The Levels of elementary mathematıcs teachers' conceptual knowledge of the dıvısıon wıth fractıons

The division with fractions is the most difficult topic of the elementary schoolmathematics. Studies showed that mathematics teachers have a limited knowledge of thedivision with fractions and lack of conceptual knowledge of this domain. Teachers? limitedknowledge of the content may have a negative effect on students? learning.The aim of this study is to determine how elementary school mathematics teachersinterpret the division with fractions and how their interpretation affects their teaching.Participants of the study were four elementary mathematics teachers working in differentschools. At the time of the study, two of the participants were teaching new elementarymathematics curriculum while the other two were teaching the old curriculum. Data collectionconsisted of two phases. First, four teachers? lessons on the division of fractions wereobserved and then each teacher was interviewed individualy.The results of the study showed that the teachers? knowledge of the division withfractions was mostly procedural. Three of the four teachers oftenly focused on the use ofinvert and multiply rule, and had hard time in explaining why they used this rule and inproviding an alternative algorithm. Two teachers interpreted the division situations as equalsharing and that?s why, they were unable to provide a reasonable explanation for thesiştuations in which the divisor was a fraction. In addition to equal sharing meaning ofdivision, one of the teacher was able to think of the measurement meaning but was unable toapply this knowledge to the problem situations. Only one of the four teachers was able tointerpret the given situations using both meaning of the division and apply this understandingalternatively when appropriate. Moreover, except one teacher, the rest of the teachers couldnot explain the relationships among the quantities involved in a division situation. This wasevident in their explanations when asked to provide different strategies for estimating theremainder in a division situations. Only one teacher was able to provide four differentstrategies for estimating the remainder the others were not.Results showed that three of the four teachers? knowledge of the division withfractions were at procedural level, one?s was at conceptual level. The teaching of the teachersat the procedural level can be characterized as the teaching situations in which the proceduralunderstanding can be developed. These teachers repeatedly emphasized the use of rules andpaid almost no attention to how their students think. In contrast, the teacher with theconceptual knowledge paid more attention to her students? thinking and enabled them todevelop their own strategies and understanding. This teacher?s lesson on division withfractions lasted longer than the other teachers?.Key Words: Elementary mathematics teachers, conceptual knowledge, division withfractions, pedagogical content knowledge.