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