Abstract

The present study investigated whether Grade 5 students, who are learning a procedure for a whole number by a fraction using repeated addition, would develop conceptual knowledge of fractions. The study aimed to answer three questions: 1 – Does practicing a procedure to multiply a whole number by a fraction through repeated addition result in acquiring greater procedural accuracy in fraction multiplication? 2 - Does practicing a procedure to multiply a whole number by a fraction through repeated addition result in greater conceptual knowledge? and 3 - Does self-explaining contribute to developing conceptual knowledge when practicing a procedure to multiply a whole number by a fraction through repeated addition?
For this pretest-intervention-posttest study, 56 Grade 5 students were selected from two schools located in the greater Montreal area (two classes from each school) Three randomly-selected groups were created within each class. Two groups received instruction on how to use the procedure: one was prompted while the other was not. The third group explored geometry notions without receiving any instruction on fractions.
As expected, the results demonstrate that after the 4-week intervention period, practicing exercises involving the multiplication of whole numbers by fractions enhanced procedural accuracy, whereas those who did not receive such instruction did not. In contrast to expectations, students' conceptual understanding of fraction magnitude was not enhanced by practicing a procedure for multiplying whole number by fractions. To clearly identify the mechanisms that would facilitate this transfer, more research is necessary.