The aim of this study is to study learning the positional ten base notation by the increase of students' test scores during the learning study process. Five teachers, one researcher and 53 students participated. Three research lessons in three different groups of students were conducted. The improvement in the third lesson (C) correlates with the more developed theoretical based assumptions the design is made, which resulted in a pattern of variation that stronger pointed out the aspect needed to discern to understand the object of learning in a new and more developed way. The differences in the third research lesson (C) was significant** p = 0.005 while the differences in research lessons A and B were not significant.