This study explored 14 to 15 year old pupils' graphical understanding and their teachers' pedagogical content knowledge. A diagnostic instrument was developed from the research literature to suit the UK National Curriculum, and was administered to 425 pupils. The problems were deliberately posed in such a way as to encourage relevant errors and misconceptions to surface. The test was 'scaled' using Rasch methodology and the result was a hierarchy of responses, each level of which was described as a characteristic performance including key misconceptions. Results showed that pupils were able to solve tasks involving both reading and interpretation of graphs from an early level. The hierarchy was generally consistent with previous literature. The errors were validated apart from one which is believed to be a new version of the so called 'interval-point' confusion. The instrument was also further developed to function as a questionnaire for assessing teachers' Pedagogical Content Knowledge (PCK). Teachers' estimation of the difficulty of the items, their proposed learning sequences and their awareness of errors and misconceptions were examined. Furthermore, teachers' perceptions of what is difficult were correlated with the children's actual difficulty estimates. Results showed that these teachers' estimation of what is difficult seemed to be partly structured by the curriculum sequence. Some of the teachers overestimated the difficulty of some tasks involving global interpretation and underestimated the difficulty of those which entailed pointwise reading or algebraic manipulation. Also, their knowledge was highly sensitive to the method adopted to collect the data. The teachers' mis-estimation of (relative) difficulties could be explained by one of two reasons: sometimes teachers apparently misunderstood the actual question themselves, and so underestimated the difficulty of the item. At other times, teachers overestimated the difficulty because they did not realise that children could answer the question without a sophisticated understanding of some concepts. Pupils' and teachers' responses were confirmed and enriched through group interviews and semi-structured interviews respectively.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:631233 |
| Date | January 2002 |
| Creators | Hadjidemetriou, Constantia |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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