This project investigates primary 4 children's difficulties when solving word problems. It consists of an exploratory study examining the feasibility of using task-based interviews in the school setting; and a main study divided into three phases. The tasks set to the children are selected/adapted word problems from SPNG textbook Stage 2. Phase 1 investigates the difficulties of forty "average" primary 4 children from five different schools. Task-based interviews are used in conjunction with an error analysis. Phase 2 makes structural alterations to six of the most difficult Phase 1 word problems to investigate more closely the possible cause of difficulty. These altered word problems are re-presented to the Phase 1 sample. The original problems are not re-presented to this sample as the task-based interviews allowed for considerable practice of these original problems. Phase 3 took place a year later than Phase 2 and presents the structurally altered word problems alongside the original problems to a different, but similar sample. This sample consists of 126 children from the five schools participating during Phase 1/2. It is suggested that the findings do not support the view that a small unvarying number of variables consistently affect problem difficulty. Rather the sources of difficulty are likely to stem from a number of highly complex interacting sources; and the language itself need not be the block it sometimes appears to be. Informal strategies were evidently important for a significant minority of children, particularly in relation to subtraction problems. This seems well worth investigating further. The use of these strategies suggested that the language of the word problem could be understood when the child could link it to his/her informal strategies. Also, given simpler numbers, the semantic implications of the problem could often be mastered.

Doctorat en sciences psychologiques / info:eu-repo/semantics/nonPublished

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Thesis (DEd)--Stellenbosch University, 1995. / ENGLISH ABSTRACT: The rationale for this study essentially is the perceived and reported misconceptions in algebra that exist within pupils in the Junior Secondary phase. These misconceptions are the direct result of the incomplete mastery of algebra. The purpose of this research is to attempt to contribute towards pupils' complete mastery of algebra and the ensuing elimination of certain pupil misconceptions, by trying to increase primary school pupils' level of awareness of the general number properties. Primary school pupils who learn arithmetic in a problem based environment intuitively use the general number properties to execute arithmetical calculations, while pupils in the traditional teaching approach are taught standard algorithms which they must apply, often without comprehension. In the latter, the existence of the number properties is concealed. When these pupils officially encounter the general number properties for the first time in standard 4 or 5, they are probably not capable of integrating these new concepts into their existing knowledge structure. This may lead to incomplete mastery and ensuing misconceptions, which can become worse when pupils must apply exactly the same number properties in algebra to execute algebraic manipulations. The fact that primary school pupils in the problem based approach intuitively apply the number properties, earlier led to the hypothesis that these pupils possess a higher level of awareness of the number properties. However, research has indicated that these pupils possess only a moderately higher level of awareness. This has led to this study during which a specific attempt is made to take pupils' intuitive knowledge of the number properties, which they spontaneously apply, as a point of departure, and to develop it to such an extent that they become explicitly aware of the existence and nature of these fundamental concepts in mathematics. The technique how to link up with pupils' intuitive knowledge and to increase their level of awareness of the number properties inside a problem based environment, was developed during the first two years of this study. At the end of this period, a suitable teaching strategy was formulated. This strategy is essentially based on the following parameters: Group discussion, the use of calculators, and creating a cognitive disequilibrium. During the third year of this study this strategy was implemented at a number of schools. During this phase research concentrated on the distributive property only. Judging by the results, it appears as if a considerable increase in level of awareness has taken place within these pupils. During this study a hierarchical model of levels of awareness was also formulated. This model was used as a guide in the attempt to increase pupils' level of awareness of the number properties. / AFRIKAANSE OPSOMMING: Die rasionaal vir hierdie studie is hoofsaaklik gelee in die waargenome en gerapporteerde wanbegrippe in algebra wat by leerlinge in die Junior Sekondere fase bestaan. Hierdie wanbegrippe is die direkte gevolg van die onvolledige beheersing van algebra. Die doel van hierdie navorsing is om 'n hydrae te probeer lewer tot leerlinge se volledige beheersing van algebra, en die gepaardgaande uitskakeling van bepaalde leerlingwanbegrippe, deurdat gepoog word om laerskoolleerlinge se vlak van bewustheid van die algemene bewerkingseienskappe te verhoog. Laerskoolleerlinge wat probleemgebaseerde rekenkunde-onderrig ontvang, benut intu'itief die algemene bewerkingseienskappe ten einde rekenkundige berekeninge uit te voer, terwyl aan laerskoolleerlinge in die tradisionele onderrigbenadering standaardalgoritmes onderrig word wat hulle dikwels sonder begrip moet toepas. In laasgenoemde geval word die bestaan van die bewerkingseienskappe erg versluier. Wanneer hierdie leerlinge in standerd 4 of 5 vir die eerste keer amptelik met die algemene bewerkingseienskappe in aanraking kom, is hulle waarskynlik nie in staat om hierdie nuwe begrippe met hul bestaande kennisstruktuur te integreer nie. Dit kan tot onvolledige beheersing en gevolglike wanbegrippe lei, wat kan vererger wanneer leerlinge presies dieselfde eienskappe in algebra moet benut ten einde algebra!ese manipulasies uit te voer. Die feit dat laerskoolleerlinge in die probleemgebaseerde benadering intu'itief die bewerkingseienskappe toepas, het tevore reeds tot die hipotese dat hierdie leerlinge oor 'n hoer vlak van bewustheid van die bewerkingseienskappe beskik, aanleiding gegee. Navorsing het egter aangetoon dat daar slegs 'n matige hoer vlak van bewustheid by hulle bestaan. Dit het tot hierdie studie aanleiding gegee waartydens spesifiek gepoog word om leerlinge se intuitiewe kennis van die bewerkingseienskappe wat hulle spontaan aanwend ten einde rekenkundige bewerkings uit te voer, as vertrekpunt te neem, en te ontwikkel sodat hulle eksplisiet bewus sal raak van die bestaan en wese van hierdie grondliggende waarhede in wiskunde. Die tegniek hoe om by laerskoolleerlinge se intui'tiewe kennis aan te sluit en hul vlak van bewustheid van die bewerkingseienskappe binne 'n probleemgebaseerde omgewing te verhoog, is gedurende die eerste twee jaar van hierdie studie ontwikkel. Aan die einde van hierdie periode is 'n toepaslike onderrigstrategie geformuleer. Hierdie strategie steun sterk op die volgende parameters: Groepsbespreking , die benutting van sakrekenaars, en die skep van 'n kognitiewe disekwilibrium. Gedurende die derde jaar van hierdie studie is hierdie onderrigstrategie in verskeie skole toegepas. Daar is gedurende hierdie fase slegs op die distributiewe eienskap gekonsentreer. Volgens die resultate wil dit voorkom asof daar 'n aansienlike verhoging in die betrokke leerlinge se vlak van bewustheid van die distributiewe eienskap plaasgevind het. Gedurende hierdie studie is ook 'n hierargiese model van vlakke van bewustheid geformuleer aan die hand waarvan die poging aangewend is om leerlinge se vlak van bewustheid van bewerkingseienskappe te verhoog.

The purpose of this study was to evaluate the effects of a training package consisting of response restriction and the reinforcement of self-evaluation on letter reversal errors. Participants were 3 typically developing boys between the age of 5 and 7. The results indicated that the training package was successful in correcting reversals in the absence of a model during training and on application tests. These improvements maintained during subsequent follow-up sessions and generalized across trainers. Fading was not always necessary in correcting reversals, but was effective in correcting reversals that persisted during the overlay training procedures. The advantages to implementing a systematic intervention for reducing letter reversal errors in the classroom, as well as directions for future research, are discussed.

published_or_final_version / Education / Master / Master of Education