A microgenetic study of proportional reasoning using balance scale problems

The effects of initial knowledge and different types of learning experiences on proportional reasoning strategies were investigated. Students were screened for rule use on balance scale problems (Siegler, 1981), and those who made torque comparisons were excused from further participation. The remaining 153 sixth- and 105 ninth-graders were assigned to one of three groups: directed mentoring, unaided manipulation, and control. Groups were balanced in terms of number, sex, academic achievement, and initial proportionality performance. Directed mentoring students worked on a new set of balance scale problems under the guidance of an adult who asked a series of questions designed to teach the torque rule. Students in the unaided manipulation condition worked on problems with no adult guidance but were encouraged to make predictions and test them by manipulating weight and distance values along the fulcrum. Control group students received no extra learning opportunities. The directed mentoring group outperformed the unaided manipulation and control groups on immediate and delayed posttests with new problems. The unaided manipulation group did not outperform the control group on the posttests. Within the directed mentoring group, ninth graders were more likely than sixth graders to continue to use the torque rule on the delayed posttest. An analysis of learning performance during the treatment conditions revealed that the number of questions needed to boost performance, and the number of unaided apparatus manipulations, were each predictive of posttest performance. Pretest levels were not correlated with learning performance for the treatment groups, and were strongly related to posttest levels in the control group only. Finally, a separate study of sixth graders revealed that merely telling students which strategies to use was not as effective as directed mentoring in boosting performance levels. Findings are discussed in terms of Vygotsky's (1978) theory of dynamic assessment of cognitive performance.