Understanding Of Students Of Grades 4-7 About The Angles

Although there are only two types of simple difinitions of the angle in the primary and junior high school mathematics textbooks,the concept of angle plays an important role in plane geometry.It is necessary to make a study of the students' understanding about this concept.This paper is a report of an empirical study with questionnaire survey and interview,which purports to answer the following questions:How well do the students of grades 4-7 understand the concept of the angle? How well do they understand the such special angles as 0°,180°and 360°? How well do they identify angles in the physical situations? Based upon the analysis of the results of the survey conducted with 467 students of grades 4-7,the following conclusions are arrived at:(1) Most of students can correctly describe the definition of an angle and decide whether a figure is an angle or not according to the definition.Most of students adopt "a pair of rays with a common end-point" as the definition of an angle.There exists grade difference and gender difference in the judgement of an angle.(2) Students' understanding of the measurement of the angle consists of three modes,that is,quantity,relation and quality,of which the first two are dominant. Even if the students' understanding is affected by mathematics teaching,the historical parallelism still exists.The grade difference exists,too.(3) Most of students understand the special angles well,but they show grade difference in explaining the formation of such angles.No historical parallelism is found about the special angles except 0°.(4) Most of students can identify the angle from the figures or the word description,but they show both grade and gender difference in understanding the turn of an angle.