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ItemInvestigating the effect of mathematics problem context on the performance of Year 10 studentsAlmuna Salgado, Felipe Javier ( 2016)This thesis is to revisit and scrutinise a possible effect of problem context familiarity, context engagement, and levels of context use on the performance of Year 10 students in PISA and PISA-like problems. Two research phases (i.e. a quantitative phase and a qualitative phase) shaped the design of this study. These research phases adhere to the mixed methods explanatory sequential design. The quantitative phase investigated whether an alteration of students' context familiarity and context engagement influenced the students' performance when solving PISA and PISA-like problems—that were controlled, to the best extent possible, in their textual and problem core features. There were two experiments that differed in the criteria for choosing the problem contexts (expert judgement vs students judgment). Then, students' performance was compared at different levels of context use. Later, the relationship between students’ performance and degrees of context familiarity, degrees of context engagement, and levels of context use was examined, principally using an ordinal logistic regression model. The qualitative phase used stimulated recall interviews to understand how students interpreted and experienced context familiarity and context engagement as well as the students' behaviours towards the accessibility of problems and the solution methods to the problems, and therefore students’ performance. The results of the quantitative phase showed that more familiar and engaging contexts did not improve students’ performance in either experiment, that the performance decreased as levels of context use increased, and that neither higher degrees of context familiarity nor higher degrees of context engagement affected the students' performance but higher levels of context use did. Added to this—and as part of the research work involved in the quantitative phase— a system to classify mathematical problems in terms of levels of context use was developed theoretically and validated statistically. Main results of the qualitative phase indicated that although students appeared to have a well-established understanding of context familiarity this was not strong enough to influence the use of the problem context as a resource to solve a problem that required the students’ interaction with the real-world context.
ItemInvestigating the effect of item-context on students’ performance on mathematics itemsAlmuna Salgado, Felipe Javier ( 2010)The current research in mathematics education recommends to measure how well students are able to apply their knowledge and mathematical skills and use them to solve problems in a real-life context but an increasing body of research has been ambivalent about the effects of contextualising mathematical tasks on students’ performance. Thus, the present piece of research aims to investigate the effect of an alteration of item-context on students’ performance, if any, on mathematics items. Items with the same mathematical core whilst varying in objective figurative context are used in this study. The study will also examine to what extent the nature of demand of the item-context may affect students’ performance. A mixed method approach is used due to the character of the research aims. In this study significant differences were not been found in students’ performance when they solved items across altered contexts; but evidence indicated that students’ performance on items required the second-order use of context may be more influenced by the alteration of context. The results of this research give some insight into how the second-order use of context may influence students’ performance on mathematics items. This outcome enhances the understanding of contextualised mathematical assessment and provides a foundation for future research into contextualised mathematical tasks.