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This study aims to explore the conceptualisations of function that some students express when they are responding to fictitious students’ statements about functions. We also asked them what is meant by “function” and many voluntarily used examples in their responses. The task was developed in collaboration with teachers from two curriculum systems, England and Israel. It was given to 10 high-achieving English students from each of the years 10–13 and to 10 high-achieving Israeli students from comparable years (total of 80 students). Data analysis included identifying students’ dominant ideas for functions as expressed in their responses, and analysing the types of examples that students used to explain their responses. Differences found between the samples from the countries led to conjectures about the influence of curriculum and teaching, and in particular, about the role of word, in this case “function”, in concept image development. Whereas most students showed that they had a meaning for the word, those students whose relevant experience of earlier concepts had been organised around the word “function” generally showed stronger understanding of function as object. [ABSTRACT FROM AUTHOR]

This paper reports the activity of three secondary school mathematics departments in England in self-initiated states of change that led to overall improvements in students' achievements when compared to previous cohorts. This took place without intervention and without their participation in external projects. They provide examples of departments that can work effectively on their own development, and hence, their work adds to our knowledge of the potential for development through collaboration. The departments were monitored over 3 years, and data were analysed using the lens of activity theory. In contrast to departments in many studies, these departments worked overtly on mathematics pedagogy through the shared production and discussion of resources, shared planning and task design. Also in contrast to several other studies, they developed distinct ways to handle differences of subject knowledge among the teachers in the department. Their focus changed during the study from developing resource banks to supporting students' learning through hybrid teaching. [ABSTRACT FROM AUTHOR]

We draw on two studies of mathematics departments in 11-18 comprehensive maintained schools in England to compare and contrast the insights provided by differing theoretical perspectives. In one study, activity theory was used to describe common features of the work of three departments. In the other, a mathematics department was viewed and analysed as a complex system. In both cases, it was the learning of the departments as systems rather than of individuals that was of interest. The affordances and limitations of the analytical perspectives are discussed. Taken as a whole, this paper opens up the workings of school mathematics departments in a country which has a strong department culture. [ABSTRACT FROM AUTHOR]

Presents discussions on the interpretative judgement of teachers on the mathematical performance of students in England. Issues on the equity and fairness of on teacher assessments; Relation between assessment and instructional conditions; Significance of communicating mathematical knowledge.