Developing proportional reasoning in mathematical literacy students
Thesis (MEd (Curriculum Studies)--Stellenbosch University, 2010.
ENGLISH ABSTRACT: The aim of this research is three-fold. Firstly I aimed to show the difficulty of the concept of proportional reasoning through empirical research. Several researchers have shown the degree of difficulty learners experience with proportional reasoning and have even indicated that many university students (and adults) do not have sound proportional reasoning skills. Piaget’s controversial developmental levels classify proportional reasoning as a higher order thinking skill in his highest level of development, formal operational thought, and claims that most people do not reach this level. The difficulty of proportional reasoning and the fact that it is a skill needed within all Learning Outcomes of Mathematical Literacy creates a predicament in terms of the difficulty of the subject in general. Is it then fair to classify Mathematical Literacy as an inferior subject in the way it has been done over the last few years if it is a subject that requires learners to operate at such a high level of thought through proportional reasoning? Secondly, I would like to confirm with the use of a baseline assessment that learners entering Grade 10 Mathematical Literacy have poor proportional reasoning skills and have emotional barriers to Mathematics and therefore Mathematical Literacy. The research will be done in three private schools located in the West Coast District of the Western Cape in South Africa. If learners in these educationally ideal environments demonstrate poor proportional reasoning skills even though they were privileged enough to have all the possible support since their formative years, then results from overcrowded government schools may be expected to be even worse. The learners in Mathematical Literacy classes often lack motivation, interest and enthusiasm when it comes to doing mathematics. Through the baseline assessment I confirm this and also suggest classroom norms and values that will help these learners to become involved in classroom activities and educational discourse. Thirdly and finally this research will focus on the design of activities that will aim to build on learners’ prior knowledge and further develop their proportional reasoning skills. I argue that activities to develop proportional reasoning should take equivalence of fractions as basis to work from. The activities will aim to help learners to set up questions in such a way that they can solve it with techniques with which they are familiar. Interconnectivity will form a vital part to this investigation. Not only do I indicate the interconnectivity between concepts in the Mathematical Literacy Learning Outcomes of the National Curriculum Statement, but I would like to make these links clear to learners when working through the proposed activities. Making links between concepts is seen as a higher order thinking skill and is part of meta-cognition which involves reflection on thoughts and processes. In short, this research can be summarised as the design of activities (with proposed activities) that aims to develop proportional reasoning by making connections between concepts and requires of learners to be active participants in their own learning.
AFRIKAANSE OPSOMMING: Die doel van hierdie navorsing is drieledig. Eerstens will ek die probleme met die konsep van proporsionele denke uitlig deur eksperimentele ontwerp navorsing. Verskeie navorsers verwys na die moeilikheidsgraad van probleme wat leerders ondervind met proporsionele denke. Sommige van hierdie navorsers het ook bevind dat verskeie universiteitstudente (en ander volwassenes) nie oor die vaardigheid van proporsionele denke beskik nie. Piaget se kontroversiële ontwikkelingsvlakke klassifiseer proporsionele denke as ‘n hoër orde denkvaardigheid in sy hoogste vlak van ontwikkeling, formele operasionele denke, en noem dat meeste mense nooit hierdie vlak bereik nie. Die hoë moeilikheidsgraad van proporsionele denke en die feit dat dit ‘n vaardigheid is wat binne al die Leeruitkomste van Wiskundige Geletterdheid benodig word veroorsaak ‘n dilemma as mens dit vergelyk met die moeilikheidsgraad van die vak oor die algemeen. Tweedens wil ek met behulp van ‘n grondfase assessering bewys dat leerders wat Graad 10 Wiskunde Geletterdheid betree swak proporsionele denkvaardighede het, gepaardgaande met emosionele weerstand teenoor Wiskunde en Wiskunde Geletterdheid. Die navorsing sal gedoen word in drie privaatskole in die Weskus distrik van die Wes-Kaap van Suid-Afrika. Indien leerders in hierdie ideale opvoedkundige omstandighede swak proporsionele denkvaardighede ten toon stel, ten spyte van die feit dat hulle bevoorreg was om sedert hulle vormingsjare alle moontlike opvoedkundige ondersteuning te geniet, dan kan verwag word dat resultate komende van oorvol staatskole selfs swakker mag wees. By leerders in Wiskunde Geletterdheid klasse kan daar gereeld ‘n gebrek aan motivering, belangstelling en entoesiasme ten opsigte van Wiskunde bespeur word. Deur gebruik van die grondfase assessering wil ek hierdie stelling bewys en ook voorstelle maak vir klaskamernorme en waardes wat sal help om die leerders meer betrokke te maak by klaskameraktiwiteite en opvoedkundige gesprekke.