The major purpose of the thesis is to attempt to understand some of the reasons for children's differential achievement in arithmetic. Research has associated various factors with arithmetic performance, however, usually in isolation. The present study examines a combination of social, environmental, and cognitive factors as related to arithmetic achievement, based on a sample of 91 8-9-year-old Greek children who were identified as belonging into one of three levels of arithmetic ability, above average, average, and below average, and a group of children with mild reading difficulties. Children in the math ability groups had at least average reading performance. Social and environmental factors included self-concepts, attitudes and home practices, parental help and encouragement, and parentschool relations and academic status. Cognitive components included knowledge and skill in formal and informal arithmetic and working memory efficiency. As part of the study, children were interviewed on the social and environmental factors and went through a battery of tests on the cognitive factors. Children's parents filled out a questionnaire. From the total of social and environmental factors, children's attitudes to arithmetic, parents' beliefs of children's attitudes, and mothers' academic status were associated with children's arithmetic achievement. From the total of cognitive factors, knowledge and skill in informal arithmetic and base ten system, knowledge of addition facts, problem-solving skills, speech articulation, and speed of reciting even numbers predicted children's arithmetic achievement. When both social and environmental and cognitive factors regressed on children's performance, mothers' beliefs of their child's attitudes, mothers' academic level, knowledge of informal arithmetic and base ten system, and problem-solving skills predicted children's achievement in arithmetic.

Deficiencies in mathematics skill constrain students’ educational achievement and subsequently, their employment outcomes. This study included 265 school-identified students with mild intellectual disabilities. The research questions investigated the extent to which phonological awareness, color naming speed, and vocabulary knowledge, was related to mathematics skill after controlling for grade level via regression analyses. Further, the mediating effects of expressive vocabulary on the relationship between receptive vocabulary and mathematics skill as well as the indirect effect of receptive vocabulary knowledge on mathematics skill through expressive vocabulary were examined. The findings indicated that after controlling for grade level, phonological awareness, naming speed, and vocabulary knowledge were significantly related to mathematics skill. The mediating effects of expressive vocabulary as well as the indirect effects of receptive vocabulary knowledge on mathematics skill were also significant.

Deficiencies in mathematics skill constrain students’ educational achievement and subsequently, their employment outcomes. This study included 265 school-identified students with mild intellectual disabilities. The research questions investigated the extent to which phonological awareness, color naming speed, and vocabulary knowledge, was related to mathematics skill after controlling for grade level via regression analyses. Further, the mediating effects of expressive vocabulary on the relationship between receptive vocabulary and mathematics skill as well as the indirect effect of receptive vocabulary knowledge on mathematics skill through expressive vocabulary were examined. The findings indicated that after controlling for grade level, phonological awareness, naming speed, and vocabulary knowledge were significantly related to mathematics skill. The mediating effects of expressive vocabulary as well as the indirect effects of receptive vocabulary knowledge on mathematics skill were also significant.