Investigating teaching and learning of Grade 9 Algebra through excel spreadsheets : a mixed-methods case study for Lesotho

Ntsohi, Mamosa M. E. (2013-12)

Thesis (PhD)-- Stellenbosch University, 2013.

Thesis

ENGLISH ABSTRACT: The teaching and learning of algebra in the middle school grades in Lesotho is dominated by the mechanistic approach where learners are drilled on procedures for solving certain types of problems in algebra, without making any connection to the experience learners had with arithmetic. This is one of the sources of learners’ difficulties in mathematics. Research indicates that use of spreadsheets such as Excel has a potential of bridging the gap between arithmetic and algebra and thus enhancing the teaching and learning of algebra, making it meaningful to the learners. The study sought to answer the question: How do Grade 9 learners in Lesotho experience teaching and learning of algebra through Excel spreadsheets? The research commenced with a literature review that was followed by the empirical study. The theories of instrumental genesis and instrumental orchestration were identified as the framework for the investigation. Instrumental genesis is the process in which learners develop facility with the artifact as they use it towards achieving lesson objectives; technical (conceptual, mechanical) and personal (attitudes, behavior and preferred learning styles) aspects of learners’ experiences were identified. Instrumental orchestration is the steering of learners’ instrumental genesis by the teacher and the manner in which this process is carried out, depends on the teacher’s Technological Pedagogical Content Knowledge (TPCK). The research was a multi-case study following a mixed-methods approach, where both qualitative and quantitative methods were used. The empirical study was conducted in two schools in Lesotho. In each school, fifteen learners volunteered participation. The investigation was done through classroom teaching by me as the researcher. The focus was on what challenges learners encountered and how they benefited from their “spreadsheets algebra” learning experience. Data were collected through classroom observations where field notes were recorded and an observation schedule was used by the researcher and the Assistant Observer respectively. A questionnaire was also administered to all learner participants after the whole teaching period. Six learners, representative of high, medium and low performances in class, were also interviewed with a goal of finding out their experiences. The Assistant Observer was also interviewed to reduce the bias that may result from to the researcher studying her own practice The study found that learners experiences with learning algebra through spreadsheets, comprised of both challenges and benefits. The challenges encountered by learners could be classified into those that were school-based and those that were instruction-based. The school-based challenges related to inadequate physical structures and lack of well-functioning equipment in the computer laboratories. Instruction-based challenges encountered by learners were both technical and personal. Technical challenges related to the physical manipulation of the artifact and the lack of understanding of concepts involved, where the spreadsheets meet the algebra. Personal challenges related to learners’ attitude and behavior towards use of spreadsheets for algebra teaching and learning. While school authorities could address some of the challenges, it was found that both the teacher and learners could initiate strategies that could be used to overcome the instruction-based challenges. Teaching strategies such as “technical-demo”, “explain-the-screen”, “discuss-the–screen”, “link-screen-board” and “spot-and-show” (building on learners’ responses), and the general organization of classroom environment were helpful in orchestrating algebra learning within the spreadsheets. It was also found that use of spreadsheets had both cognitive and affective values for the learners. Even though use of spreadsheets may benefit both teachers and learners in algebra teaching and learning, implementation of the practice would require critical considerations in terms of teacher preparation and infra-structural improvements in the schools.

