Pupils' understanding of angle is investigated. Areas of difficulty and misconceptions are highlighted with a view to recommending improvements in the presentation of angle in primary school and remedial work to overcome problems in secondary school. The material opens with a historical and mathematical background and a brief review of research. Presented next is a survey of primary work and an analysis of the angle content of five major tests. This is followed by details of the following research of the secondary level: (1) the administration and analysis of a test on angle concepts and an examination on angle measurement; (2) a comparison of the effectiveness of two types of protractors; and (3) a presentation of nine transcripts of interviews which probed pupil understanding, along with an analysis of each presented transcript. It is felt that the findings support a number of practical recommendations for instructional improvement. Among these are findings which are thought to show clearly the advantages of full rotatable protractors over conventional half protractors in both pupil concept formation and in measurement. The document concludes with an appendix of angle worksheets. (MP)