In this article we are presenting the results of the research "The Connection between the Results in the National Assessment of Knowledge and the Pupils' Socio-cultural Environment, Instruction and Homework," taking place at the National Education Institute, Slovenia, in the years 2008/2009. In the introduction we are writing the importance of national assessment of knowledge in the primary school and presenting its significance in certain European countries. External knowledge assessment at the end of the primary school, being at present in Slovenia called "national assessment of knowledge," has got since 2005/2006 an information and formation significance. The achievements in the "national assessment of knowledge" are not a part of the school mark, but additional information on pupils' knowledge. In the central part of the article we are presenting the findings of the study on the interconnectedness of approaches to internal (school) testing and assessment of knowledge with the school success of pupils in the national assessment of knowledge in mathematics and Slovenian language. The research has shown that none of the single elements can have a decisive influence on the results by itself, but rather interdependence between them. A change of one element can influence the structure and efficiency of other elements, thus their consistency is required. The results also show that pupils make differences between teachers of mathematics or Slovenian language, i.e., a closer cooperation with mathematical teachers than with Slovenian language teachers. [For complete volume, see ED567040.]