Mathematics and Computer Science Education

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An exploration of preservice teachers’ use of educational technologies as visualization tools when teaching mathematics.
(2022) Zulu, Mzwandile Wiseman.; Mudaly, Vimolan.
This interpretive qualitative study explores the use of educational technologies by preservice teachers as visualization tools during mathematics teaching at secondary schools. Sfard’s commognitive framework and Koehler and Mishra’s technological pedagogical content knowledge theoretical frameworks undergird the study. Data were collected from ten preservice mathematics teachers at a university in the province of KwaZulu-Natal, South Africa. Performance tests, semi-structured interviews, focus group discussions, and observations were employed to collect data, which was analyzed using reflexive thematic analysis. The study found that preservice teachers employed two primary visualization strategies when they engaged in mathematical problem-solving: symbolic mental visualization, which they combined with their understanding of word usage, endorsed narratives and routines to arrive at a solution; and graphic visual mediators, such as diagrams, which they sketched to contextualize the problem statement and verify they solutions and use of mathematical word usage, routines, and endorsed narratives. Participants were found to be unable to solve a mathematics problem if they had not visualized it effectively; using a graphic visual mediator to understand the problem statement did not, however, guarantee success when solving a problem. A relationship was found between the visualization techniques that the participants used in their own attempts to solve mathematical problems and the visualization techniques they used in their lesson planning and teaching of mathematics in the same content area. Participants used innovative strategies to mediate learning, including educational technologies that facilitated visual mediators to enhance learners’ engagement with concepts. Synergies were found between the elements of the commognition and TPACK frameworks as these were used in tandem to analyze data. A model was developed (C+TPACK) that integrates the key elements of these frameworks. Further research is recommended to establish the viability, credibility and generalizability of the model.
Exploration of Grade 11 learners’ mental constructions and difficulties in learning and solving trigonometric equations: a case of one school in Umlazi district = Ukuhlolwa kwezincazelokuzakhela engqondweni kanye nezinkinga zokufunda nokuxazululwa kwama-equation esifundo seminxamithathu kubafundi beBanga 11: ucwaningo kwesinye sezikole esifundeni saseMlazi.
(2023) Dube, Njabulo Happyboy.; Ngcobo, Zanele Annatoria.
Trigonometry is a particularly challenging area of mathematics for high school learners. This study investigated South African Grade 11 learners' mental constructions and difficulties when learning and solving trigonometric equations. Participants were selected from an after-school mathematics programme that they attended on a voluntary basis. Data was collected using an activity sheet and semi-structured interviews. Baseline data was collected using an activity sheet from 17 learners Grade 10 learners; data was collected from the same learners a year later using another activity sheet with a different set of problems. Semi-structured interviews were conducted with 7 learners to probe their responses on the activity sheet. Most of the learners were found to be unable to make the necessary mental constructions to solve trigonometric problems at the Grade 11 level. Dubinsky’s (1991) constructivist APOS theory, which describes how learners construct their knowledge of mathematics concepts in stages characterised by action, process, object and schema, was used to analyse the mental constructions of learners. During both phases of data collection, most learners were found to rely on explicit step-by-step calculations to solve problems, indicating that they were operating at the action stage; a smaller number were able to do some of the steps mentally