How Can We Design Effective Instructions to Promote Transfer?

A major hurdle to learning occurs when a student has to master a skill that requires appreciating hidden structure in a problem. For instance, in understanding that 5x – x = 4x, the student has to appreciate that 5x – x = 5*x – 1*x and that this can be factored to be (5 – 1)*x. Without this understanding, the student may learn superficial rules to deal with specific cases, but not be able to generalize to new cases. For instance, in this example a student may infer the superficial rule of decrementing the integer and faced with -5x – x produce -4x. To enable understanding of the hidden structure, typical instruction combines an effort to represent the hidden structure along with verbal explanation.