This paper is a part of a wider research about understanding levels of primary school’s arithmetic and algebra of university students of teaching faculties in Bosnia and Herzegovina. Our intention is argumentation of a suspicion, i.e. to form the following hypothesis: Student understands of arithmetic structures, acquisition of algebraic meaning tools and assimilation of fundamental algebraic ideals in our school systems either realized in the high grades in primary school or (almost) not realized in general. Therefore, we conclude deductive that the following hypothesis is legitimate: Generally spiking, majority of student during learning in secondary school do not reach understanding levels of mathematics ideas planed for that school. The development of mathematics thinking and acquisition of basic arithmetic-algebraic ideas became stable in primary school levels.