Teaching and testing mathematical problem solving by offering optional assistance

Transfer capability is usually defined as the ability to apply acquired knowledge and skills in novel situations. The experiment reported here concerned transfer in mathematics education. An experimental programme was constructed, based on strengthening the connection of strategic and domain specific knowledge and offering hints during teaching as well as during testing. Subjects were first graders from secondary education in the Netherlands, from two schools, two classes each. Students from these four classes were randomly allocated either to the experimental or the control group. The experimental computer-supported teaching programme was offered once a week during six weeks; the control group received regular mathematics instruction. After controlling for the effects of the covariates intelligence, mathematics aptitude and anxiety, it was shown that the experimental subjects performed significantly better on a posttest than subjects in the control group. The results suggest that the experimental instruction method enhances mathematics problem solving ability more strongly than traditional instruction. Upon closer examination this effect appears to be restricted to subjects already relatively high in intelligence and mathematical ability. This finding is not uncommon in intervention research, and is sometimes referred to as the Matthew or the fan-spread effect.