Thesis (MEd)--Stellenbosch University, 2002. / ENGLISH ABSTRACT: In many countries, due to a growing criticism of the inadequacy of mathematics
curricula, reforms have been undertaken across the world for meeting new social and
technological needs and many researchers have begun to pay attention to the way
mathematics is learned and taught. In the same vein, this study aims to investigate
innovative and appropriate teaching strategies to introduce in the Rwandan
educational system in order to foster students' mathematical thinking and problem
solving skills. For this, a classroom-based research experiment was undertaken,
focusing on meticulous observation, description and critical analysis of mathematics
teaching and learning situations.
In the preparation of the research experiment, three mathematics teachers were helped
to acquire proficiency in doing mathematics and to refine their teaching strategies, as
well as to enable them to create a mathematics classroom culture that fosters students'
understanding of mathematics through the problem solving process.
Three classes of 121 students of the second year, their ages ranging from 14 years to
16 years, chosen from three different secondary schools in Rwanda, participated in
this research experiment. Students were taught an experimental programme based on
solving contextualised algebra problems in line with the constructivist approach
towards mathematics teaching and learning. Twenty-four mathematics lessons were
observed in the three classes and students' learning activities were systematically
recorded, focusing on teacher-students and student-student interaction.
The participating teachers experienced many difficulties in implementing new
teaching strategies based on a problem solving approach but were impressed and
encouraged by their students' abilities to generate different and unexpected ways of
solving problem situations. However, the construction of mathematical models of
non-routine problems constituted the most difficult task for many students because it
required a high level of abstraction, characterising algebraic reasoning. Despite
evident cognitive obstacles, a substantial improvement in students' systematic
reasoning with respect to the different steps in the problem solving process, namely
formulating a mathematical model, solving a model, verifying the solution and
interpreting the answer, was progressively observed during the experiment. Many
students had to overcome a language problem, which inhibited their understanding
and interpretation of mathematical problem situations and deeply affected their active
participation in classroom discussions.
In this study, small group work and group discussions gave rise to excellent and
successful teaching and learning situations which were appreciated and continuously
improved up by the teachers. They provided students with opportunities for learning
to argue about their mathematical thinking and to communicate mathematically. This
kind of classroom organisation created an ideal learning environment for students but
an uncomfortable teaching situation for teachers. It required much effort from the
teachers to transform the mathematics classroom into a forum of discussion in setting
up stimulating and challenging tasks for students, in working efficiently with different
groups and in moderating the whole class discussion.
It was unrealistic to expect spectacular changes in teaching practices established over
years to take place during a period of a month. This type of change requires sufficient
time and support. However, teachers did develop a new and practical vision of
mathematics teaching strategies focusing on students' full engagement in exploring
and grappling with problematic situations in order to solve problems. Teachers made
remarkable efforts in internalising and adopting their new role of mediators of
students' mathematics learning and in being more flexible in their teaching styles.
They learned to communicate with their students, to accept students' explanations and
suggestions, to encourage their logical disagreement and to consider their errors and
misconceptions constructively.
Students' results in the pre-test and the post-test showed their low performance in
building mathematical models especially when they had to use symbols but revealed a
significant progress in the students' ways of thinking which was observed through the
variety and originality of their strategies, their systematic work and their perseverance
in solving algebra problems. Students also developed positive attitudes to do
mathematics; this was exhibited by their pride and satisfaction to accomplish nonroutine
tasks by themselves.
Teachers' comments indicated that they work under pressure to cover an overloaded
mathematics curriculum and have poor support from educational authorities. For them,
mathematics IS socially considered as a difficult subject. For many students,
mathematics IS a gatekeeper to access higher levels of education; to fail in
mathematics unfortunately implies to fail at school and in life. Students' negative
attitudes towards mathematics were mainly due to their repeated failures in
mathematics, but also to some mathematics teachers who intimidate and discourage
their students.
Both educational authorities and teachers should make efforts to rethink an
appropriate mathematics curriculum and alternative teaching strategies in order to
efficiently prepare students to meet new societal and technological requirements. / AFRIKAANSE OPSOMMING: As gevolg van toenemende kritiek oor die kwaliteit van wiskundekurrikula, is
bewegings vir hervorming wêreldwyd geïnisieer om nuwe sosiale en tegnologiese
behoeftes aan te spreek en baie navorsing is gedoen oor die wyse waarop wiskunde
geleer en onderrig word. In lyn hiermee, is die doel van hierdie studie om innoverende
en geskikte onderrigstrategieë te ondersoek om in die Rwandese onderwysstelsel in te
voer om leerders se wiskundige denke en probleemoplossingsvaardighede te
ontwikkel. Om dit te bereik, is 'n klaskamergebaseerde navorsingseksperiment
uitgevoer, met die klem op fyn waarneming, beskrywing en kritiese ontleding van
wiskunde leer- en onderrigsituasies.
As voorbereiding tot die navorsingseksperiment is drie wiskunde-onderwysers gehelp
om vaardighede te verwerf in die doen van wiskunde en om hulonderrigstrategieë te
verfyn, asook om hulle in staat te stelom 'n wiskunde-klaskamerkultuur te vestig wat
leerders se begryping van wiskunde deur die probleemoplossingsproses ontwikkel.
