Teaching and testing mathematical problem solving by offering optional assistance

Transfer capability is usually defined as theability to apply acquired knowledge and skillsin novel situations.The experiment reported here concerned transferin mathematics education. An experimental programme was constructed, based on strengtheningthe connection of strategic and domain specificknowledge and offering hints during teaching aswell as during testing.Subjects were first graders from secondaryeducation in the Netherlands, from two schools,two classes each. Students from these fourclasses were randomly allocated either to theexperimental or the control group.The experimental computer-supported teachingprogramme was offered once a week during sixweeks; the control group received regularmathematics instruction.After controlling for the effects of thecovariates intelligence, mathematics aptitudeand anxiety, it was shown that the experimentalsubjects performed significantly better on aposttest than subjects in the control group.The results suggest that the experimentalinstruction method enhances mathematics problemsolving ability more strongly than traditionalinstruction. Upon closer examination thiseffect appears to be restricted to subjectsalready relatively high in intelligence andmathematical ability. This finding is notuncommon in intervention research, and issometimes referred to as the Matthew orthe fan-spread effect.