Investigation On A Certain Misconception On Fraction

讲座内容：The origin of the research project reported in this paper is the well-known misconception 1/2+1/5=2/7 which is one of the objects studied here. The method used is an empirical study in terms of a questionnaire on 60 fresh university students at a Swedish university on the one side and the current Swedish curriculum on the other side, and the study is also supplemented by a theoretical discussion. The theoretical discussion is conducted within the theoretical framework of conceptual and procedural knowledge as well as that of diagnostic teaching.The focus of this research project is on causes of the misconception from global perspective in which case we treat the knowledge on fraction as a whole and examine it on both empirical level and on curricular level. In inquiring for the causes of the misconception we compare the addition of two fractions with the addition of numbers with two different but commensurable units, say 3 cm + 7dm = 7.3dm. These two additions are similar from mathematical aspect, for what is involved is a change of unit; in the case of fraction, the change amounts to prolonging or shortening a fraction. The comparison indicates that weak sense of unit together with lack of proficiency in prolonging or shortening a fraction could be one of causes for the misconception. Our empirical study seems to confirm this contention which can have some impact on teaching designing, curriculum designing and textbook writing.