# Learning about and understanding fractions and their role in the high school curriculum

Pienaar, Etienne (2014-04)

Thesis (MEd)--Stellenbosch University, 2014.

ENGLISH ABSTRACT: Many learners, even at high school level, have difficulty with fractions and computations involving fractions. A report from the Department of Basic Education (DBE, 2012c: 15) has highlighted that the lack in basic fraction sense was one of the areas of concern that contributed to the low achievement in matriculation mathematics examinations in 2012. Fractions play an important role in our ever-advancing technological society. Many occupations today rely heavily on the ability to compute accurately, proficiently, and insightfully with fractions. High school learners’ understanding or the lack thereof is carried over to their tertiary studies and workplaces. It is for that reason that in this dissertation, the learning and understanding of fractions and their role in the high school curriculum are studied through a critical literature review. Fractions are compound constructs and can therefore be interpreted in many different ways, depending on the area of study within mathematics. The concept of fractions consists of five sub-constructs, namely, part-whole, ratio, operator, quotient, and measure (Behr, Lesh, Post, & Silver, 1983; Kieren, 1980). This thesis starts with discussion of the background of the study and its importance. Thereafter the elements that assist in the understanding of the fraction concept is discussed. Then, the five different sub-constructs are elaborated on, and how these different sub-constructs are used in the high school curriculum is demonstrated. The conclusion offers some implications for classroom teaching and mathematics teachers’ professional development.

AFRIKAANSE OPSOMMING: Talle leerders, tot op hoërskool vlak, ervaar probleme met breuke en berekeninge met breuke nie. ‘n Verslag van die Departement van Basiese Onderwys (DBE, 2012c: 15) het beklemtoon dat die gebrek aan basiese breuk vaardighede een van die oorsake was wat daartoe gely het dat die prestasie in die 2012 matriek wiskunde eksamen so laag was. Breuke speel ‘n belangrike rol in ons voortdurende tegnologiese voor uitgaande samelewing. Talle beroepe vandag is grootliks afhanklik van die akkurate, bekwame en insiggewende berekeninge van breuke. Hoërskool leerders se begrip, of die gebrek daaraan word oorgedra na hul tersiêre studies en werksplekke. Dit is vir dié rede dat hierdie tesis die leer en begrip van breuke en hul rol in die hoërskool kurrikulum bestudeer deur middel van ‘n kritiese literatuur studie. Breuke is ‘n saamgestelde konsep en kan vir hierdie rede op verskillende wyses geïnterpreteer word, afhangende van die area van studie in wiskunde. Die konsep van ‘n breuk bestaan uit vyf sub-konstrukte, naamlik deel-van-‘n-geheel, ‘n verhouding, operateur, kwosiënt en meting (Behr, Lesh, Post, & Silver, 1983; Kieren, 1980). Hierdie tesis begin met ‘n bespreking oor die agtergrond van hierdie studie en die belangrikheid daarvan. Daarna word die faktore wat bydra tot die verstaan van die breuk konsep. Dit word gevolg deur ‘n uitbreiding op die vyf verskillende sub-konstrukte en waar hierdie verskillende sub-konstrukte in die hoërskool kurrikulum voorkom. Die bevinding bied ‘n paar implikasies vir onderrig. Hierdie studie fokus nie op die ontwerp van enige take of ander leermateriaal vir ‘n intervensie program nie, maar konsentreer op die belangrike kwessies rondom breuke. My hoop is dat die bevindinge van hierdie studie implikasies inhou vir wiskunde onderwysers se professionele ontwikkeling deur hul te motiveer om nuwe leerondersteuningsmateriaal te ontwikkel en die aanbieding van breuke in klaskamers aan te pas sodat die begrip van breuke by leerders ten volle ontwikkel kan word.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/86269

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