Department of Mathematics Education
https://hdl.handle.net/10500/6424
2024-03-28T16:05:35ZGrade 9 mathematics teachers’ strategies to address mathematical proficiency in their teaching of linear equations : a case of selected schools in Gauteng North District
https://hdl.handle.net/10500/30643
Grade 9 mathematics teachers’ strategies to address mathematical proficiency in their teaching of linear equations : a case of selected schools in Gauteng North District
Mothudi, Teresa Ntsae
The purpose of this research was to look into Grade 9 mathematics teachers’ strategies to address mathematical proficiency in their teaching of linear equations. The study was intrigued by the performance of learners in the TIMSS study, and my personal experience as a mathematics teacher, departmental head, Senior Education Specialist for mathematics, and provincial moderator. Grade 9 mathematics teachers were purposively chosen for the study’s main subjects. A qualitative method, and case study strategy were used for this research. Videos of lessons conducted by the teachers were viewed to collect data, and interviews were conducted through Microsoft Teams as a follow-up to the lessons. The reason for conducting the research remotely was due to the outbreak of the COVID-19 pandemic; therefore, researchers were not allowed to visit the schools.
The research was conducted in Gauteng North District involving three schools, of which one school was for piloting purposes. Three Grade 9 mathematics teachers were observed on videos; one out of the three was for piloting purposes, and interviews were conducted based on their lessons. The data acquired for this study were analysed using thematic analysis. The study contributes towards a better understanding of teachers’ strategies to address learners’ mathematical proficiency. Also, some strategies are suggested on how to improve learners’ mathematical proficiency.
The research was inspired by Kilpatrick (2001) mathematical proficiency strands which comprise conceptual understanding, procedural fluency, strategic planning, adaptive reasoning, and productive disposition. The conceptual framework and the instruments used were derived from the above-mentioned strands. Each strand consisted of a criterion to use when data were collected.
The analysis shows that teachers were focusing mostly on strategies that addressed learners’ procedural fluency when teaching linear equations. The study further shows that lessons were teacher centred. Teachers were providing learners with methods to solve linear equations instead of allowing them to come up with their own initiatives. Thus, the study recommends that teachers should refrain from centralising the lesson around themselves, refresher training on mathematical proficiency to be conducted, enough time to be allocated for the concepts like linear equations to allow exploration of different methods and representations so that all the mathematical proficiency strands can be addressed.
2022-12-10T00:00:00ZGrade 6 mathematics teachers’ development of learner mathematical proficiency in addition and subtraction of common fractions, in the Tshwane South District of Gauteng
https://hdl.handle.net/10500/30642
Grade 6 mathematics teachers’ development of learner mathematical proficiency in addition and subtraction of common fractions, in the Tshwane South District of Gauteng
Lendis, Ashley Pearl
The study was motivated by the fact that learners are not performing well in the topic of
fractions due to the lack of conceptual understanding of the concept. The purpose of this
qualitative study based on an interpretive paradigm, which draws upon Kilpatrick et al.’s
(2001), was to explore how Grade 6 mathematics teachers develop learners’ mathematical
proficiency in the addition and subtraction of common fractions topic. The aim of the study was
to answer the following question: How do Grade 6 mathematics teachers develop learners’
proficiency when teaching the addition and subtraction of common fractions? Four Grade 6
mathematics teachers, from Tshwane South District in Gauteng, were purposively selected,
and data was collected through classroom lesson observations (observing and analysing the
video lessons) and semi-structured interviews. Three key findings were revealed: Firstly,
teachers provided opportunities for developing procedural fluency and productive disposition.
Secondly, teachers provided limited opportunities for learners to develop conceptual
understanding and strategic competence. Lastly, it was a challenge for teachers to understand
that mathematical proficiency is developed over time, working consistently with learners, and
ensuring there are more equal opportunities for the development of each strand. It is
essentially recommended in this study that a developmental intervention workshop be
conducted and should focus on making sense of what it means to teach fractions for
proficiency.
2022-11-30T00:00:00ZThe performance and learning difficulties of Grade 10 learners in solving euclidean geometry problems in Tshwane West District
https://hdl.handle.net/10500/30609
The performance and learning difficulties of Grade 10 learners in solving euclidean geometry problems in Tshwane West District
Olabode, Adedayo Abosede
There is a growing trend of declining performance in the final year (Grade 12) mathematics examinations in the South African public school system. The study aimed to evaluate Grade 10 learners in the Tshwane West District on their performance and learning difficulties in solving Euclidean Geometry problems. The study utilized a mixed method approach under a pragmatic paradigm to determine the achievement and the challenges experienced by learners when solving Euclidean geometry problems. The Van Hiele levels of geometry thinking and constructivist theory, underpinned the theoretical framework used to determine the actual performance and how they understand geometry concepts. The population was Grade 10 learners, and the sample size was 80 learners, purposively selected from two secondary schools in the Tshwane West district in the Gauteng Province. The Geometric Achievement Test instrument was used to determine firstly, the overall performance of learners in Euclidean geometry, secondly, the level of Grade 10 learners on Van Hiele levels of thinking and lastly to specify the area where learners have the most difficulties when engaging with geometry problems. A semi-structured interview guide and class observation checklist were used to further understand the challenges experienced by grade 10 when they are faced with Euclidean geometry questions.
