Optimizing Mathematic Learning: Effects of Continuous and Nominal Practice Format on Transfer of Arithmetic Skills

Should we give learners a lot of practice with a few problems, or a little practice with a variety of problems? The best practice set depends on the way people are learning. We describe two models people employ when learning arithmetic problems. We show that features of the task environment influence model use. When problems are presented in a purely symbolic format, people learn an item-specific model. When the task format linked problems to representations of magnitudes, people learn a continuous model. We also test the effects of different practice sets on learning. In both formats people learned the practice sets well with a few repeated examples. With a continuous magnitude format people showed better transfer with a wide variety of practice problems. Variety led to poor learning in the symbolic format. In ongoing research we are attempting to identify the optimal practice set for each type of learning model.