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The long-standing debate into the potential benefit of developing mathematical thinking skills through learning to program has been reignited with the widespread introduction of programming in schools across many countries, including England where it is a statutory requirement for all pupils to be taught programming from 5 years old. Algorithm is introduced early in the English computing curriculum, yet there is limited knowledge of how young pupils view this concept. This paper explores pupils' (aged 10-11) understandings of algorithm following their engagement with 1 year of ScratchMaths, a curriculum designed to develop computational and mathematical thinking skills through learning to program. A total of 181 pupils from 6 schools undertook a set of written tasks to assess their interpretations and evaluations of different algorithms that solve the same problem, with a subset of these pupils subsequently interviewed to probe their understandings in greater depth. We discuss the different approaches identified, the evaluation criteria they used, and the aspects of the concept that pupils found intuitive or challenging, such as simplification and abstraction. The paper ends with some reflections on the implications of the research, concluding with a set of recommendations for pedagogy in developing primary pupils' algorithmic thinking.

This paper reports research on effects on teachers' classroom practices resulting from their engagement in sustained professional development and classroom teaching of a resource that embeds carefully designed dynamic technology within middle school mathematics (11-14 years). The research investigated the self-reported evolution of teachers' classroom and departmental practices as they sought to integrate the materials and the technology into their teaching. The sample comprised 203 English middle school mathematics teachers who participated in the professional development and taught the materials during 2013-2014. The methodology used questionnaires, administered to match individual teachers' teaching schedules, and the resulting data were analyzed quantitatively to give summative statistics, and qualitatively to elicit more nuanced contextualised information. The questionnaire data were thus supplemented by two case studies to illustrate how the trajectory of development of teacher practices was shaped, first by their initial motivations to participate in the innovation, but later more strongly by the ways they chose to align their practices to the institutional goals of their schools in order for the innovation to be sustained.

Despite recommendations, few have reported on quality improvement initiatives to implement length of rehabilitation stay benchmarks, while actively monitoring functional outcomes. This article describes the development, implementation, and evaluation of a precision case management model across all inpatient rehabilitation client groups in a Canadian facility. To develop the length of rehabilitation-stay (LoRS) benchmarks, patient data was retrospectively analyzed. A severity specific method was used to stratify median length of stay. A target reduction on 8.6 days in LoRS was established. Functional discharge targets were also set and monitored at specific intervals via the Functional Independence Measure (FIM®). The implementation used an incremental quality improvement phased approach. Following 12-months, a statistically significant reduction in mean LoRS of 13.2 days was achieved, along with a small increase in FIM® change across all rehabilitation client groups. A similar pattern was seen across the three main client groups, where a LoRS reduction greater than the target was achieved, along with important improvements in LoRS efficiency. This study demonstrates how the implementation of a precision case management model can assist a facility in markedly reducing LoRS across inpatient groups, without compromising functional change or community discharge rates and begin its transformation to a value-based organization.