The findings from this study showed the underperformance of learners in three Euclidean geometry topics: these included parallel lines, congruency, and parallelograms. The findings further indicated that the low performance was a result of a lack of understanding of the computational and spatial thinking that characterises Euclidean geometry. These findings were supported by the quantitative findings of the study.
The pass mark stipulated in Euclidean geometry is 30%; less than 10% of the participants in the GAT obtained 30% and above. The findings of the study showed that less than 5% of the learners obtained a score of 38 on the achievement test, which was the highest score obtained. Of the 80 participants, 1,25% (1 of 80) obtained a score of 2. Euclidean geometry requires learners to use their spatial and logical skills in solving mathematical questions; for this sample, making connections and comprehending the visual and spatial aspects of parallel lines, congruency, and parallelograms were found to be difficult. The findings also showed that learner lack an understanding of the properties of parallel lines, resulted in difficulties in calculating the magnitudes of unknown angles using these properties. The findings further indicated that Grade 10 learners have difficulty solving geometry requiring knowledge of corresponding, alternating, and co-interior angles. A notable difficulty was that for the learners to apply the conditions of congruency and execute the proof for parallelograms, learners must understand parallel lines and its properties. Teachers must ensure that learners understand the procedures of naming angles correctly. The understanding of properties of parallel lines, congruency, and proof of parallelograms is essential for enhancing learner abilities in Euclidean geometry.
2023-01-31T00:00:00ZA collaborative model for teaching and learning mathematics in secondary schools
https://hdl.handle.net/10500/30392
A collaborative model for teaching and learning mathematics in secondary schools
Ngwenya, Vusani
Mathematics pass rates in South African schools, as in many developing nations, continue to be a source of concern for educators and policymakers alike. Improving mathematics performance is non-negotiable if Africa is to meet the African Union Agenda 2063 and the SADC Industrialization Strategy 2063. The study sought to corroborate the findings and provide an empirical model to improve mathematics performance in secondary schools, as research studies attest to a relationship between attitude to science and science achievement, as well as a correlation between mathematics underperformance and inadequate home and school resources and underqualified and incompetent teachers.
The research focused on creating a collaborative secondary school math model. Twenty Grade 10 mathematics students, five teachers, and two subject advisers participated in the desk review, interviews, and group discussions. The study's purpose was to create a collaborative secondary school mathematics teaching and learning approach to help educators learn more about their subject. Four contextual factors—student, educator, school, and classroom—calibrated the model. Teacher-classroom activities were examined as a way to improve classroom performance. Research data to answer the research questions was collected from mathematics teachers, subject advisors, learners, and Departmental Heads(DHs) using classroom observations, semi structured interviews, questionnaires, focus group interviews and performance tests.
The study revealed that educators lack pedagogical content expertise and reform proposals. Math teachers teach in isolation. Thus, the development of a collaborative model used learners' and educators' inherent inclination to work in groups, share viewpoints, and solve problems to develop classroom and staffroom relationships.
Establishing a community of progressive, collegial, and interdependent specialists to improve mathematics education in secondary schools will enhance interest in the subject. Due to its case study of five schools in a cluster, the research was inconclusive, but the results were enlightening. Due to university time and money constraints, the research was constrained. To improve the model, an extensive follow-up investigation is needed. To improve the notion, researchers are studying educator isolation vs. cooperation, peer assessments, and teacher and student learning.; Amazinga okuphasa kwezibalo ezikoleni zaseNingizimu Afrika, njengakwamanye amazwe asathuthuka, asaqhubeka nokuba yinkinga kothisha nabakhi benqubomgomo ngokufanayo. Ukwenza ngcono ukusebenza kwezibalo akunakuxoxiswana uma i-Afrika izohlangabezana ne-African Union Agenda 2063 kanye ne-SADC Industrialization Strategy 2063. Lolu cwaningo belufuna ukuqinisa lokho okutholakele futhi lunikeze imodeli enamandla yokuthuthukisa ukusebenza kwezibalo ezikoleni zamabanga aphezulu, njengoba ucwaningo lufakazela ukuthi ubudlelwano phakathi kwesimo sengqondo ekuphumeleleni kwesayensi nesayensi, kanye nokuhlobana phakathi kokungenzi kahle kwezibalo kanye nezinsizakusebenza zasekhaya nezesikole ezinganele kanye nothisha abangaqeqeshiwe nabangakwazi ukusebenza kahle.
