Addressing the struggle to link form and understanding in fractions instruction


Helena P. Osana, Concordia University, 1455 de Maisonneuve Blvd. Ouest, LB-583-2, Montréal, Québec, Canada (e-mail: ).


Background. Although making explicit links between procedures and concepts during instruction in mathematics is important, it is still unclear the precise moments during instruction when such links are best made.

Aims. The objective was to test the effectiveness of a 3-week classroom intervention on the fractions knowledge of grade 5/6 students. The instruction was based on a theory that specifies three sites during the learning process where concepts and symbols can be connected (Hiebert, 1984): symbol interpretation, procedural execution, and solution evaluation.

Sample. Seventy students from one grade 5/6 split and two grade 6 classrooms in two public elementary schools participated.

Method. The students were randomly assigned to treatment and control. The treatment (Sites group) received instruction that incorporated specific connections between fractions concepts and procedures at each of the three sites specified by the Sites theory. Before and after the intervention, the students’ knowledge of concepts and procedures was assessed, and a random subsample of 30 students from both conditions were individually interviewed to measure their ability to make specific connections between concepts and symbols at each of the three sites.

Results. While all students gained procedural skill (p < .001), the students in the Sites condition acquired significantly more knowledge of concepts than the control group (p < .01) and were also better able to connect fractions symbols to conceptual referents (p < .025).

Conclusions. The current study contributes to the literature because it describes when it might be important to link concepts and procedures during fractions instruction.