
02322398
a
1999c.01726
Tzur, Ron
Timmerman, Maria
Why do we invert and multiply? Elementary teachers' struggle to conceptualize division of fractions.
Dossey, John A. et al., Proceedings of the nineteenth annual meeting: Psychology of mathematics education (PMENA XIX). Vol. 2. ,. 553559 (1997).
1997
,
EN
F49
To study elementary teachers' construction of understanding of division of fractions, we conducted a teaching experiment with a class of 12 teachers and case studies with three of the teachers. Initially, the teachers were able to create meaningful division situations of fractions and solve them using the invertandmultiply (I\&M) algorithm, but they could not make sense of the algorithm. During instruction, teachers solved tasks in a computer microworld which led to their construction of fractions as comeasure units, a process that had previously been observed in children. The teachers observed that the result of using the comeasure units was consistent with the algorithmic answer. However, they were not able to pose and solve tasks in the ``opposite of multiplication'' context, which would allow them to relate their mental operations with the algorithm. The study demonstrates how a teacher educator can use research on stages of children's learning about fractions to organize observations of teachers' knowledge and to devise situations that promote teachers' understanding. (Abstract)