Ucwaningo lugxile ekudaleni imodeli yezibalo zesikole samabanga aphakeme esebenzisanayo. Abafundi bezibalo beBanga le-10 beBanga le-10, othisha abahlanu, nabeluleki bezifundo ababili babambe iqhaza ekubuyekezweni kwedeski, ezingxoxweni nasezingxoxweni zamaqembu. Inhloso yocwaningo kwakuwukwakha indlela yokusebenzisana yokufundisa nokufunda izibalo zesikole samabanga aphezulu ukusiza othisha bafunde okwengeziwe ngesifundo sabo. Izici ezine zomongoΓÇöumfundi, uthisha, isikole, nekilasiΓÇözilinganise imodeli. Imisebenzi yasekilasini lothisha yahlolwa njengendlela yokuthuthukisa ukusebenza kwekilasi. Idatha yokuphendula imibuzo yocwaningo iqoqwe kothisha bezibalo, abeluleki bezifundo, abafundi, kanye neziNhloko zoMnyango(ama-DH) kusetshenziswa okubonwa ekilasini, izingxoxo ezihleliwe ezihleliwe, uhlu lwemibuzo, izinhlolokhono zamaqembu kanye nezivivinyo zokusebenza.
Ucwaningo luveze ukuthi othisha abanabo ubungcweti bokuqukethwe kokufundisa kanye neziphakamiso zezinguquko. Othisha bezibalo bafundisa bodwa. Ngakho-ke, ukuthuthukiswa kwemodeli yokusebenzisana kusebenzise ukuthambekela okungokwemvelo kwabafundi nothisha ekusebenzeni ngamaqembu, ukwabelana ngemibono, nokuxazulula izinkinga ukuze kuthuthukiswe ubudlelwano bekilasi nothisha.
Ukusungula umphakathi wochwepheshe abathuthukayo, abafundayo, nabancike komunye ukuze kuthuthukiswe imfundo yezibalo ezikoleni zamabanga aphezulu kuzothuthukisa intshisekelo kulesi sifundo. Ngenxa yocwaningo lwayo lwezikole ezinhlanu eziqoqweni, ucwaningo belungaphelele, kodwa imiphumela ibikhanyisa. Ngenxa yesikhathi sasenyuvesi kanye nezingqinamba zemali, ucwaningo lwaba nengcindezi. Ukuze uthuthukise imodeli, uphenyo olunzulu lokulandelela luyadingeka. Ukuze kuthuthukiswe lo mbono, abacwaningi bafunda ukuhlukaniswa kothisha ngokumelene nokubambisana, ukuhlola kontanga, nokufunda kothisha nabafundi.; Wiskunde-slaagsyfers in Suid-Afrikaanse skole, soos in baie ontwikkelende lande, bly steeds 'n bron van kommer vir opvoeders en beleidmakers. Die verbetering van wiskundeprestasie is ononderhandelbaar indien Afrika aan die Afrika-unie Agenda 2063 en die SAOG Industrialiseringstrategie 2063 wil voldoen. Die studie het gepoog om die bevindinge te staaf en 'n empiriese model te verskaf om wiskundeprestasie in sekondêre skole te verbeter, soos navorsingstudies getuig van 'n verband tussen houding teenoor wetenskap en wetenskapprestasie, sowel as 'n korrelasie tussen wiskunde-onderprestasie en onvoldoende huis- en skoolhulpbronne en ondergekwalifiseerde en onbevoegde onderwysers.
Die navorsing het gefokus op die skep van 'n samewerkende sekondêre skool-wiskundemodel. Twintig graad 10-wiskundestudente, vyf onderwysers en twee vakadviseurs het aan die lessenaarhersiening, onderhoude en groepbesprekings deelgeneem. Die doel van die studie was om 'n samewerkende sekondêre skool wiskunde-onderrig-en-leerbenadering te skep om opvoeders te help om meer oor hul vak te leer. Vier kontekstuele faktore - student, opvoeder, skool en klaskamer - het die model gekalibreer. Onderwyser-klaskameraktiwiteite is ondersoek as 'n manier om klaskamerprestasie te verbeter. Data om die navorsingsvrae te beantwoord is ingesamel van wiskunde-onderwysers, vakadviseurs, leerders en departementele hoofde (DH's) deur gebruik te maak van klaskamerwaarnemings, semi-gestruktureerde onderhoude, vraelyste, fokusgroeponderhoude en prestasietoetse.
Die studie het aan die lig gebring dat opvoeders nie pedagogiese inhoudskundigheid en hervormingsvoorstelle het nie. Wiskunde-onderwysers onderrig in isolasie. Dus het die ontwikkeling van 'n samewerkende model gebruik gemaak van leerders en opvoeders se inherente geneigdheid om in groepe te werk, standpunte te deel en probleme op te los om klaskamer- en personeelkamerverhoudings te ontwikkel.
Die vestiging van 'n gemeenskap van progressiewe, kollegiale en interafhanklike spesialiste om wiskunde-onderrig in sekondêre skole te verbeter, sal belangstelling in die vak verhoog. As gevolg van die gevallestudie van vyf skole in 'n groepering, was die navorsing onbeslis, maar die resultate was verhelderend. Weens universiteitstyd- en geldbeperkings was die navorsing beperk. Om die model te verbeter, is 'n uitgebreide opvolgondersoek nodig. Om die idee te verbeter, bestudeer navorsers opvoeder-isolasie vs. samewerking, portuurassesserings en onderwyser- en studenteleer.
2021-11-01T00:00:00Z