An exploration of the barriers to effective geometric thought in the Further Education and Training phase of selected secondary schools in the Umlazi District.

Abstract

ENGLISH ABSTRACT: Geometry, a branch of mathematics has a history from the study of practical measurement in ancient Egypt to properties of shapes in Greek geometry. Learning and teaching of geometry in South Africa has posed many challenges for educators and learners. In 2011 Euclidean geometry was reintroduced after the removal to redress the inequalities of apartheid and to provide uniform access to mathematics for all learners. This study was therefore conducted in three secondary schools, conveniently selected, to explore the barriers that hamper the performance of Euclidean geometry in the FET phase and to explore ways of eradicating these barriers. Research questions generated data from educators and learners aimed at identifying factors influencing effective geometric thought. This study was guided by the two metaphors, namely acquisition and participation and their impact on the teaching and learning of geometry. The study focussed primarily on the cognitive developmental theory of Piaget and social constructivist theory of Vygotsky both of which supported the acquisition metaphor. It further examined the participative metaphor of Sfard’s theory of commognition. The study adopted the interpretive paradigm with the qualitative design. Purposive sampling was used since the study was conducted with grade 11 learners and educators teaching in the FET phase. Questionnaires, semi structured interviews and focus group discussions were used to collect the data. Lesson observations were used for triangulation purposes. The research instruments were piloted in order to ensure validity and reliability. Data was first organized according to the research questions which was then coded and divided into themes. It was found that many of the barriers to learning geometry are primarily attributed to a lack of engagement of learners in meaningful learning situations. Findings also highlighted language, attitude, the classroom environment, and gaps in educators’ methodology and content knowledge has being some of the factors that contributed to the poor learner participation. Recommendations are made for stakeholders to develop effective geometric thought. This study proposes that greater emphasis be placed on learner-centred methods of teaching. Communication in the form of verbal, written and visual should be considered when teaching geometry. Allowing learners to express their experiences to think and develop new knowledge is essential. Learners need to become active participants of their learning and learning needs to take place in more realistic situations to improve understanding. IQOQA LOCWANINGO: I-Jiyomethri, igatsha lezibalo linomlando osuka ekutadisheni kwesilinganiso esisebenzayo Egibhithe lasendulo kuya azakhiweni zomumo weJiyomethri yamaGrikhi. Ukufunda nokufundisa iJiyomethri eNingizimu Afrika kudale izingqinamba eziningi kothisha nabafundi. Ngo-2011 iJiyomethri yaphinde yafakwa ngemuva kokususwa ukuze kulungiswe ukungalingani kobandlululo kanye nokuhlinzeka ngokulingana ukuthola izibalo zabo bonke abafundi. Ngakho-ke lolu cwaningo lwenziwe ezikoleni zamabanga aphakeme ezintathu, ezikhethwe kalula, ukuhlola imigoqo ephazamisa ukusebenza kweJiyomethri esigabeni seFET nokuhlola izindlela zokuqeda lezi zithiyo. Imibuzo yocwaningo yakhiqiza idatha evela kothisha nakubafundi ehlose ukukhomba izinto ezinomthelela ekucabangeni okusebenayo kweJiyomethri. Lolucwaningo beluqondiswa izingathekiso ezimbili, okungukuthi ukuzuza nokubamba iqhaza kanye nomthelela wazo ekufundisweni nasekufundweni kweJiyomethri. Ucwaningo lugxile kakhulu kumqondo wokuthuthuka wokuqonda kaPiaget kanye nethiyori yezakhi zenhlalo kaVygosky zombili ezazisekela isingathekiso sokutholwa. Iphinde yahlola umbono kaLave noWenger (1991) owawugqamisa ukubaluleka kwesifaniso sokubamba iqhaza futhi okokugcina, umbono kaSfard wokuhlonishwa. Ucwaningo lwamukele ipharadigm yokuhumusha ngomklamo wekhwalithi. Isampuli enenhloso isetshenzisiwe kusukela isifundo senziwa nabafundi bebanga le-11 nothisha abafundisa esigabeni se-FET. Amaphepha emibuzo, izingxoxo ezihleleke kancane kanye nezingxoxo zamaqembu okugxila kuwo kusetshenziselwe ukuqoqa imininingwane. Ukubheka izifundo kusetshenziselwe izinhloso zonxantathu. Amathuluzi zocwaningo ahlolwa ukuze kuqinisekiswe ukuba semthethweni nokwethembeka. Idatha yayihlelwe ngokuya ngemibuzo yocwaningo eyabe isibhalwa ngamakhodi yahlukaniswa yaba ngamatimu. Kunconyelwa ababambiqhaza ukuthi bathuthukise umcabango weJiyomethri osebenzayo. Lolu cwaningo luphakamisa ukuthi kugxilwe kakhulu ezindleleni ezigxile kubafundi zokufundisa. Ukuxhumana ngendlela yokukhuluma, okubhaliwe nokubukwayo kufanele kubhekwe lapho kufundiswa iJiyomethri. Ukuvumela abafundi ukuthi baveze ulwazi lwabo ukuze bacabange futhi bathuthukise ulwazi olusha kubalulekile. Abafundi kudingeka babe ngabahlanganyeli abakhuthele ekufundeni nasezidingweni zokufunda kwabo okumele ukwenzeke ezimeni ezingokoqobo ukuthuthukisa ukuqonda.