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The purpose of this study is to investigate the effects of task difficulty and magnitude of reinforcement upon the performance of mentally retarded institutionalized individuals in a level of aspiration situation.

Animals performing on simple fixed-ratio (FR) schedules vi typically pause after reinforcement delivery. The present study demonstrated systematic control of pause length in multiple fixed ratio schedules by manipulating FR size and reinforcement magnitude. In Experiment I, two adult male rabbits were stabilized on an alternating, two component, multiple FR 10 FR 10 schedule. Different colored lights were correlated with both FR components. Stability was determined and mean pause lengths were calculated as one FR component was increased in size until the schedule was FR 10 FR 50. Pausing was longer before the large FR component and was positively correlated with increases in FR size. Schedule and stimulus control were demonstrated by randomizing the order of FR presentations and by reversing the colored lights previously correlated with either the small or large FR components. Existing pause differentials were not disrupted under the light reversal or random conditions. In Experiment II, the same rabbits were stabilized at mult FR 10 FR 30 with 1/2 cc of water delivered after each component. In subsequent conditions the magnitude of reinforcement (cc's of water) delivered at the completion of the large FR component, was systematically shifted from 4 cc, to 3 cc, 2 cc, 1 cc and finally back to 1/2 cc. Pausing before the large FR was found to be inversely related to the magnitude of reinforcement delivered in that component. Clearly the animals in this experiment discriminated upcoming schedule conditions and paused relative to FR size and reinforcement magnitude. Hence, it is proper to point out that the term "post-reinforcement pause" is a misnomer since it incorrectly implies a functional relation between pause length and prior schedule conditions.

The learning of mathematics covers a variety of skills, such as comparing quantities, counting the number of items in a set, dealing with the numerical systems (i.e., writing and reading numbers), performing simple and complex calculations, or solving word problems. Typically, a majority of children are able to master these abilities, but an appreciable percentage of them does not and are then referenced as having developmental dyscalculia. It is clear that not being able to count efficiently, to understand the meaning of numbers, or to calculate as other children do, rapidly becomes a handicap during the development, not only at school but also in society in general, in the same way as not being able to read is. Despite the growing interest observed over these last few years, research on developmental dyscalculia or more general mathematical disability is actually much less advanced than research on dyslexia. It could be due to the complexity of the mathematics field. Several hypotheses have been proposed to account for this learning deficit, but the origin(s) of developmental dyscalculia remain(s) unclear. Research first focused on the role of the auxiliary cognitive functions not directly related to number processing. In particular, the different components of the working memory were extensively measured in children with mathematical difficulties. Other theories are based on potential weak spatial abilities, low speed of processing, or difficulties in retrieving information from long-term memory. More recently, Butterworth (1999b) proposes that humans are born with a capacity specialised for recognising and mentally manipulating numerosities. Unlike the previous hypotheses, he argues for “a highly selective and specific deficit of a very basic capacity for understanding numbers, which leads to a range of difficulties in learning about number and arithmetic”. In the same vein, Dehaene (1997) speaks about the “number sense” as the ability to represent and manipulate number magnitude nonverbally that could be impaired in developmental dyscalculia. In this thesis, we have focused on four main questions with respect to number development. First, we wanted to test whether or not difficulties encountered by mathematically disabled children are specific to the numerical domain. Children with mathematical disabilities manifesting poor calculation abilities were compared to control children of the same age during various tasks of retrieving information from long-term memory (Experiment 1). The second aim was to examine the integrity of the number magnitude representation in dyscalculia. We analysed potential differences in the slope of the numerical distance effect, which reflects the nature of analog magnitudes, in children with or without mathematical disabilities when they had to select the larger of two quantities presented in different formats (Experiment 2). These experiments are presented in Chapters 4 and 5. The two other questions are dedicated to the analysis of brain areas involved in number development using functional magnetic resonance imaging (fMRI). Our third objective was to examine age-related changes in frontal and parietal regions between children and adults during number comparison (Experiment 3). Finally, we conducted a second neuroimaging study to explore the potential neural correlates of dyscalculia. Cerebral activity of both children with pure dyscalculia and control children was analysed during a numerical and a non-numerical comparison tasks (Experiment 4). We also investigated whether or not these differences in brain activation were specific to number processing. These experiments are reported in Chapters 6 and 7.

