Robert F. Mawer’s scientific contributions

Investigated the distinctive strategies employed by expert and novice problem solvers (forward-chaining and means–ends, respectively) in 7 experiments using 14 mathematics graduates and 162 9–12 yr olds. Exp I studied the course of development of expertise using a subset of kinematics problems. Ss demonstrated the switch from a means–ends to a forward-chaining strategy. This was associated with the conventional concomitants of expertise such as a decrease in the number of moves required for solution. Ss appeared to categorize problems according to the order in which equations would be required. Exps II and III tested the hypothesis that the means–ends strategies used by novices retarded the acquisition of appropriate schemata. The use of nonspecific rather than specific goals was found to enhance the acquisition of expertise, the number of moves required for solution, and the number of equations written without substitutions. Exps IV and V, using geometry problems, duplicated the enhanced rate of strategy alteration found with reduced goal specificity. Results of Exps VI and VII indicated that reduced goal specificity also enhanced the rate at which problem solvers induced appropriate problem categories. It is concluded that in circumstances in which the primary reason for presenting problems is to assist problem solvers in acquiring knowledge concerning problem structure, the use of conventional problems solved by means–ends analysis may not be maximally efficient. (20 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)

There are two broad processes that people can use when attempting to solve a problem. The first of these is a means-ends strategy in which attempts are made to reduce differences between a given problem state and a goal or subgoal. Moves are generated by the goal or subgoals. The second is a history-cued process in which people use previous moves to generate subsequent moves. It is suggested that a means-ends strategy tends to reduce transfer effects. A history-cued strategy may facilitate rule induction, which in turn may be an important contributing factor to transfer. A series of four experiments using hybrid problems that are soluble either by rule induction or by means-ends analysis supported the above suggestion. Two additional experiments indicated that with respect to the "insoluble problem effect," the use of history-cued strategy was, of itself, insufficient to induce transfer effects. In order for transfer to occur, the structure of the problems and the manner in which they were presented had to be such as to ensure that problem solvers perceived a close relation between problems.

Transformation problems are usually solved by a means–ends strategy that involves reducing differences between a current problem state and a goal or subgoal. However, when an easily learned rule governing the pattern of moves is available, it should be possible to induce Ss to switch to a history-cued strategy involving the extrapolation of a learned sequence of moves, as occurs during serial-pattern learning. This may be accomplished in appropriate problems by presenting subgoals that should be attained during problem solving. In the present study, 2 experiments with 128 9th and 10th graders investigated the effects of subgoal density and location on serial-pattern learning during problem solving. It was found that when subgoal location was appropriate to the serial pattern, Ss were more likely to use a history-cued strategy resulting in enhanced rule induction and transfer with increased subgoal density. When subgoal location was not appropriate to the serial pattern, Ss tended to continue using a means–ends strategy resulting in considerably reduced rule induction and transfer. (16 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)