ABSTRACT
By applying the first coordination rule of Chapter 5, Eq. (6.1) may be converted into a model for children’s understanding of length-relations. For each subject the model makes predictions based on Table 3. To illustrate these predictions, let us consider a certain subject of the length experiment. This child passed axiom-tasks LAI, LA2, LA3, LA4, and LA6. Table 3 shows that the model predicts that he will also pass LT1, LT2, LT3, LT4, and LT7. In contrast, the subject’s failure on LA5 implies that he will fail LT5, LT6, and LT8: The lack of LA5 indicates that an axiomatic process necessary for these three theorem-tasks is not operating. In fact, this subject passed LT1, LT2, LT3, LT5, and LT7, and failed LT4, LT6, and LT8. Hence the model has so far made six correct predictions and two false ones.
