Abstract:

Fractions' division is one of the most difficult basic math concepts for both students and teachers. This is due to the fact that it combines:
(a) the concept of division and
(b) the concept of the fraction, two complicated concepts that are not particularly emphasized for deeper conceptual understanding by the primary school teachers.

Many researchers have shown that both students and teachers are driven to sterile memorization of the fraction division algorithm and to mechanistic learning and teaching. Thus, students are not given the opportunity to build and deepen into the under study concept via real-life situations and problems, as well as visual representations. The teachers -from their part- end up handling and teaching this concept algorithmically -without conceptual comprehension- by also presenting many difficulties in managing and creatively exploiting the mistakes and misconceptions of their students, as well as the causes that create and reproduce them. In this context, the current study is a teaching proposal for the comprehension of the "measurement or repeated subtraction division" model by the students in fraction-by-fraction division problems. The teaching intervention -lasting 2 teaching hours- was implemented to 11 students attending the 5th grade of a Greek primary school in the city of Patras. The results showed a statistically significant difference between students’ performance before and after the didactic intervention. Complementary, the misconceptions, weaknesses and mistakes of the students in the first activity of the proposed curriculum are discussed. To this end, the present didactic intervention constitutes an alternative curriculum for students' deeper comprehension of the fractions' division which is proposed to be implemented to primary school students of this age.

Keywords:

Measurement division, fraction-by-fraction division, primary education.