Thesis (Ph. D.)--University of Texas at Austin, 2005. / Vita. Includes bibliographical references.

<p>During my time as a student of education I have learnt that it is my responsibility, as a teacher, to adjust the ways in which I teach to the needs, abilities, experiences, and thoughts of each individual child. What I have not yet gained much knowledge on is how to go about finding the children’s thoughts.</p><p>In this thesis I investigate the interview as a method of finding out how sixth graders think about their mathematics education. Four children were interviewed. In addition to these inter-views, as a means of giving a broader perspective to and a greater understanding of the chil-dren’s answers, one math lesson was filmed and the math teacher was interview on two sepa-rate occasions.</p><p>What I found was that a number of factors seemed to influence the children’s thoughts and answers, and that their answers were most likely not always a mirror of their thoughts. From this follows that we, as teachers, must be careful and not assume that we know about a child’s thoughts when, in fact, what we know is what the child chooses to communicate about his or her thoughts. I also found that the children seemed unaccustomed to speaking about mathe-matics in the way that I wanted them to. One reason for this seemed to be the way in which their teacher organized the lessons.</p>

During my time as a student of education I have learnt that it is my responsibility, as a teacher, to adjust the ways in which I teach to the needs, abilities, experiences, and thoughts of each individual child. What I have not yet gained much knowledge on is how to go about finding the children’s thoughts. In this thesis I investigate the interview as a method of finding out how sixth graders think about their mathematics education. Four children were interviewed. In addition to these inter-views, as a means of giving a broader perspective to and a greater understanding of the chil-dren’s answers, one math lesson was filmed and the math teacher was interview on two sepa-rate occasions. What I found was that a number of factors seemed to influence the children’s thoughts and answers, and that their answers were most likely not always a mirror of their thoughts. From this follows that we, as teachers, must be careful and not assume that we know about a child’s thoughts when, in fact, what we know is what the child chooses to communicate about his or her thoughts. I also found that the children seemed unaccustomed to speaking about mathe-matics in the way that I wanted them to. One reason for this seemed to be the way in which their teacher organized the lessons.

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Literature review abstract Background: Domain-general processes, such as working memory (WM), short-term memory (STM), and attention, have been found to be related to mathematical performance in children. The relationship between these abilities, however, is not well understood. Objective: This systematic review aimed to evaluate the literature investigating the relationship between mathematical performance and WM, STM, and attention in typically developing primary school aged children. Methods: Three databases were searched for studies published between January 1974 and February 2015 reporting associations between mathematics performance and at least one measure of WM, STM, and attention. Study selection was undertaken by applying inclusion and exclusion criteria and 43 studies were selected for inclusion. The methodological quality of the included studies was assessed using a validated checklist. Results: WM, STM, and attention were all significantly related to mathematics performance. Visuospatial STM and WM were strongly related to mathematics performance in younger children, while verbal STM and WM were more strongly related in older children; although some studies found the opposite pattern. The relationship between attention and mathematics performance increased in strength with age. Conclusions: There are many factors relevant to the relationship between mathematical performance and WM, STM, and attention which can affect the strength of the association, including the types of tasks used to measure the constructs, the confounding variables considered, and the age of the participants. Future research needs to focus on the construction of an integrated model of mathematical development.   Empirical paper abstract Background: Moderate to late preterm children (MLPT; born between 32 weeks and 36 weeks and 6 days) are at increased risk of developing cognitive difficulties compared to term children (born between 37 weeks and 41 weeks and 6 days). Mathematical attainment is an important area of academic development. Domain-general cognitive abilities, which constrain all learning, and domain-specific mathematical precursors are both important for mathematical development. Objectives: The current study had two aims: 1) to investigate the relationship between gestational age (GA), mathematical attainment, working memory (WM), short-term memory (STM), and attentional control; and 2) to investigate WM, STM, and attentional control as domain-general predictors of mathematical attainment. It was hypothesised that WM would predict additional variance in mathematical attainment after attentional control, STM, and demographic variables (intellectual ability (IQ) and socioeconomic status) were accounted for. Methods: A cross-sectional and correlational design was used to investigate the study aims. Participants were 34 MLPT children and 25 term children who were between 72 and 107 months at the time of the study. Children who weighed less than 1500 grams at birth, had cerebral palsy, epilepsy, severe hearing or vision loss, or had a diagnosed learning disability were excluded. Each participant completed a cognitive assessment which measured their mathematical attainment and components of WM, STM, and attentional control. Results: GA was only significantly correlated with IQ. In the model of mathematical attainment, GA also significantly moderated the relationship between attentional switching and mathematical attainment. The hypothesis regarding the role of WM in predicting mathematical attainment was partially supported as only verbal WM predicted significant additional variance in mathematical attainment. Attention behaviour and IQ also predicted significant additional variance in mathematical attainment. Conclusion: These findings suggest that birth weight greater than 1500g, higher socioeconomic status, and lower levels of co-morbid medical conditions may serve as protective factors against the potential negative consequences of MLPT birth. Findings regarding the domain-general predictors of mathematical attainment supported some previous findings and highlighted the need for a variety of tasks to be used to measure each domain-general ability. Longitudinal studies in MLPT children would be helpful for further understanding the role of GA and domain-general abilities in the development of mathematical attainment.

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