without writing them out, indicating that they had advanced to the process stage. No evidence was found of learners having advanced to the object or schema stages. Moreover, the findings showed that, while the learners perform procedures correctly, they applied rules without giving reasons. Piaget and Garcia’s (1989) triad mechanism were used to analyse the difficulties that hindered learners’ mental construction of concepts. Learners’ difficulties included incorrect conceptions of the equal sign, overgeneralization of rules, and failure to integrate algebra concepts into their construction of trigonometric concepts. Based on the findings, the study recommends that teachers reinforce basic algebraic skills—such as collecting like and unlike terms, using brackets, and addition and subtraction of algebraic terms—before introducing trigonometric concepts. Teachers are urged to explore different methods for teaching trigonometric equations to enable learners to construct knowledge effectively, such as collaborative learning and differentiated classroom activities. Iqoqa. Isifundo seminxamithathu siyingxenye eyinselelo enkulu ezibalweni ze-mathematics kubafundi bamabanga aphezulu. Lolu cwaningo lwahlola izincazelokuzakhela engqondweni kanye nezinkinga uma abafundi beBanga 11 befunda nalapho bexazulula izinkinga zesifundo seminxantathu eNingizimu Afrikha. Ababambiqhaza bakhethwa kulabo abasohlelweni lokufunda izibalo emva kokuphuma kwesikole abaziyela kulo ngokuzinikela. Kwasetshenziswa ishidi lemisebenzi kanye nezingxoxo ezingahlelelwe ukuze kuqoqwe imininingo. Imininingo eqoqwa ekuqaleni kocwaningo yatholakala kubafundi abayi-17 beBanga le-10 kusetshenziswa ishidi lemisebenzi; imininingo yaqoqwa kubo labo bafundi ngonyaka olandelayo kusetshenziswa ishidi leminye imisebenzi elinezibalo ezihlukile. Kwabanjwa izingxoxo ezingahleliwe nabafundi abayi-7 ukuthola izimpendulo zabo mayelana neshidi lemisebenzi. Iningi lalaba bafundi kwatholakala ukuthi abakwazi ukuqhamuka nezincazelokuzakhela emakhanda ukuze bakwazi ukuxazulula izinkinga zesifundo seminxantathu ezingeni lomsebenzi weBanga 11. Ukuhlaziya izincazelokuzakhela ezingqondweni zabafundi kwasetshenziswa injulalwazi ye-constructivist APOS kaDubinsky (1991) echaza ukuthi abafundi balwakha kanjani ulwazi lwabo lwemiqondomsuka yezibalo ngokwamazinga/ngokwezigaba ahambisana nokwenza, inqubo, okufundwayo/okuxazululwayo, kanye ne-schema. Kulezi zigaba ezimbili zokuqoqwa kwemininingo kwatholakala ukuthi abafundi abaningi bathembela ekubaleni isinyathelo ngasinye ukuze baxazulule inkinga. Lokhu kukhombisa ukuthi basezingeni lokwenza; abafundi abambalwa bakhombisa ukukwazi ukulandela izinyathelo ezithile ngekhanda bengabhalanga phansi, okukhombisa ukuthi babethuthukile kancane sebesezingeni lenqubo. Abutholakalanga ubufakazi obuveza ukuthi abafundi base bethuthukele emazingeni okufundwayo noma e-schema. Okunye futhi ukuthi imiphumela yakhombisa ukuthi abafundi balandela izinyathelo ngendlela efanele; basebenzisa imithetho ngaphandle kokunikeza izizathu. ukuhlaziya izinkinga ezithikameza ukwakha ezingqondweni izincazelokuzakhela zemiqondomsuka. Izinkinga zabafundi zazihlanganisa ukungaqondisisi ngendlela uphawu lokulingana, imithetho yokucacisa ngokwedlulele, kanye nokwehluleka ukuhlanganisa imiqondomsuka ye-algebra nokusebenzisana kwayo neyesifundo seminxantathu. Ngokwemiphumela yocwaningo kuphakanyiswa ukuthi othisha baqinise amakhono e-algebra ayisisekelo – njengokuhlanganisa amatemu afanayo kanya nangafani, ukusetshenziswa kwabakaki, kanye namatemu e-algebra okuhlanganisa nokusuza – ngaphambi kokuqalisa ngemiqondomsuka yesifundo seminxantathu. Bayanxuswa othisha ukuba bahlole izindlela ezihlukahlukene zokufundisa ama-equation esifundo seminxantathu ukuze abafundi bakwazi ukuzakhela ulwazi ngendlela efanele. Lezi zindlela kungaba ukufunda ngokubambisana noma ukunikezwa kwemisebenzi ehlukene ngokwamazinga abafundi.
Teachers' perceptions of the effectiveness of in-service education and training (inset) for senior secondary school mathematics teachers in the greater Durban area.
(1991) Ntenza, Philemon Simangele.; Winter, Paul.; Graham-Jolly, Mike.
