This paper builds up a theoretical perspective and supports a possibility of creating a special assessment environment for students, where mathematical knowledge and understanding can be assessed with a reduced number of external psychological factors that may affect such assessment. A concept of a zone with minimal effect of anxiety is introduced and described. Students’ successful work on extending the zone by means of a carefully selected chain of questions, where some questions only are part of a real assessment, allows students to reconsider their attitudes towards mathematics and assist teachers to identify some students’ main learning difficulties as of psychological character. Further suggestions about developing and investigating special assessment environments are outlined and discussed.