sodat effektiewe onderrig kan plaasvind. Hierdie studie het bevind dat die meeste voordiensonderwysers van mening is dat buigsame hoofrekene belangrik is en dat konkrete voorwerpe en die gebruik van die potlood-en-papier-metode die ontwikkeling daarvan ten grondslag lê. Voorintervensie-onderhoude het aangedui dat voordiensonderwysers (pre-serviceteachers=PSTs) buigsame hoofrekenevaardighede deur probleemoplossing of die memorisering van die vermenigvuldigingstabel ontwikkel. Voordiensonderwysers het ook aangedui dat hulle op skool hoofrekene gedoen het met behulp van strategieë wat deur hul onderwyser voorgeskryf is. Gevolglik het sommige PST’s tydens die intervensie ’n voorskrif ten opsigte van strategieë verwag en moes hulle oorreed word om die nodige denkgewoontes te ontwikkel ten einde strategieë te kan bedink. In die voorintervensietoets het 49% van die PST’s meer as 50% behaal, terwyl 53% in die ná-intervensietoets meer as 50% behaal het. Voorintervensie-onderhoude het aan die lig gebring dat alhoewel korrekte antwoorde vir spesifieke items verskaf is, nie alle antwoorde op ’n buigsame manier bereken is nie. In onderhoude is daar aangedui dat vingers en standaardalgoritmes gebruik word om hoofrekene te doen. Dit is tydens en ná die intervensieproses gedoen, en hierdie bestaande metodes was moeilik om te verander. Uit die bevindings kon daar bevestig word dat die uitdink van buigsame strategieë aansienlike inspanning van die voordiensonderwysers verg wat betref die oplossing van konteksryke probleme, met ander woorde besprekings, denke, voorstelle, redenasies en motiverings rondom strategieë wat uitgedink word. Daar is egter gedemonstreer dat alle voordiensonderwysers vlotheid en buigsaamheid in hoofrekene kan ontwikkel, mits hul kennis van getalle en bewerkings, die vermoë om patrone te veralgemeen, en kennis van verhoudings tussen getalle aan die hand van oefening verbeter kan word. Uiteindelik word ’n probleemoplossingsbenadering aanbeveel, aangesien dit kritiese en strategiese denke bevorder vir die herbedinking van berekeningstrategieë en die ontwikkeling van die begeerte om konstruktief te onderrig.Doctora
Teacher Reflection Templates: Tools For Whole-Hearted, Open-Minded And Responsible Teachers
No full textThis research paper aims to present four reflection templates in-service and pre-service teachers may use to reflection any subject. The templates were designed by the researcher and are a product of a study conducted on three in-service teachers who are successful in their teaching practice. The study found that the three teachers do reflect critically before the lesson, during the lesson and after the lesson. Critical reflection on the three teachers was found to promote teaching and learning in a classroom environment. The empirical study was informed by the interpretive paradigm that used a qualitative research method. Data was collected through individual interviews conducted face-to-face by the researcher and through document analysis. The reflection templates presented in this paper are outlines of aspects teachers need to reflect on that are imperative in the teaching and learning process. The reflection templates may be used by practicing teachers and prospect teachers to think about their teaching to identify strength and weaknesses for improved teaching and learning
Crtitical reflective teaching practice: enhancing teachers' consciousness of their teaching
No full textThis paper emphasises the aspects that teachers should critically focus on when reflecting on their teaching practices. The paper emerged from a case study that was conducted in three secondary schools in Rundu- northern Namibia. Critical reflective teaching involves thought and action, and it raises teachers' consciousness pertaining to what they do. Through critical reflective practice, teachers scrutinize their beliefs and knowledge of the subject and their practice, through purposeful thoughtfulness. The selection of the three participants was based on their rich practical professional knowledge and exemplary teaching practices as evidenced. Interviews focused on 'when, what, how and why these selected teachers reflected critically on their practice. Data collection and analysis were done through an interpretive approach. Interviews and document analyses were the two research tools used for data collection and triangulation. Interpretations of the findings were validated through member checking where participants verified the interpretations made of their interview respectively
Crtitical reflective teaching practice: enhancing teachers' consciousness of their teaching
No full textThis paper emphasises the aspects that teachers should critically focus on when reflecting on their teaching practices. The paper emerged from a case study that was conducted in three secondary schools in Rundu- northern Namibia. Critical reflective teaching involves thought and action, and it raises teachers' consciousness pertaining to what they do. Through critical reflective practice,
teachers scrutinize their beliefs and knowledge of the subject and their practice, through purposeful thoughtfulness. The selection of the three participants was based on their rich practical professional knowledge and exemplary teaching practices as evidenced. Interviews focused on 'when, what, how and why these selected teachers reflected critically on their practice. Data collection and analysis were done
through an interpretive approach. Interviews and document analyses were the two research tools used for data collection and triangulation. Interpretations of the findings were validated through member checking where participants verified the interpretations made of their interview respectively
ANALYZING GRADE 4 LEARNERS’ MATHEMATICS EXERCISE BOOKS IN PURSUIT OF QUALITY BASIC EDUCATION IN NAMIBIA
No full textThis paper presents the findings of a qualitative study that focused on the state of grade 4 learners’ mathematics exercise books. Identification of challenges in mathematics learning in early grades presents the opportunity for early stakeholder intervention to improve the quality of basic education. The random sampling strategy was used by the subject teacher to select fifteen books from one class comprising 5 below-average, 5 average, and 5 above-average learners for analysis. The document analysis method was used to establish the status of learners’ written work, how well the work was written, and to establish their performance in mathematics. This study found that learners’ writing skills are underdeveloped, they have challenges pertaining to comprehension of instruction and challenges in learning specific mathematics topics. The quality of mathematics written work is generally neglected in school, as mathematics learning is perceived to be a process that focuses on the acquisition of facts. This study confirms that the quality of learners’ written work has received little attention from relevant stakeholders. The state of learners’ written work calls for immediate intervention to improve mathematics learning
