A review of knowledge acquisition promoting transfer in mathematical problem solving

This review focuses on knowledge acquisition which promotes transfer in mat hematical problem (especially, algebra word problem) solving. Within mathem atical problem solving, similar (nonisomorphic) target problems have been s hown to be difficult for the learner to solve. The purpose of this review w as to discuss what type of knowledge facilitated transfer to similar target s. We distinguished between three types of knowledge : knowledge based on e xamples, knowledge based on solution structures, and knowledge based on str ucture generation. In the example-based approach, the knowledge which facil itated transfer consisted of multiple examples and their solutions. We argu ed that this approach did not address the facilitation of transfer to simil ar targets. The solution structure-based approach suggested that the acquis tion of abstract knowledge at the level of solution structures or forms of equations was necessary for transfer to occur. We found little experimental evidence supporting this approach. In the structure generation-based appro ach, the knowledge of how to construct solutions was considered to be the o ne promoting transfer. We think that this approach was the most promising o f the three. We discussed further directions as to the acquisition of the k nowledge of generating solution structures, and stressed the importance of clarifying the process of acquiring such knowledge.