The project of the Shell Science Centre (SSC) started in 1985, in response to the high failure rate in mathematics amongst black pupils, the perceived inadequacy of college mathematics curricula for prospective mathematics teachers, and generally because of the destructive policies of apartheid and the inferior system of education for black pupils. One of the programmes is to organise and run in-service education and training (INSET) courses for senior mathematics teachers, in collaboration with teachers' Action Committees, with the hope of effecting curriculum change and teacher behaviour in the classroom. It is important, therefore, for the SSC to know whether the INSET programmes meet the needs of the teachers, especially those who graduated from colleges of education in KwaZulu with a Secondary Teachers' Diploma, since they form the majority of the INSET participants. Hence, this investigaton aimed to survey and analyse: (i) mathematics teachers' and college mathematics lecturers' perceptions of the college mathematics curriculum; and (ii) mathematics teachers' perception of the effectiveness of INSET courses. Initial data, about the effectiveness of INSET courses and the pre-service training of prospective mathematics teachers, was gathered through informal talks with mathematics teachers during INSET courses. Issues and themes that emerged were "fleshed out" using unstructured interviews with five (5) mathematics teachers. From these it was possible to draw up a detailed structured interview schedule, which was administered to a further seventeen (17) mathematics teachers in senior secondary schools in Umlazi and KwaMashu townships. Data, about the college mathematics curriculum, was also gathered by means of structured interviews with college mathematics lecturers, in the two colleges of education in KwaZulu, and with graduate teachers with a Secondary Teachers' Diploma in mathematics. Among the significant findings were: o Limitations in the college mathematics curriculum in as far as the mathematics content and the methodology courses were concerned; o Problems with SSC INSET courses such as teaching methods suggested by INSET tutors, timing of INSET courses, group work, etc.; o Problems with teaching mathematics at school such as the shortage of mathematics textbooks, large classes, inadequate resources, etc.; and o Problems with incorrect 'overlearnt' rules from inadequate college mathematics textbooks. The implications of these findings for the SSC were considered. It is suggested inter alia that the SSC should adopt strategies which would emphasize direct contact with the pupils of INSET participants. It is hoped that these strategies will help correct the various problems experienced by mathematics teachers in the schools.
The effect of blended massive open online courses on students’ perceptions of their engagement and learning outcomes = Uphenyo ngezifundo eziningi ezivulelekile ze-inthenethi ehlanganisiwe yokufunda nokusebenza kwabafundi.
(2023) Edumadze, John Kwame Eduafo.; Govender, Desmond Wesley.
Massive open online courses (MOOCs) have arisen in recent years and have sparked significant discourse regarding education. MOOCs have become firmly established in the educational landscape and have undergone various adaptations, including the emergence of blended MOOCs integrating campus-based courses with MOOCs, resulting in a more profound learning experience. Blended MOOCs enable the use of various blended pedagogies, which can be used to offset the numerous challenges facing higher education in the global south, such as 1) limited access, 2) inadequacies and obsolescence infrastructure, 3) limited resources, 4) students’ enrolment that is far beyond what they were designed to accommodate, 5) overcrowding in lecture halls, 6) shortage of lecturers, especially research-active and experienced senior academics, 7) poor quality of education to meet the needs of today’s workforce and 8) mismatch between the skills of graduates. This study examines how blended MOOCs relate to students' learning and perceived academic performance. It