Previous studies have shown the continuation of a failing project occurs in many aspects of business and government, and that the commitment to and continuation of a previous decision can even apply to waiting on a bus, attending a play and mountain climbing. The continuation of a failing project or decision has also been called escalation of commitment. Several theories have been suggested to explain the reasons managers continue failing or doubtful projects. Among those theories are Agency Theory, Self-Justification Theory, Prospect Theory, Approach Avoidance Theory, Self-Efficacy Theory and National Culture Theory. This study incorporates Agency Theory, Approach Avoidance Theory and Self-Justification Theory to explain the effects of an alternative investment, magnitude of loss and monitoring on the likelihood of continuing a project. The experimental design of the study was a 2 (presence of an alternative investment: yes or no) x 2 (monitoring: low or high) x 3 (magnitude of loss: low, medium or high) between-subjects factorial design. Likelihood of continuing a project was measured in two ways: first, dichotomously (either "yes" the subjects continued the project, or "no" they did not) and second, on a 0-100 continuous scale. Data were analyzed using an analysis of variance for both dependent variables, as well as a priori contrasts to make planned comparisons. As predicted, main effects were found for the presence of an alternative investment and magnitude of loss. However, no significant effect was found for monitoring. It was also hypothesized that the combination of the presence of an alternative investment, "high" monitoring and "high" magnitude of loss would be enough of a psychological deterrent to cause decision makers to stop the project, even though it was 90% complete. However, this prediction was not validated. Interestingly, though, the combination of the presence of an alternative investment, "high" magnitude of loss and "low" monitoring was enough to cause decision makers to stop the project at a level significantly less than by chance for the continuous dependent variable, and marginally significant less than by chance for the dichotomous dependent variable. Most importantly, these findings suggest for the first time that decision makers are willing to stop a project even though it is 90% complete.

In everyday decision making, people often face decisions with outcomes that differ on multiple dimensions. The tradeoff in preferences between magnitude of reinforcement, delay to reinforcement, and probability of reinforcement is a fundamental concern in the decision making literature. Yet, the relative impacts of probability of reinforcement, delay to reinforcement, and magnitude of reinforcement have not been studied together even though researchers have been advocating for the combined study of these variables for decades. The proposed project was designed to determine the relative impacts of magnitude of reinforcement and probability of reinforcement when they were both increasing over a 10 s delay to maximum charge. A first-person shooter video game was adapted for the study of choice when outcome magnitude and probability of reinforcement were increasing either simultaneously (Experiment 1) or separately (Experiment 2) over a 10 s delay. Experiment 1 showed that participants waited longer to ensure a greater probability of reinforcement than to ensure a greater magnitude of reinforcement. The results of Experiment 2 indicated that probability of reinforcement had a stronger impact on behavior than magnitude of reinforcement when they were increasing separately. These experiments indicated that probability of reinforcement outweighed magnitude of reinforcement by a ratio of approximately 3:1.

Percentile reinforcement schedules have been used to systematically alter inter-response times, behavioral variability, breath carbon monoxide levels, duration of social behaviors, and various other properties of behavior. However, none of the previous studies have examined the effectiveness of percentile schedules in relation to the magnitude of muscular contractions. This control over magnitude of muscular responding has important implications relating to the strengthening of muscles and correct movements for patients receiving physical rehabilitation. There would be great utility in percentile schedules that can be implemented in rehabilitation situations by physical therapists and patients themselves to improve treatment outcomes – all of which could be possible without any behavioral training if the procedure is implemented via body sensors and smartphone applications. Using healthy adults and the aforementioned technology, this thesis focused on the design and testing of three percentile reinforcement schedule procedures to increase the strength of the vastus medialis muscle. Results indicate that the magnitude of muscular responses can be shaped using body sensors and contingent feedback, and the percentile schedule procedures have promising applications in the domain of physical therapy.

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