Locus of Difficulty in Multistage Mathematics Problems

Previous studies have suggested that the use of a means-ends problem-solving strategy imposes a heavy cognitive load which interferes with learning.This research discusses some of the contributing factors.A computational model was constructed that suggested that cognitive load is at a maximum when subgoals are manipulated and calculated.This allowed the prediction that on two move problems, most errors should occur during the calculation of the subgoal rather than the goal.This event was referred to as the stage effect.Experiments 1-5 supported this hypothesis.They further revealed that if the problem-solving environment was altered to reduce the likelihood of a means-ends strategy being used, error location became random.This in turn, presented the possibility that error location could be used as an indicator of the use of a means-ends strategy.Using three move problems, most errors were located at the subgoal immediately preceding the goal.This suggested that a means-ends strategy was more likely to be used at this location than at more distant locations.Protocol analysis supported this suggestion.Finally, if no-goal problems enhance learning by eliminating the use of means-ends analysis as has been found previously, then the stage effect found using conventional problems should be eliminated using equivalent no-goal problems.This was confirmed in a final experiment.It was concluded that (1) means-ends analysis imposes a heavy cognitive load during the calculation of subgoal stages and this may explain the detrimental effect of the strategy on learning and (2) this may be an identifying feature of a means-ends strategy.