Perceptions of difficulty

Seventy students from a first semester calculus course ranked 8 mathematics tasks as to perceived difficulty before attempting these tasks and actual difficulty after completing the tasks. Students also completed two examinations, one based on facts and procedures and the other based on applications and concepts. The tasks were designed to fit into a taxonomy of mathematical skills. We have found that students perceive questions to be difficult for a number of reasons. In general, questions requiring conceptual understanding ae regarded as more difficult that those which require factual recall or the use of routine procedures. There was not a strong link between familiarity with the question type and ranking of difficulty. Students were sufficiently familiar with the some typ es of question to be able to perceive inherent difficulties, such as a complex differentiation. We found that in five out of eight cases, students' perceptions of the difficulty did not change after they had done the task. In one case they found the question to be more difficult than expected and in two cases to be easier. It is not clear to us why students found one question to be more difficult than expected. It may be that some of the complexities (such as the use of the intermediate value theorem) were not immediately apparent. It is also significant that NESB students rated this question as easier than ESB students. This was the case both before and after attempting the question. Student comments are also presented