The majority of research on the mathematics teaching and learning of students with mathematics learning dis/abilities is not performed in the field of mathematics education, but in the field of special education. Due to this theoretical divide, students with mathematics learning dis/abilities are far more likely to be in classes that emphasize memorization, direct instruction, and the explicit teaching of rules and procedures. Additionally, students with mathematics learning dis/abilities are often seen as "unable" to succeed in school mathematics and are characterized by their academic difficulties and deficits. The negative assumptions, beliefs, and expectations resulting from ableistic practices in the education system color the interactions educators, parents, and other students have with students with mathematics learning dis/abilities. These interactions in turn influence how students with mathematics learning dis/abilities view and position themselves as learners and doers of mathematics. My study builds on the theoretical framework of positioning theory (Harré, 2012) in order to better understand the mathematical identities of students with mathematics learning dis/abilities. The results of my study show how these students use their prepositions and enduring positions to inform the in-the-moment positions they take on in the mathematics classroom.

This thesis systematically examined the link between developmental dyscalculia, a specific learning difficulty of mathematics, and mathematics anxiety, a negative emotional reaction to mathematics tasks. The link between these maths learning issues was examined by measuring their prevalence in large samples of English primary (N = 1004; N= 830) and secondary school (N = 927) students. Gender differences were also explored. Systematically varying diagnostic criteria for dyscalculia revealed that its prevalence ranged between 0.89-17.23 percent. When absolute performance thresholds were used, there was no gender difference in dyscalculia prevalence. The association of mathematics performance with other cognitive skills and mathematics anxiety was investigated longitudinally in subsamples of children with dyscalculia (n =10), typical mathematics performance (n=10) and high maths ability (n = 11). 80 percent of the children in the dyscalculia group still met the criteria for diagnosis at the final time point. Mathematics performance was positively associated with working memory performance and negatively associated with mathematics anxiety. Furthermore, children with dyscalculia had higher maths anxiety than the other two groups. The relationship between dyscalculia and high maths anxiety was estimated in a larger sample (N = 1757). Relatively few children with dyscalculia had high maths anxiety and the majority of students with high maths anxiety in fact had mathematics performance within or above the average range. Girls had higher maths anxiety than boys, and more girls had both dyscalculia and maths anxiety than boys. There was an expected negative correlation between maths anxiety and maths performance in the total sample, but this correlation was negligible in the children with dyscalculia. Collectively, these results suggest that cognitive and emotional mathematics problems are dissociable, and indicate that children with dyscalculia and maths anxiety likely require different types of intervention. Furthermore there appears to be no gender difference in maths performance or in the prevalence of dyscalculia. However, girls have higher maths anxiety than boys, and are more likely to be affected by maths anxiety alongside developmental dyscalculia. Maths anxiety may be a potential explanation for the underrepresentation of females in careers involving mathematics.