Abstract
The National Senior Certificate examination is the most important school examination in South Africa. Analysis of learners’ performance in Mathematics in this examination is normally carried out and presented in terms of the percentage of learners who succeeded in the different bands of achievement. In some cases item difficulties are presented – item refers to the subsection of each examination question. Very little attention is paid to other diagnostic statistics, such as the discrimination indices and item difficulties taking into consideration partial scores examinees achieve on items. In this article we report on a study that, in addition to the usual item difficulties, includes a discrimination index of item difficulties taking into account partial scores examinees achieved. The items, considered individually, are analysed in relation to the other items on the test. The focus is on the topic sequences and series and the data were obtained from a stratified sample of the marked scripts of the candidates who wrote the National Senior Certificate examination in Mathematics in November 2010. Rasch procedures were used for the analysis. The findings indicate that learners perform differently on subsections of topics, herein referred to as items, and that focusing on scores for full topics potentially mask these differences. Mathematical explanations are attempted to account for difficulties learners exhibit in these subsections, using a hierarchy of scale. The findings and our analysis indicate that a form of measurement-driven testing could have beneficial results for teaching. Also, for some items the difficulty obtained from the work of examinees runs counter to the commonly perceived wisdom that an examination ought to be structured in such a way that the less difficult items are at the start of a topic. An explanatory device anchored around the construct of ‘familiarity with problem types through repeated productive practice’ is used to account for the manifested hierarchy of difficulty of the items.
Highlights
In most countries schooling culminates with learners having to write examinations in various subjects in order to obtain a certificate to matriculate
Mathematics is seen as the gatekeeper subject to access many degree programmes as Mathematical Literacy has only been differentially accepted by higher education institutions and not at all in most cases to degree programmes requiring Mathematics
Productive practising (Selter, 1996) is the notion that repeated practice is not just senseless drill for automated responses to cue-based questions. It includes drilling for mastery as well as activities for developing learners’ mathematical thinking skills of the constructs that are being drilled. It is different from the kind of drill in which, for preparation for the National Senior Certificate (NSC) Mathematics examination, learners only work through previous examination papers
Summary
In most countries schooling culminates with learners having to write examinations in various subjects in order to obtain a certificate to matriculate. In South Africa the matriculation or the final National Senior Certificate (NSC) examination is a high-stakes examination and the outcome is a public event in which results are announced by the Minister of Basic Education and published in national newspapers. The NSC results can offer access to higher certificate programmes, diploma courses and the much sought-after degree courses at higher education institutions in the country. Mathematics or Mathematical Literacy is taken by all learners as a qualifying subject in the NSC examination. Mathematics is seen as the gatekeeper subject to access many degree programmes as Mathematical Literacy has only been differentially accepted by higher education institutions and not at all in most cases to degree programmes requiring Mathematics. A point score system is used at most universities in South Africa and the Mathematics score is usually weighted higher (it is doubled) in the score
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