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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.

This paper describes the design of a mathematical microworld to tackle the persistent difficulties that secondary school students have with the idea of algebraic generalization, which is a key stumbling block in secondary-school mathematics classrooms. Our focus is to characterize algebraic ways of thinking and to design both affordances of the system as well as suitable tasks and pedagogies that provide a substrate of activity and experience for the teaching and learning of algebraic generalizations. Using as reference illustrative cases of 12 to 13-year-old students' interaction with the microworld, we demonstrate the strong interplay between epistemology and the design of the microworld and draw conclusions regarding its potential to support the development of algebraic ways of thinking. (Contains 10 figures, 2 tables, and 4 notes.)

In this paper, we give a detailed account of the design principles and construction of activities designed for learning about the relationships between position, velocity and acceleration, and corresponding kinematics graphs. Our approach is model-based, that is, it focuses attention on the idea that students constructed their own models--in the form of programs--to formalise and thus extend their existing knowledge. In these activities, students controlled the movement of objects in a programming environment, recording the motion data and plotting corresponding position-time and velocity-time graphs. They shared their findings on a specially designed Web-based collaboration system, and posted cross-site challenges to which others could react. We present learning episodes that provide evidence of students making discoveries about the relationships between different representations of motion. We conjecture that these discoveries arose from their activity in building models of motion and their participation in classroom and online communities.

Discussion of group processes in computer assisted instruction highlights a research program being developed in the United Kingdom to explore computer groupwork with 9-to 12-year-olds. Variables to be considered in the research strategy are described, data collection methods are explained, and student attitudes and teacher roles are discussed. (24 references) (LRW)

Abstract: 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. [ABSTRACT FROM AUTHOR]

This paper describes the design of a mathematical microworld to tackle the persistent difficulties that secondary school students have with the idea of algebraic generalization, which is a key stumbling block in secondary-school mathematics classrooms. Our focus is to characterize algebraic ways of thinking and to design both affordances of the system as well as suitable tasks and pedagogies that provide a substrate of activity and experience for the teaching and learning of algebraic generalizations. Using as reference illustrative cases of 12 to 13-year-old students' interaction with the microworld, we demonstrate the strong interplay between epistemology and the design of the microworld and draw conclusions regarding its potential to support the development of algebraic ways of thinking. [ABSTRACT FROM AUTHOR]

In this paper, we give a detailed account of the design principles and construction of activities designed for learning about the relationships between position, velocity and acceleration, and corresponding kinematics graphs. Our approach is model-based, that is, it focuses attention on the idea that students constructed their own models – in the form of programs – to formalise and thus extend their existing knowledge. In these activities, students controlled the movement of objects in a programming environment, recording the motion data and plotting corresponding position–time and velocity–time graphs. They shared their findings on a specially designed Web-based collaboration system, and posted cross-site challenges to which others could react. We present learning episodes that provide evidence of students making discoveries about the relationships between different representations of motion. We conjecture that these discoveries arose from their activity in building models of motion and their participation in classroom and online communities. [ABSTRACT FROM AUTHOR]

Describes a study that set out to identify changes in single honors undergraduate degrees in mathematics in England and Wales between 1989 and 1996. Main areas of change that have taken place; Range of mathematics covered in the study; Reasons for changes in content.

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.