Regardless of the vast amount of research on the topic of mathematical development, there is limited understanding on its development in different types of students. For instance, mathematics anxiety and preterm birth are risk-factors for lower mathematical achievement. However, there is a gap in research on how these individual factors affect the development of specific skills, such as rational number knowledge and skills, amongst primary school students. This is unfortunate as all students need rational number knowledge for learning more complex mathematics topics and within everyday mathematical reasoning. Students’ ability to apply their mathematical knowledge in various situations, for example in everyday life or to solve novel mathematical tasks, is another aspect examined in this research. The current dissertation includes four articles that aim to provide novel insights on individual differences in the mathematical knowledge and skills of primary school students. More specifically, it expands our knowledge on how individual factors, mathematics anxiety and preterm birth, relate to the learning of rational number knowledge and flexible mathematical skills.

Studies I-III aimed to investigate how mathematics anxiety is related to a wide range of mathematical knowledge and skills of primary school students. In Study I, the participants were 412 fifth and sixth graders. Studies II and III focused specifically on two subgroups of low performing students, those with or without a tendency for a fraction misconception, referred to as the natural number bias (NNB). These studies expand our knowledge on the complex relation between mathematics anxiety and fraction understanding amongst students who are still learning about fractions. Study IV compared fifth grade mathematical skills (including rational numbers), mathematics motivation, and cognitive abilities of 11-year-old children born very preterm (n = 67) and full-term (n = 72). This study expands our understanding on the role of preterm birth related cognitive difficulties in the development of rational number knowledge and the ability to apply mathematical knowledge in everyday contexts.

Study I showed that mathematics anxiety has a negative relation with mathematics performance already in primary school. It also showed that the mathematics anxiety-performance relation differed across the mathematical tasks and the two measures of mathematics anxiety: trait and state mathematics anxiety. For instance, lower fraction arithmetic knowledge was related to higher mathematics trait anxiety, but not state anxiety. Then again, state anxiety explained students’ performance on a novel rational number arithmetic task, even after controlling for trait mathematics anxiety and relevant mathematical knowledge. Intriguingly, mathematics anxiety was not related to students’ ability to notice multiplicative relations embedded in pictures. Thus, differences in task characteristics influenced the relation between mathematics anxiety and performance.

Studies II and III examined the relation between a fraction related misconception, namely the NNB, and mathematics anxiety. Study II showed that the NNB group reported lower state anxiety related to fraction arithmetic than the No-NNG group. Study III showed that the fraction state anxiety significantly increased after fraction instruction in the NNB group. These results support the notion that the NNB is a misconception. The initially low fraction state anxiety in the NNB group suggests that the students are unaware of their incorrect answers and low fraction performance. As their awareness increased, their anxiety increased. Thus, increased mathematics performance may lead to increased mathematics anxiety when overcoming a misconception. Intriguingly, the qualitative difference in fraction understanding between the two low performing groups was not captured by trait mathematics anxiety. Thus, the situational nature of state anxiety could be valuable for measuring qualitative differences and dynamic changes within mathematical understanding, for example the overcoming of a misconception. In general, the two measures of mathematics anxiety unveiled different nuances in students’ mathematical understanding and task perceptions.

Study IV further emphasises that mathematical knowledge and skills should be measured in various subpopulations and across multiple tasks. The children born very preterm and full-term did not significantly differ on multiple fifth grade mathematical skills, including whole number and rational number magnitude knowledge, or in mathematics motivation. However, the children born very preterm had weaker spontaneous mathematical focusing tendencies meaning difficulties with recognising and applying their mathematical knowledge in situations that are not explicitly mathematical. This finding implies that the children born very preterm may have difficulties applying their mathematical knowledge in everyday life contexts. This difficulty could not be fully explained by group differences in cognitive abilities. Moreover, this study yields further evidence that individual factors do not necessarily affect all mathematical skills similarly.

Overall, the current dissertation sheds light on individual differences in rational number knowledge and skills, including the ability to apply mathematical knowledge in novel contexts. The findings reveal that the challenges in developing mathematical competence are multifaceted, as they are influenced by both individual factors, such as mathematics anxiety and preterm birth, but also task characteristics. This highlights the importance of examining subpopulations and various mathematical skills. These findings also emphasise the importance of acknowledging individual differences in mathematics teaching, as mathematical skills are relevant within the everyday lives of all individuals.