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ABSTRACT
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 constructivist 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.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1. In this paper, the two terms ‘performance mastery’ and ‘algorithm mastery’ are used alternately in order to express the same idea.
2. The curriculum in mathematics – Israel 2006.
3. The term ‘beautiful numbers’ implies numbers with which the operation of division can be easily performed. In the case of equal denominators, the numerator of the divisor is included in the numerator of the divided.