The missing link in teachers' knowledge about common fractions division

摘要

The current study explored the difficulties teachers encounter when teaching common fractions division, focusing on teachers' knowledge concerning this issue. Nine teachers who study towards a M.Ed, degree in mathematics education demonstrated the algorithms they apply in order to solve fractions division problems, described how they teach the subject, and attempted to explain a student's mistake, in understanding a word problem involving dividing by fraction. The findings indicate there is a missing link in the teachers' pedagogical capability, stemming from insufficient content knowledge. They presented different solution algorithms and reported using construc-tivist teaching methods, yet the methods they described couldn't lead a student to understand the logic behind the algorithm they teach (invert-and-multiply - multiplication by an inverse number, in accordance with the requirements of the curriculum). Furthermore, the participating teachers did not possess specialized mathematics content knowledge (SCK) and knowledge of content and students (KCS), enabling them to identify the source of a student's misconception.