analyses students' acceptance and use, engagement, and factors influencing their satisfaction and perceived academic performance. This analysis incorporates the revised Community of Inquiry (CoI) framework, including learning presence and the extended Unified Theory of Acceptance and Use of Technology (UTAUT 2) models. An empirical study was conducted with 2875 students from the University of Cape Coast, Ghana, selected via two-stage cluster sampling to accomplish this objective. The respondents were levels 100, 200, 300 and 800 students who were instructed to enrol into MOOCs as open educational resources (OERs) to supplement their campus-based for a semester. Upon the conclusion of the semester, the students were requested to complete a questionnaire. Subsequently, the collected data underwent analysis utilising SmartPLS v4 and SPSS v28 software. In general, the model demonstrates a strong alignment with the gathered data and possesses an adequate level of efficacy in elucidating the phenomenon of students’ usage acceptance (UTAUT 2) of blended MOOCs and its impacts on engagement (CoI), satisfaction and academic performance. The findings have several implications for research and EdTech integration practices among sub-Saharan nations, which were also discussed. Consequently, this study offers significant contributions to the theory and practice of active learning in a blended MOOC environment. Iqoqa. Izifundo Eziningi Ezivulelekile Ze-inthenethi (ama-MOOC) zivele eminyakeni yamuva nje futhi zivuse izinkulumo ezibalulekile mayelana nemfundo. Ama-MOOC asezinze aqina emkhakheni wezemfundo futhi abhekane nezimo ezihlukahlukene, okuhlanganisa ukuvela kwama-MOOC ahlanganisa izifundo ezisekelwe ekhampasini nama-MOOC, okuholela ekuhlangenwe nakho okujulile kokufunda. Ama-MOOC ahlanganisiwe anika amandla ukusetshenziswa kwezifundo ezihlukahlukene ezixubile, ezingasetshenziswa ukulungisa izinselelo eziningi ezibhekene nemfundo ephakeme eningizimu yomhlaba, njengokuthi 1) ukufinyelela okulinganiselwe, 2) ukuntuleka kwengqalasizinda kanye nesasetshenziswa, 3) izinsiza ezilinganiselwe, 4) abafundi ukubhaliswa okungaphezu kwalokho obekuklanyelwe ukukuthatha, 5) ukuminyana emahholo okufundisa, 6) ukushoda kwabafundisi, ikakhulukazi izifundiswa eziphezulu ezimatasa nokucwaninga, 7) izinga eliphansi lemfundo ukuze kuhlangatshezwane nezidingo zabasebenzi banamuhla kanye 8) nokungafani phakathi kwamakhono abafundi abathweswe iziqu. Lolu cwaningo luphenya ubudlelwano phakathi kwama-MOOC ahlanganisiwe kanye nokufunda kwabafundi nokusebenza kwezemfundo ngokuhlaziya umthelela wokwamukela ukusetshenziswa kwabafundi nokuxhumana nabo kanye nokuhlola izici ezithinta ukusetshenziswa kwabo kwangempela, ukuzibandakanya, ukwaneliseka kanye nokusebenza kwezemfundo kusetshenziswa inhlanganisela yomphakathi obuyekeziwe (CoI) okuhlanganisa ukuba khona kokufunda kanye nenjulalwazi Ehlanganisiwe Enwetshiwe Yokwamukela Nokusetshenziswa Kobuchwepheshe (UTAUT 2). Ucwaningo olunobufakazi lwenziwa nabafundi abangu-2875 abavela enyuvesi yaseGhana, abakhethwe ngesampula yezigaba ezimbili ukuze kufezwe le nhloso. Abaphendulile bekungabafundi bezinga le-100, 200, 300 kanye ne-800 ababeyalelwe ukuthi babhalise kuma-MOOC njengezinsiza zemfundo ezivulekile (ama-OER) ukuze bangezelele ekhempasini yabo ngesemester. Ekupheleni kwesemester, abafundi bacelwa ukuthi bagcwalise uhlu lwemibuzo. Kamuva, idatha eqoqiwe yahlaziywa kusetshenziswa isoftware ye-SmartPLS v4 kanye ne-SPSS v28. Ngokuvamile, imodeli ibonisa ukuqondana okuqinile nedatha eqoqiwe futhi inezinga elanele lokusebenza kahle ekucaciseni ukwenzeka kokwamukela ukusetshenziswa kwabafundi (i-UTAUT 2) yama-MOOC ahlanganisiwe kanye nomthelela wawo ekubandakanyekeni kwe-CoI, ukwaneliseka nokusebenza kwezemfundo. Okutholakele kunemithelela eminingana yocwaningo kanye nezinqubo zokuhlanganisa ze-EdTech phakathi kwezizwe eziseNingizimu yeSahara, nazo okwaxoxwa ngazo. Ngakho-ke, lolu cwaningo lunikeza iminikelo ebalulekile kuthiyori nokusebenza kokufunda okusebenzayo endaweni ehlanganisiwe ye-MOOC.

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