The present study was motivated by theoretical considerations in cognitive linguistics associated with the concept projection as well as by theories in cognitive science related to self-directed learning on computers, to apply them in developing Japanese learners' knowledge of the different degrees of sureness attached to CERTAIN, PROBABLE, and POSSIBLE ITEMS. It evaluated the relative effects of cognitive and non-cognitive approaches and of self- and teacher-directed approaches on computers. The cognitive approach involved concept projection, a process through which the participants understand an abstract concept, namely the degree of certainty, in terms of the spatial concept of distance, whereas the non-cognitive approach involved rote learning of a list of target expressions related to the degree of certainty. The results of the present study demonstrated that the cognitive approach groups outperformed the non-cognitive approach and control groups in writing, comparison, and categorization tests, and further demonstrated that the cognitive approach is effective as a mnemonic device generating long-term memory encoding. The results of the present study also showed that the self-directed approaches were no less effective than the teacher-directed approaches, and the difference between self-directed and teacher-directed learning did not seem to have had a major impact on the overall performance of the self- and teacher-directed groups.