AFRIKAANSE OPSOMMING: Die onderrig en leer van algebra in die middelbare skoolgrade in Lesotho word oorheers deur die meganiese benadering waarvolgens leerders gedril word in prosedures om oplossings vir sekere tipe algebraprobleme te vind en die ervaring wat leerders in rekenkunde opgedoen het, nie daarmee in verband gebring word nie. Dit is een van die oorsake waarom leerders met wiskunde sukkel. Navorsing toon dat die gebruik van sigblaaie soos Excel moontlik die gaping tussen rekenkunde en algebra kan oorbrug, en dat die onderrig en leer van algebra daardeur kan verbeter, wat dit sinvol vir leerders sal maak. Die studie was daarop gemik om ’n antwoord op die volgende vraag te vind: Hoe ervaar graad 9-leerders in Lesotho die onderrig en leer van algebra deur middel van Excel-sigblaaie? Die navorsing het met ’n literatuuroorsig begin en is deur ’n empiriese studie opgevolg. Die teorieë instrumentele genese en instrumentele orkestrasie is uitgewys as die raamwerk vir die ondersoek. Instrumentele genese is die proses waarvolgens leerders bedrewenheid in die produk ontwikkel namate hulle dit gebruik om lesdoelstellings te bereik; tegniese (konseptuele, meganiese) en persoonlike (ingesteldheid, gedrag en voorkeurleerstyle) aspekte van leerders se ervarings is geïdentifiseer. Instrumentele orkestrasie is die stuur van leerders se instrumentele genese deur die onderwyser; en die wyse waarop hierdie proses uitgevoer word, hang van die onderwyser se Tegnologiese Pedagogiese Inhoudskennis (TPCK) af. Die navorsing het ’n meervoudige gevallestudie gebruik en ’n gemengde metodebenadering is gevolg, terwyl beide kwalitatiewe en kwantitatiewe metodes gebruik is. Die empiriese studie is in twee skole in Lesotho uitgevoer. Vyftien leerlinge uit elke skool het vrywillig deelgeneem. Die ondersoek is by wyse van klaskameronderrig deur my as die navorser gedoen. Daar is gefokus op die uitdagings wat leerders teëgekom het en hoe hulle by die “sigbladalgebra”-leerervaring gebaat het. Data is aan die hand van klaskamerwaarnemings versamel, waar veldnotas afgeneem is en ’n waarnemingskedule onderskeidelik deur die navorser en die assistentwaarnemer gebruik is. ’n Vraelys is na die volle onderrigtydperk by al die leerderdeelnemers afgeneem. Onderhoude is gevoer met ses leerders, wat hoë, medium en lae prestasies in die klaskamer verteenwoordig, met die doel om hulle ervarings te bekom. ’n Onderhoud is ook met die Assistentwaarnemer gevoer om vooroordeel, deurdat die navorser moontlik haar eie praktyk kon bestudeer, te verminder. Die studie het bevind dat leerders se ervarings met die leer van algebra deur middel van sigblaaie uitdagings sowel as voordele inhou. Die uitdagings wat leerders teëgekom het, kan onderskeidelik as skoolgebaseerde uitdagings en onderrig-gebaseerde uitdagings geklassifiseer word. Die skoolgebaseerde uitdagings hou verband met onvoldoende fisiese strukture en ’n gebrek aan behoorlik funksionerende toerusting in die rekenaarlaboratoriums. Die onderrig-gebaseerde uitdagings vir leerders is beide tegnies en persoonlik. Tegniese uitdagings hou verband met die fisiese manipulering van die produk en ’n gebrek aan begrip ten opsigte van die betrokke konsepte, naamlik waar die verband tussen die sigblaaie en algebra bestaan. Persoonlike uitdagings hou verband met leerders se ingesteldheid en gedrag rakende die gebruik van sigblaaie by die onderrig en leer van algebra. Alhoewel die skoolowerhede bepaalde uitdagings kan aanspreek, is daar bevind dat onderwysers sowel as leerders strategieë kan aanvoor om onderrig-gebaseerde uitdagings te oorkom. Onderrigstrategieë soos “tegniese demo”, “verduidelik die skerm”, “bespreek die skerm”, “koppel-skerm-bord” en “vind-en-wys” (wat op leerders se reaksie voortbou), asook die algemene organisasie van die klaskameromgewing, dra tot die orkestrasie van algebraonderrig met die sigblaaie by. Daar is ook bevind dat die gebruik van sigblaaie kognitiewe sowel as affektiewe waarde vir die leerders inhou. Selfs al sou onderwysers en leerders voordeel uit die gebruik van sigblaaie in die onderrig en leer van algebra kon trek, sou die implementering van die praktyk kritiese oorwegings moet geniet ten opsigte van onderwyservoorbereiding en infrastruktuurverbetering by die skole.

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