Drie klasse van 121 leerders in die tweede jaar, tussen 14 en 16 jaar oud, is uit drie
verskillende hoërskole in Rwanda gekies om aan die navorsing deel te neem. Die
leerders is deur middel van 'n eksperimentele program onderrig wat gebaseer is op die
oplossing van gekontekstualiseerde algebraprobleme in ooreenstemming met 'n
konstruktivistiese benadering tot wiskunde-leer en -onderrig. Vier-en-twintig
wiskundelesse is in die drie klaskamers waargeneem en leerders se leeraktiwiteite is
stelselmatig opgeskryf, met die klem op onderwyser-leerder en leerder-leerder
interaksie.
Die betrokke onderwysers het baie probleme ondervind om nuwe onderrigstrategieë
gebaseer op 'n probleemoplossingsbenadering te implementeer, maar was baie
beïndruk en begeesterd deur hulleerders se vermoë om verskillende en onverwagte
planne te beraam om probleme op te los. Die opstelling van wiskundige modelle vir
nie-roetine probleme was vir baie leerders die moeilikste taak omdat dit 'n hoë vlak
van abstraksie wat kenmerkend is van algebraïese denke verteenwoordig. Ten spyte
van kognitiewe struikelblokke was daar nogtans 'n merkbare verbetering in leerders
se logiese redeneringsprosesse soos geopenbaar in die toepassing van die verskillende
stappe van die probleemoplossingsproses, naamlik die formulering van 'n wiskundige
model, die oplossing van die model, verifiëring van die oplossing en interpretasie van
die antwoord. Baie studente is gekniehalter deur 'n taalprobleem wat hul begrip en
interpretasie van wiskundige probleemsituasies en hul vrymoedigheid om aan
klaskamergesprekke deel te neem, aan bande gelê het.
Inhierdie studie het kleingroepwerk en groepbesprekings suksesvolle onderrig- en
leersituasies geskep wat deur die onderwysers raakgesien en verder uitgebou is. Dit
het geleenthede geskep vir die leerders om oor hul wiskundige denke te argumenteer
en om wiskundig te kommunikeer. Hierdie soort klaskamerorganisasie het 'n ideale
leeromgewing vir leerders geskep maar 'n ongemaklike onderrigomgewing vir
onderwysers. Dit het baie van onderwysers geverg om die wiskundeklaskamer in 'n
gespreksforum te omskep deur stimulerende en uitdagende probleme aan leerders te
stel, deur met verskillende groepe te werk en deur die algemene
klaskamerbesprekings te fasiliteer.
Dit was onrealisties om binne die bestek van 'n maand grootskaalse veranderinge in
onderwyspraktyke wat oor 'n tydperk vanjare posgevat het, te verwag. Hierdie soort
verandering benodig genoeg tyd en ondersteuning. Onderwysers het nogtans 'n nuwe
en praktiese visie ontwikkel van wiskunde-onderrigstrategieë wat fokus op leerders se
betrokkenheid by die ondersoek en oplossing van probleme wat vir hulle uitdagend en
nie-roetine was. Onderwysers het daadwerklike pogings aangewend om hul nuwe
rolle as mediators te internaliseer en te aanvaar, en om meer soepel onderrigstyle te
ontwikkel. Hulle het geleer om met hulleerders te kommunikeer, om leerders se
verduidelikings en voorstelle te aanvaar, om logiese argumentering aan te moedig en
om foute en wankonsepte konstruktief te benader.
Leerders se resultate in die voor- en na-toetse dui op swak vermoë om wiskundige
modelle te bou veral wanneer hulle simbole moes gebruik, maar wys beduidende
vordering in leerders se denke, wat gemanifesteer het in die verskeidenheid en
oorspronklikheid van hul strategieë, hul sistematiese werk en hul voortgesette pogings
om algebraprobleme op te los. Leerders het ook positiewe instellings teenoor die
doen van wiskunde ontwikkel; dit is getoon deur hul trots en tevredenheid wanneer
hulle self nie-roetine take opgelos het.
Onderwysers se kommentaar openbaar dat hulle onder druk werk om 'n oorlaaide
wiskundekurrikulum af te handel en dat hulle min ondersteuning van onderwyshoofde
kry. Hulle sê ook dat wiskunde deur die breë gemeenskap as 'n moeilike vak beskou
word. Vir baie leerders is wiskunde 'n hekwagter wat toegang tot verdere onderwys
en opleiding beheer; om in wiskunde te faal beteken om op skool te faal en om in die
lewe te faal. Leerders se negatiewe instellings teenoor wiskunde was hoofsaaklik as
gevolg van hul herhaalde mislukkings in skoolwiskunde maar ook as gevolg van
sommige wiskunde-onderwysers wat hulleerders intimideer en ontmoedig.
Beide onderwyshoofde en onderwysers behoort pogings aan te wend om te besin oor
'n geskikte wiskundekurrikulum en alternatiewe onderrigstrategieë om leerders meer
doeltreffend voor te berei om aan nuwe sosiale en tegnologiese eise te voldoen.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/52884 |
| Date | 12 1900 |
| Creators | Mudaheranwa, G. |
| Contributors | Olivier, A. I., Murray, J. C., Stellenbosch University. Faculty of Education. Dept. of Curriculum Studies. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
| Format | 94 p. |
| Rights | Stellenbosch University |
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