The increasing emphasis on teaching arithmetic meaningfully intensifies the search for materials of instruction which can effectively communicate arithmetical understandings to children. Though manipulative aids are widely approved as effective teaching media for achieving this purpose, most of the endorsements are subjective opinions rather than objective evaluations based on experimentation. This study is an attempt to determine the effectiveness of group instruction use of certain manipulative aids in teaching decimal fraction concepts to Grade VII pupils. The effectiveness was determined by comparing the achievement of two unselected groups, randomly assigned, on a test of understanding of the processes involved in decimal fractions. The two groups were given teaching treatments identical except in so far as the materials of instruction were concerned. One group used manipulative aids; the other used static representations of these aids. These materials were intended to differ only with respects to the characteristic of manipulability. Since manipulability of concepts is the most essential property of manipulative aids, it was isolated as the experimental variable. Because the groups were randomly assigned, analysis of covariance was selected to control statistically the initial differences between groups in the four variables considered likely to influence achievement on the criterion test: initial understanding of the processes involved in decimal fractions, computational ability in decimal fractions, mental ability, and reading ability. The data obtained from the investigation were analyzed and the following conclusions reached. 1. The pupils taught by means of group instruction with the manipulative aids used in this investigation did not acquire a significantly better understanding of decimal fractions than did the pupils taught with static representations of these aids. In other words, the manipulation of the concepts, performed by using the manipulative aids in group demonstrations, was not effective in contributing to the pupils’ understanding of these concepts. 2. A study of the correlations for both treatment groups between achievement on the criterion variable and achievement on each of the independent variables indicates that the manipulative aids proved to be neither more nor less effective than the static representations as media for conveying an understanding of decimal fractions to pupils of any particular ability in the areas represented by the independent variables. 3. It must not be inferred that any generalization concerning the effectiveness of these specific materials of instruction, used exclusively by the teacher for group demonstration purposes, would be applicable also to similar materials if they were used in a teaching procedure in which the pupils themselves, participated individually in the manipulative activity. It must not be inferred that any generalization concerning the effectiveness of these specific materials of instruction, which were used in a brief teaching assignment devoted exclusively to the rationalization of processes, would be applicable also to the same materials if they were used in a teaching assignment of longer duration, and/or a teaching assignment in which the emphasis on the WHY of the processes was taught concurrently with, or preceded, the emphasis on the HOW of the processes. 5. Independently of treatment groups, the achievement on the initial test of understanding of the processes involved in decimal fractions was the variable most predictive of achievement on the final test of understanding. Computational ability in decimal fractions and mental ability each shared approximately one-half the predictive capacity of the initial test of understanding. Reading ability was a negligible predictor of achievement on the final test of understanding. / Education, Faculty of / Graduate

Thesis (MEd)--University of Stellenbosch, 2005. / ENGLISH ABSTRACT: Research shows that misconceptions about calculations develop in many classrooms without being noticed and these are not corrected by repeated routine exercises. The misconceptions formed are at times the result of inappropriate models used to solve problems. An even bigger concern is that these particular models sometimes provide the correct answers by accident. This may result in the learner's belief in the models being reinforced, as described by Swan (n.d.). The aim of this study is to identify the misconceptions related to the use of decimal fractions by Grade 8 and 9 learners and then, through the use of an intervention program, to address the learners' misconceptions and attempt to correct them. Two schools were involved in this study. The group of learners from school A served as a control group to determine the success of the intervention in learners from school B. The results of school A, the frequency and nature of errors were compared with the test results of school B as well as described by interviews with learners from school B. After the diagnostic tests and interview, the learners' answers were compared with those already described in literature. The learners from school B participated voluntarily in the intervention program. Learners from both schools wrote a post-test and the results were compared with those of a pre-test. The conclusion of this study is that there are misconceptions concerning calculations with decimal fractions at Grade 8 and 9 level. These misconceptions are formed during the intermediate phase and are not suitably corrected. The intervention program, for various reasons, had limited success. These reasons are discussed and recommendations are made for future intervention programs. / AFRIKAANSE OPSOMMING: Navorsing toon dat wanbegrippe ten opsigte van berekeninge in baie klaskamers onopgemerk verbygaan en dat dit nie reggestel word deur herhaalde roetine oefeninge nie. Wanbegrippe wat kinders vorm is onder andere die gevolg van onvanpaste modelle wat gebruik word vir die oplos van probleme. 'n Groter gevaar is dat hierdie onvanpaste modelle toevallig die regte antwoord lewer. Dit kan dan veroorsaak dat die leerder se vertroue op die modelle net versterk word, soos Swan (s.j.) dit beskryf. Die doel van hierdie studie is om wanbegrippe ten opsigte van bewerkings met desimale breuke by Graad 8 en 9 leerders te identifiseer en dan deur middel van 'n intervensieprogram die leerders se wanbegrippe aan te spreek en te probeer regstel. Twee skole is by hierdie studie betrek. Die groep leerders van skool A sou dien as 'n kontrolegroep om die intervensie-sukses van die leerders van skool B te bepaal. Die skool A resultate en frekwensie van foute asook die aard daarvan is vergelyk met die toetse van skool B en beskryf op grond van onderhoude met die leerders van skool B. Ná die diagnostiese toets en onderhoud is die leerders se antwoorde vergelyk met dié wat reeds in die literatuur beskryf is. Die leerders van skool B is op vrywillige basis by 'n intervensieprogram betrek. Beide skole se leerders het daarna 'n natoets geskryf en die resultate is vergelyk met dié van die voortoets. Die gevolgtrekking wat uit hierdie studie gemaak word, is dat daar wanbegrippe ten opsigte van bewerkings met desimale breuke op graad 8 en 9 vlak aanwesig is. Hierdie wanbegrippe is in die intermediêre fase gevorm en nie reggestel nie. Die intervensieprogram het om verskeie redes slegs beperkte sukses gehad. Hierdie redes word bespreek en aanbevelings word gemaak vir toekomstige intervensieprogramme.