This paper presents findings from a study that examined the strategies that children, who had only been taught the part-whole fraction sub-construct at school, used for finding the fraction associated with solving varied partitive quotient problems. A qualitative, microgenetic research design was used involving nine year 5 (aged 9–10) children engaged in eight individual task-based interviews over a 6-week period. The data analyzed showed that across the eight tasks, six of the nine children used more than one strategy for quantifying each person’s share but, by the third task, in general, each child had settled into a regular pattern of strategy use. The analyzed variations in children’s approaches to solving the partitive quotient problems revealed instances of when and how the part-whole fraction sub-construct interfered with children’s engagement with the partitive quotient problems. Considering that, internationally, the part-whole sub-construct is still the first fraction sub-construct that many children learn in schools, the findings are significant, since they provide new, in-depth insights into emerging approaches to solving partitive quotient tasks that are influenced by children’s existing part-whole knowledge. The findings provide new evidence for intra- and inter-individual variation in strategy use and strategy selection in tasks related to the partitive quotient meaning of fractions. The paper highlights for education, the need for teaching that introduces different fraction sub-constructs to learners early in their schooling so that one meaning of fractions does not become representative of all fraction knowledge.

A key aim of mathematics teaching is for children to develop appropriate and efficient strategies for solving tasks. The analysis presented in this paper moves beyond the exploration of changes in the strategies that children employ to solve tasks and extends to observation and exploration of changes that occur when their overall solving approach remains seemingly stable. We present an analysis of data from two qualitative studies, each of which combined a microgenetic design with task-based interviews, to examine changes that occur in 5-6-year-old children's verbal reports when solving an additive task, and in 9-10-year-old children's verbal reports when solving fraction word problems. Children's verbal reports were analysed through the lens of the theory of shifts of attention. We found that phases of stability are underlain by dynamic changes in how the same strategy is communicated and conceptualised over a number of sessions and these changes appear to be accounted for by changes related to shifts in the object and structure of children's attention, i.e. what children attend to and how, when reporting on their solving approach. The paper extends the theory by revealing and studying microqualities that underlie different learners' structure of attention during phases of stability in arithmetic tasks. The findings provide new, significant insights for understanding qualitative dynamics of change in learning. Sensitivity to differences and changes in learners' shifts of attention is essential for teachers to make sense of what learners experience and identify opportunities conducive to further learning.

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This paper presents findings from a quantitative, survey research study that investigated the prevalence of mathematics anxiety (MA) in two Grade 7 cohorts and how students’ MA compared by gender. The research sample consisted of 467 Grade 7 students (276 females and 186 males) from two high schools in Jamaica. The data were collected using the Modified Abbreviated Math Anxiety Scale (mAMAS) and analyzed using descriptive statistics and a Mann-Whitney U test. The results showed that students experienced a range of MA (Low, Slight, Moderate, and High). Most students experienced Slight MA and 7.5% of the students reported High MA. Another key finding was that the MA distributions for males and females were not statistically significant. Considering the relatively high percentage of students who reported high MA, additional research involving more schools relating to prevalence of MA is warranted.

This research investigated the impact of using manipulatives on 56 Grade 5 students’ (27 male, 29 female; age 10-11 years) mathematics achievement. A quasi experimental, action research design was utilized in which the experimental group was taught selected topics from the Number strand using manipulatives during a 3-week intervention, while the control group’s instruction did not include the use of manipulatives. Data were collected using a pre- and post-test and analysed using descriptive statistics and a Mann-Whitney U test. This analysis revealed that there was a statistically significant difference in the post-test performance of the two groups in favour of the experimental group. The effect size (r = .3) for this data was moderate. A significant difference was also found between the boys’ and girls’ post-test mathematics scores in the experimental group, with the girls outperforming the boys. A key implication of these findings is that since manipulatives were effective in significantly improving student achievement, its use could be extended and investigated further for other grade levels and mathematical topics. Strategies could also be adopted to address the disparity in performance based on gender in the sample.