This paper presents a qualitative study in which an attempt was made to extend the debate surrounding the use of real life contexts to make mathematics more meaningful and real. The study investigated Grade 8 learners’ knowledge of number, understanding of number concepts and the kinds of connections they make between number and the context in which number is used. An important aspect of the study’s methodological approach involved an examination of the comments that learners made about what they said they know about number. A response to the question: “Why is the number in the picture?” provided a framework for establishing how learners saw relationships between number and the context in which numbers are used. A face scenario with four questions was given to learners to elicit these relationships. Results pointed to the usefulness of real life contexts as tools that have a central role in uncovering what learners know about number and how they use that knowledge to understand situations that call for proficiency in mathematics.

In the current study, three possible interpretations of children’s number line estimation (NLE) performance were examined for appropriateness and possible correlates of performance were tracked over time in a classroom exemplifying recommended mathematics pedagogy for young children. In December and May, 21 4-year-olds completed the NLE task (0-10 range) and measures of numerical knowledge, spatial skills, and visual-motor integration. With high-quality teaching, children made large gains in these skills (d = 0.96-1.28). Due to uniformly high achievement, few expected correlations were observed, however. A strategy account of NLE performance was supported over the traditional logarithmic-to-linear shift account and the newly proposed proportion-judgement account. Patterns of error in estimation provide a better indication of understanding of the linear number line than models of best fit. Indeed, interpreting linearity of NLE as indicative of an underlying representation of number could lead to inappropriate conceptualizations of math learning disabilities and misguided interventions.

In the current study, three possible interpretations of children’s number line estimation (NLE) performance were examined for appropriateness and possible correlates of performance were tracked over time in a classroom exemplifying recommended mathematics pedagogy for young children. In December and May, 21 4-year-olds completed the NLE task (0-10 range) and measures of numerical knowledge, spatial skills, and visual-motor integration. With high-quality teaching, children made large gains in these skills (d = 0.96-1.28). Due to uniformly high achievement, few expected correlations were observed, however. A strategy account of NLE performance was supported over the traditional logarithmic-to-linear shift account and the newly proposed proportion-judgement account. Patterns of error in estimation provide a better indication of understanding of the linear number line than models of best fit. Indeed, interpreting linearity of NLE as indicative of an underlying representation of number could lead to inappropriate conceptualizations of math learning disabilities and misguided interventions.

This paper presents a qualitative study in which an attempt was made to extend the debate surrounding the use of real life contexts to make mathematics more meaningful and real. The study investigated Grade 8 learners’ knowledge of number, understanding of number concepts and the kinds of connections they make between number and the context in which number is used. An important aspect of the study’s methodological approach involved an examination of the comments that learners made about what they said they know about number. A response to the question: “Why is the number in the picture?” provided a framework for establishing how learners saw relationships between number and the context in which numbers are used. A face scenario with four questions was given to learners to elicit these relationships. Results pointed to the usefulness of real life contexts as tools that have a central role in uncovering what learners know about number and how they use that knowledge to understand situations that call for proficiency in mathematics.

Children’s early mathematics learning and development have become a topic of increasing interest over the past decade since early mathematical knowledge and skills have been shown to be a strong predictor of later mathematics performance. Understanding how children develop mathematical knowledge and skills and how they can be supported in their early learning could thus prove to be a vital component in promoting learning of more formal mathematics. In light of the above, with this thesis I sought to contribute to an increased understanding of children’s early mathematics learning and development by examining effects of playing different number games on children’s number knowledge and skills, and by investigating children’s representations of numbers on number line tasks. Two number game intervention studies were performed, and effects of three different number game conditions (linear number, circular number and nonlinear number) were investigated by examining 5- and 6-year-old children’s pre- and posttest performance on different numerical tasks. The findings indicate that playing number games in general support children’s development of number knowledge and skills, where the specific learning outcomes are affected differently depending on the type of number game utilized. To elucidate children’s representations of numbers, their performance on two different  umber line tasks have been analyzed using a latent class modeling approach. The results reveal that there is a heterogeneity in 5- and 6-year-old children’s number line estimations and subgroups of children showing different estimation patterns were distinguished. In addition, it is shown that children’s number line estimations can be associated to their number knowledge as well as to task specific aspects. The findings presented in this thesis contribute to the discussion of the value of selecting game activities in a conscious way to support children’s early mathematics learning and development. They also add to the discussion regarding the number line task and how children’s number line estimations can be analyzed and interpreted.