A behavioral approach to teaching in the public school system is difficult because of the inherent difficulty of finding positive reinforcers and administering them simultaneously to large groups of students. This study attempts to apply the same tangible reinforcers to two groups of students under different schedules of reinforcement. The students in the study were in special classes termed "learning adjustment" classes because of their failure to perform at grade level in regular classroom settings. One group was on a continuous schedule of reinforcement using tokens and gold strike stamps as reinforcers. The second group was also on a continuous schedule of reinforcement but with a punishment contingency added. Reinforcers were the same for this group as the first group. The third group was a comparison group. Performance rates were studied under the above schedules of reinforcement and were found to increase the number of arithmetic units completed for each group. Achievement level change in mathematics as measured by the mathematics section of the California Achievement Test was a second major aspect of this study. Although there was a very definite difference in the number of arithmetic units completed by the three groups there was not a corresponding difference in the amount of change in achievement level.

The thesis deals with the topic of dyscalculia, which is officially recognized as a learning disability. The theoretical part of the thesis is focused on the current status of knowledge about development of mathematical skills and their disorders in the context of dyscalculia. The empiric part of this thesis describes a research which compares the performances of individuals with dyscalculia and control participants on a range number and numerosity processing tasks. The main goal was to describe the image of possible causes of difficulties. Deficits in the processing of symbolic and nonsymbolic numerosities were observed in group of dyscalculic participants. We conclude that dyscalculia is related to specific disabilities in basic numerical and numerosity processing which affects ability to acquire arithmetical skills. KEYWORDS Klíčová slova (anglicky): Dyscalculia, numerosity, arithmetic skills, mathematical skills, specific learning difficulties